Metrics for 2cos (problem 3.3.5)

analyze150.0ms (0.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	74.7%	0%	0%	0%	3
0%	0%	25.3%	74.7%	0%	0%	0%	4
0%	0%	19%	81%	0%	0%	0%	5
0%	0%	15.8%	84.2%	0%	0%	0%	6
0%	0%	11.1%	88.9%	0%	0%	0%	7
0%	0%	8.7%	91.3%	0%	0%	0%	8
0%	0%	5.9%	94.1%	0%	0%	0%	9
0%	0%	4.5%	95.5%	0%	0%	0%	10
0%	0%	3.1%	96.9%	0%	0%	0%	11
0%	0%	2.7%	97.3%	0%	0%	0%	12

Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

ival-cos: 40.0ms (41.8% of total)

ival-<=: 13.0ms (13.6% of total)

...c/correct-round.rkt:119:19: 11.0ms (11.5% of total)

ival-<: 7.0ms (7.3% of total)

ival-mult: 6.0ms (6.3% of total)

ival-add: 5.0ms (5.2% of total)

ival-fabs: 5.0ms (5.2% of total)

ival-sub: 5.0ms (5.2% of total)

ival-and: 4.0ms (4.2% of total)

const: 1.0ms (1% of total)

backward-pass: 0.0ms (0% of total)

sample17.4s (48.1%)

Results

7.3s	26153×	0	precondition
5.4s	5694×	2	valid
1.3s	2464×	1	valid
30.0ms	98×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 11.3s

ival-cos: 4.0s (35.5% of total)

...c/correct-round.rkt:119:19: 1.4s (12.4% of total)

ival-mult: 1.0s (9.3% of total)

ival-<=: 961.0ms (8.5% of total)

ival-<: 910.0ms (8.1% of total)

ival-add: 754.0ms (6.7% of total)

ival-fabs: 597.0ms (5.3% of total)

ival-sub: 577.0ms (5.1% of total)

backward-pass: 566.0ms (5% of total)

ival-and: 379.0ms (3.4% of total)

const: 84.0ms (0.7% of total)

Bogosity

preprocess128.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

414×	`fnmadd-define`
382×	`sum3-define`
370×	`fmsub-define`
356×	`fnmsub-define`
316×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	43	44
2	89	42
3	178	42
4	438	42
5	863	42
6	1279	42
7	1611	42
8	1749	42
9	1832	42
10	1850	42
0	6	7
1	9	7
2	14	7
3	21	7
4	31	7
5	63	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (cos (+ x eps)) (cos x))

Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Call 2

Inputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (+ x (neg eps))) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos (+ eps x)) (cos eps))

Outputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (- eps x)) (cos x))
(- (cos (+ x (neg eps))) (cos x))
(- (cos (- eps x)) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(- (cos x) (cos (- eps x)))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos x) (cos (- eps x)))
(- (cos (+ eps x)) (cos eps))
(- (cos (+ x eps)) (cos eps))

explain498.0ms (1.4%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
133	1	(-7.047874917298967e-162 6.852488550842544e-163)	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	1	(-95.56581935146586 6.618220566694702e-14)	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`x`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`eps`

Results

343.0ms	376×	2	valid
80.0ms	134×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-cos: 153.0ms (69.1% of total)

backward-pass: 30.0ms (13.5% of total)

ival-add: 21.0ms (9.5% of total)

ival-sub: 16.0ms (7.2% of total)

const: 1.0ms (0.5% of total)

eval1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify33.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(cos.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
x
eps
(cos x)

Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos (+ x eps))
(cos.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(cos x)
(cos.f64 x)

localize194.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

148.0ms	188×	2	valid
24.0ms	67×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 114.0ms

ival-cos: 78.0ms (68.7% of total)

backward-pass: 16.0ms (14.1% of total)

ival-sub: 10.0ms (8.8% of total)

ival-add: 9.0ms (7.9% of total)

const: 0.0ms (0% of total)

series9.0ms (0%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- (cos (+ x eps)) (cos x))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (cos x)>

Outputs
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
1.0ms	x	@	0	(- (cos (+ x eps)) (cos x))
1.0ms	eps	@	0	(- (cos (+ x eps)) (cos x))
1.0ms	x	@	inf	(+ x eps)
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))

rewrite800.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2774×	`-lowering-.f32`
2774×	`-lowering-.f64`
2160×	`fma-lowering-fma.f32`
2160×	`fma-lowering-fma.f64`
2148×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	50	16
2	408	16
3	5232	16
0	9160	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 195

Calls

Call 1

Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
(cos x)

Outputs
(+.f64 (cos.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(+.f64 (cos.f64 (+.f64 x eps)) (+.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (cos.f64 (+.f64 x eps)) (-.f64 (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps)))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (+.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64)) (cos.f64 x))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 (+.f64 x eps)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (cos.f64 (+.f64 x eps)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (cos.f64 (+.f64 x eps)))
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(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (-.f64 (.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))))
(.f64 (.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (.f64 x x) (*.f64 eps eps)))
(.f64 (-.f64 (.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x x) (*.f64 eps (+.f64 x eps))))
(cos.f64 x)

simplify478.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

3196×	`-lowering-.f32`
3196×	`-lowering-.f64`
1368×	`fnmadd-define`
1248×	`neg-lowering-neg.f64`
1248×	`neg-lowering-neg.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	481
1	304	464
2	776	463
3	2952	463
0	8504	463

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(- (cos eps) 1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (.f64 x (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (sin.f64 eps))))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (.f64 (sin.f64 eps) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+.f64 (cos.f64 eps) (.f64 x (-.f64 (.f64 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+.f64 (cos.f64 eps) (.f64 x (+.f64 (.f64 (cos.f64 eps) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 eps) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval85.0ms (0.2%)

Compiler: Compiled 7623 to 791 computations (89.6% saved)

prune105.0ms (0.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	270	9	279
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	270	10	280

Accuracy

99.8%

Counts

280 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	81.1%	(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
▶	52.9%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
▶	52.7%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	53.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	52.3%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	81.9%	(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
▶	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
▶	99.7%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Compiler

Compiled 285 to 202 computations (29.1% saved)

simplify467.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	cost-diff	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(cos.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(cos.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	(cos.f64 eps)
✓	cost-diff	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	cost-diff	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
✓	cost-diff	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Rules

1844×	`fnmsub-define`
1736×	`+-lowering-+.f64`
1736×	`+-lowering-+.f32`
1686×	`-lowering-.f32`
1686×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	270
1	107	256
2	341	256
3	978	254
4	2852	254
5	7779	254
0	8603	254

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(* eps (* eps 1/6))
(* eps 1/6)
1/6
-1
(+ (cos eps) -1)
(cos eps)
eps
-1
(- (cos (+ x eps)) (+ 1 (* x (* x -1/2))))
(cos (+ x eps))
(+ x eps)
x
eps
(+ 1 (* x (* x -1/2)))
1
(* x (* x -1/2))
(* x -1/2)
-1/2
(- (cos (+ x eps)) (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
(cos (+ x eps))
(+ x eps)
x
eps
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
1
(* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))
(* x x)
(+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))
-1/2
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(+ 1/24 (* x (* x -1/720)))
1/24
(* x (* x -1/720))
(* x -1/720)
-1/720
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(sin x)

Outputs
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
eps
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(* eps (* -1/2 (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(sin x)
(sin.f64 x)
(+ (* eps (* eps 1/6)) -1)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))
(* eps (* eps 1/6))
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
(+ (cos eps) -1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(cos eps)
(cos.f64 eps)
eps
-1
#s(literal -1 binary64)
(- (cos (+ x eps)) (+ 1 (* x (* x -1/2))))
(-.f64 (cos.f64 (+.f64 eps x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ 1 (* x (* x -1/2)))
(-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* x (* x -1/2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* x -1/2)
(*.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- (cos (+ x eps)) (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
(+.f64 (+.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
(-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
1
#s(literal 1 binary64)
(* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(* x x)
(*.f64 x x)
(+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
-1/2
#s(literal -1/2 binary64)
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(+ 1/24 (* x (* x -1/720)))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
1/24
#s(literal 1/24 binary64)
(* x (* x -1/720))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* x -1/720)
(*.f64 x #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* eps (* -1/2 (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(sin x)
(sin.f64 x)

localize1.4s (3.8%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/720 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
✓	accuracy	99.6%	(*.f64 x #s(literal -1/720 binary64))
✓	accuracy	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	54.0%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	54.8%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
✓	accuracy	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))

Results

949.0ms	187×	2	valid
190.0ms	68×	1	valid
8.0ms	1×	3	valid

Compiler

Compiled 281 to 38 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 702.0ms

ival-cos: 223.0ms (31.8% of total)

ival-mult: 199.0ms (28.4% of total)

backward-pass: 102.0ms (14.5% of total)

ival-add: 67.0ms (9.5% of total)

...c/correct-round.rkt:119:19: 64.0ms (9.1% of total)

ival-sub: 34.0ms (4.8% of total)

ival-sin: 10.0ms (1.4% of total)

const: 3.0ms (0.4% of total)

series85.0ms (0.2%)

Counts

22 → 372

Calls

Call 1

Inputs
#<alt (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))>
#<alt (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))>
#<alt (* eps (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (- (cos (+ x eps)) (+ 1 (* x (* x -1/2))))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (+ 1 (* x (* x -1/2)))>
#<alt (- (cos (+ x eps)) (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))>
#<alt (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))>
#<alt (* eps (- (* eps (* -1/2 (cos x))) (sin x)))>
#<alt (- (* eps (* -1/2 (cos x))) (sin x))>
#<alt (* eps 1/6)>
#<alt (* eps (* eps 1/6))>
#<alt (* x -1/2)>
#<alt (* x (* x -1/2))>
#<alt (* x -1/720)>
#<alt (* (* x x) (+ 1/24 (* x (* x -1/720))))>
#<alt (* x (* x -1/720))>
#<alt (cos x)>

Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (- (cos x) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (+ eps x)) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (- eps (* -1 x))) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (- (cos x) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

Calls

93 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
5.0ms	x	@	-inf	(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
4.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
3.0ms	eps	@	0	(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
2.0ms	eps	@	inf	(- (cos (+ x eps)) (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))

rewrite982.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3836×	`-lowering-.f32`
3836×	`-lowering-.f64`
2304×	`fma-lowering-fma.f32`
2304×	`fma-lowering-fma.f64`
2066×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	172
1	240	163
2	2356	163
0	8229	163

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 417

Calls

Call 1

Inputs
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
(+ (cos eps) -1)
(cos eps)
(- (cos (+ x eps)) (+ 1 (* x (* x -1/2))))
(cos (+ x eps))
(+ x eps)
(+ 1 (* x (* x -1/2)))
(- (cos (+ x eps)) (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720))))))))
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ 1/24 (* x (* x -1/720)))))))
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps 1/6)
(* eps (* eps 1/6))
(* x -1/2)
(* x (* x -1/2))
(* x -1/720)
(* (* x x) (+ 1/24 (* x (* x -1/720))))
(* x (* x -1/720))
(cos x)

Outputs
(+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 eps (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 (sin.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(fma.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (cos.f64 x) eps) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(fma.f64 (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps))))
(/.f64 (.f64 eps (+.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) #s(literal 3 binary64)))) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (-.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (.f64 eps (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) #s(literal 3 binary64))) eps) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (-.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))) eps) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) eps)
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(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))) (.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (+.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (-.f64 (.f64 (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/6 binary64)) eps)
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal -1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) x)))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(.f64 (.f64 x (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) x)
(*.f64 x #s(literal -1/720 binary64))
(*.f64 #s(literal -1/720 binary64) x)
(+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 x (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 x (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -1/720 binary64)) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/720 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) x) x (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/720 binary64))) x (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))))) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (.f64 x x)) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))) x)
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/720 binary64)) x)
(cos.f64 x)

simplify793.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

4150×	`-lowering-.f32`
4150×	`-lowering-.f64`
3728×	`+-lowering-+.f64`
3728×	`+-lowering-+.f32`
1350×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	3344
1	994	3223
2	3164	3151
0	8116	3151

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(- (cos x) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (+ eps x)) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (- eps (* -1 x))) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(- (cos x) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 eps (.f64 eps (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 eps (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 eps (.f64 eps (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 eps (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+.f64 (.f64 x (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) x))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)))))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
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1
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(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (-.f64 (*.f64 x (sin.f64 eps)) #s(literal -1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
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(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
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(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
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(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (+ eps x)) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
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(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
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(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (- eps (* -1 x))) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 (cos.f64 (+.f64 eps x)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(- (cos x) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(* -1/720 (pow x 6))
(*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/720 binary64) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1/720 binary64) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(* -1/720 (pow x 6))
(*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/720 binary64) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1/720 binary64) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 eps (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 eps (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (pow eps 2))
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(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
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(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* 1/6 (pow eps 2))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* -1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* -1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval396.0ms (1.1%)

Compiler: Compiled 31355 to 1776 computations (94.3% saved)

prune237.0ms (0.7%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	901	23	924
Fresh	3	1	4
Picked	3	2	5
Done	1	0	1
Total	908	26	934

Accuracy

100.0%

Counts

934 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
	81.9%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	98.6%	(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
	99.6%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
▶	52.3%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	30.3%	(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
	98.0%	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
	99.2%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))
	99.1%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (sin.f64 x)))
▶	99.3%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	99.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.1%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	98.1%	(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.1%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
✓	99.7%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.7%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
▶	98.6%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
▶	99.5%	(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
	53.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	51.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 968 to 648 computations (33.1% saved)

simplify492.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
✓	cost-diff	128	(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓	cost-diff	128	(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
✓	cost-diff	0	(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))
✓	cost-diff	6400	(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))

Rules

3312×	`-lowering-.f32`
3312×	`-lowering-.f64`
1550×	`sum3-define`
1254×	`fma-lowering-fma.f32`
1254×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	251
1	115	242
2	338	241
3	833	241
4	1920	237
5	3313	237
6	6463	237
0	8081	237

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
x
(+ (* eps (* eps 1/6)) -1)
(* eps (* eps 1/6))
eps
(* eps 1/6)
1/6
-1
(* (* -1/2 (cos x)) (* eps eps))
(* -1/2 (cos x))
-1/2
(cos x)
(* eps eps)
(+ 1 -1)
1
-1
(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))
eps
(+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6))))))
(* eps -1/2)
-1/2
(* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))
x
(+ -1 (* x (+ (* eps 1/4) (* x 1/6))))
-1
(* x (+ (* eps 1/4) (* x 1/6)))
(+ (* eps 1/4) (* x 1/6))
(* eps 1/4)
1/4
(* x 1/6)
1/6
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x)))
eps
(- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x))
(* eps (+ -1/2 (* x (* x 1/4))))
(+ -1/2 (* x (* x 1/4)))
-1/2
(* x (* x 1/4))
x
(* x 1/4)
1/4
(sin x)
(* eps (* eps (- (* -1/2 (cos x)) (/ (sin x) eps))))
eps
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1/2 (cos x))
-1/2
(cos x)
x
(/ (sin x) eps)
(sin x)

Outputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(.f64 eps (+.f64 (.f64 (sin.f64 x) (-.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(.f64 (sin.f64 x) (-.f64 #s(literal -1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(sin x)
(sin.f64 x)
x
(+ (* eps (* eps 1/6)) -1)
(-.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
(* eps (* eps 1/6))
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
eps
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
(* (* -1/2 (cos x)) (* eps eps))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
(* eps eps)
(*.f64 eps eps)
(+ 1 -1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
eps
(+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6))))))
(+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))
x
(+ -1 (* x (+ (* eps 1/4) (* x 1/6))))
(+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))
-1
#s(literal -1 binary64)
(* x (+ (* eps 1/4) (* x 1/6)))
(.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))))
(+ (* eps 1/4) (* x 1/6))
(+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(* eps 1/4)
(*.f64 eps #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
eps
(- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) (sin.f64 x))
(* eps (+ -1/2 (* x (* x 1/4))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(+ -1/2 (* x (* x 1/4)))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))
-1/2
#s(literal -1/2 binary64)
(* x (* x 1/4))
(.f64 x (.f64 x #s(literal 1/4 binary64)))
x
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(sin x)
(sin.f64 x)
(* eps (* eps (- (* -1/2 (cos x)) (/ (sin x) eps))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
eps
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(sin x)
(sin.f64 x)

localize468.0ms (1.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (sin.f64 x) eps)
✓	accuracy	100.0%	(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
✓	accuracy	99.6%	(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
✓	accuracy	100.0%	(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	accuracy	99.8%	(.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	99.7%	(+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
✓	accuracy	100.0%	(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))

Results

304.0ms	252×	0	valid
10.0ms	3×	2	valid
9.0ms	1×	3	valid

Compiler

Compiled 272 to 38 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult: 84.0ms (55.9% of total)

ival-add: 26.0ms (17.3% of total)

compiled-spec: 9.0ms (6% of total)

...c/correct-round.rkt:119:19: 7.0ms (4.7% of total)

ival-sin: 7.0ms (4.7% of total)

ival-sub: 6.0ms (4% of total)

ival-div: 5.0ms (3.3% of total)

ival-cos: 5.0ms (3.3% of total)

const: 2.0ms (1.3% of total)

backward-pass: 2.0ms (1.3% of total)

series84.0ms (0.2%)

Counts

24 → 456

Calls

Call 1

Inputs
#<alt (+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))>
#<alt (* (sin x) (+ (* eps (* eps 1/6)) -1))>
#<alt (sin x)>
#<alt (+ (* eps (* eps 1/6)) -1)>
#<alt (+ 1 -1)>
#<alt (* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))>
#<alt (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6))))))>
#<alt (* eps -1/2)>
#<alt (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))>
#<alt (* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x)))>
#<alt (- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x))>
#<alt (* eps (+ -1/2 (* x (* x 1/4))))>
#<alt (+ -1/2 (* x (* x 1/4)))>
#<alt (* eps (* eps (- (* -1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (* -1/2 (cos x))>
#<alt (* eps 1/6)>
#<alt (* eps (* eps 1/6))>
#<alt (* (* -1/2 (cos x)) (* eps eps))>
#<alt (* x 1/6)>
#<alt (+ (* eps 1/4) (* x 1/6))>
#<alt (* x (+ (* eps 1/4) (* x 1/6)))>
#<alt (/ (sin x) eps)>

Outputs
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt -1>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1 x)>
#<alt (* x (- (* 1/4 (* eps x)) 1))>
#<alt (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))>
#<alt (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt -1/2>
#<alt (- (* -1 (/ x eps)) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (* -1 (/ (sin x) eps))>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))>
#<alt (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/4 eps)>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 eps)>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* 1/4 eps)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 x)>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* 1/4 (* eps x))>
#<alt (* x (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* x (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* x (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))>
#<alt (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))>
#<alt (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))>
#<alt (* 1/4 (* eps x))>
#<alt (* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))>
#<alt (* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))>
#<alt (* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))>
#<alt (* 1/4 (* eps x))>
#<alt (* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))>
#<alt (/ x eps)>
#<alt (* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>

Calls

114 calls:

Time	Variable		Point	Expression
14.0ms	eps	@	inf	(* eps (* eps (- (* -1/2 (cos x)) (/ (sin x) eps))))
4.0ms	x	@	-inf	(* x 1/6)
3.0ms	eps	@	0	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))
2.0ms	eps	@	-inf	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))
2.0ms	eps	@	inf	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))

rewrite846.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4024×	`-lowering-.f32`
4024×	`-lowering-.f64`
2670×	`/-lowering-/.f32`
2670×	`/-lowering-/.f64`
2200×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	195
1	219	187
2	2093	186
0	8825	186

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 470

Calls

Call 1

Inputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(+ 1 -1)
(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))))
(+ (* eps -1/2) (* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6))))))
(* eps -1/2)
(* x (+ -1 (* x (+ (* eps 1/4) (* x 1/6)))))
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x)))
(- (* eps (+ -1/2 (* x (* x 1/4)))) (sin x))
(* eps (+ -1/2 (* x (* x 1/4))))
(+ -1/2 (* x (* x 1/4)))
(* eps (* eps (- (* -1/2 (cos x)) (/ (sin x) eps))))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1/2 (cos x))
(* eps 1/6)
(* eps (* eps 1/6))
(* (* -1/2 (cos x)) (* eps eps))
(* x 1/6)
(+ (* eps 1/4) (* x 1/6))
(* x (+ (* eps 1/4) (* x 1/6)))
(/ (sin x) eps)

Outputs
(+.f64 (.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))) (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))) (.f64 eps (-.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))))) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps eps) (.f64 eps eps))) (.f64 eps (-.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))))
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(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/6 binary64)) eps)
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)))
(.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) (*.f64 eps eps)))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))
(.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(.f64 (.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps)
(.f64 (.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))
(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 eps #s(literal 1/4 binary64)))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 x #s(literal 1/6 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
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(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))) (neg.f64 (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 #s(literal -1/6 binary64) x)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 #s(literal -1/6 binary64) x))))
(+.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (-.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(fma.f64 x (.f64 eps #s(literal 1/4 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 eps (.f64 x #s(literal 1/4 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x x) (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/4 binary64) (.f64 eps x) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 eps #s(literal 1/4 binary64)) x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) x (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 (.f64 x #s(literal 1/4 binary64)) eps (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/6 binary64) (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 (.f64 x eps) #s(literal 1/4 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (-.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))
(/.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))) x) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) (neg.f64 (-.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (neg.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 #s(literal -1/6 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x)))) x)) (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x)) (neg.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 #s(literal -1/6 binary64) x))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal 1/216 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64)))) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))))
(.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))) x)
(exp.f64 (*.f64 (log.f64 (/.f64 eps (sin.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(/.f64 (sin.f64 x) eps)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 eps (sin.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) eps)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps))))
(pow.f64 (/.f64 eps (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) eps))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) eps))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) eps))

simplify698.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

5702×	`-lowering-.f32`
5702×	`-lowering-.f64`
3412×	`+-lowering-+.f64`
3412×	`+-lowering-+.f32`
1552×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	4539
1	1318	4397
2	4566	4236
0	8531	4236

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

Calls

Call 1

Inputs
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* -1 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1 x)
(* x (- (* 1/4 (* eps x)) 1))
(* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))
(* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/4 (* eps (pow x 2)))
(* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* eps (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* 1/4 (* eps (pow x 2)))
(* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1 (* eps (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* -1 (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps (- (* -1/2 (cos x)) (/ (sin x) eps)))
-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1 (/ (sin x) eps))
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* 1/4 (* eps x))
(* x (+ (* 1/6 x) (* 1/4 eps)))
(* x (+ (* 1/6 x) (* 1/4 eps)))
(* x (+ (* 1/6 x) (* 1/4 eps)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 (pow x 2))
(+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))
(+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))
(+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))
(* 1/4 (* eps x))
(* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))
(* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))
(* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))
(* 1/4 (* eps x))
(* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))
(/ x eps)
(* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)

Outputs
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps x)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps x)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 x (+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (.f64 eps #s(literal 1/4 binary64))))))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)))
(* x (- (* 1/6 (pow eps 2)) 1))
(.f64 x (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(.f64 x (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(.f64 x (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (.f64 (.f64 x x) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) #s(literal -1 binary64))))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 x))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (.f64 eps eps))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
-1
#s(literal -1 binary64)
(- (* 1/6 (pow eps 2)) 1)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))
(- (* 1/6 (pow eps 2)) 1)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))
(- (* 1/6 (pow eps 2)) 1)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))
(* 1/6 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* 1/6 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(.f64 eps (-.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(.f64 eps (-.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(.f64 eps (-.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
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(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
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(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)

eval285.0ms (0.8%)

Compiler: Compiled 26935 to 2246 computations (91.7% saved)

prune237.0ms (0.7%)

Pruning

31 alts after pruning (28 fresh and 3 done)

	Pruned	Kept	Total
New	951	15	966
Fresh	6	13	19
Picked	4	1	5
Done	0	2	2
Total	961	31	992

Accuracy

100.0%

Counts

992 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	98.0%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
	81.9%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	99.6%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
▶	98.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
	81.0%	(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
	81.3%	(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
▶	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	97.0%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
	99.2%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))
	99.1%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (sin.f64 x)))
	98.9%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
	98.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
	98.1%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.1%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	99.3%	(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
✓	99.7%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.7%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
✓	98.6%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
	98.6%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
	21.8%	(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
▶	52.1%	(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
	98.0%	(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
▶	98.5%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
	53.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	51.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	53.4%	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
▶	52.3%	#s(literal 0 binary64)

Compiler

Compiled 1165 to 777 computations (33.3% saved)

simplify406.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64))))
✓	cost-diff	128	(.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))
✓	cost-diff	128	(.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64))))))
✓	cost-diff	512	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))) eps)))))
✓	cost-diff	0	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/6 binary64) (.f64 x x))
✓	cost-diff	0	(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓	cost-diff	0	(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
✓	cost-diff	128	(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))
✓	cost-diff	128	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	cost-diff	128	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	128	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))

Rules

2274×	`fma-lowering-fma.f32`
2274×	`fma-lowering-fma.f64`
2076×	`-lowering-.f32`
2076×	`-lowering-.f64`
1938×	`sum3-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	46	384
1	125	358
2	536	353
3	2756	346
4	5506	341
5	7261	334
0	8113	334

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(sin (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
-2
0
(* eps (* x (* 1/6 (* x x))))
eps
(* x (* 1/6 (* x x)))
x
(* 1/6 (* x x))
1/6
(* x x)
(* eps (* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))))
eps
(* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))))
(+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))
-1/2
(* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))
x
(+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))
(* x 1/4)
1/4
(/ (+ -1 (* 1/6 (* x x))) eps)
(+ -1 (* 1/6 (* x x)))
-1
(* 1/6 (* x x))
1/6
(* x x)
(+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))
(* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))))
x
(* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))
(* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))
eps
(+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))
(* (+ -1 (* 1/6 (* eps eps))) (* x -1/6))
(+ -1 (* 1/6 (* eps eps)))
-1
(* 1/6 (* eps eps))
1/6
(* eps eps)
(* x -1/6)
-1/6
(* eps 1/4)
1/4
(* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2)))
(+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))
(* x (+ -1 (* 1/6 (* eps eps))))
(* eps -1/2)
-1/2

Outputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)))
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(sin (/ (+ eps 0) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (+ eps 0) 2)
(/.f64 eps #s(literal 2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
(sin (/ (+ eps (* x 2)) 2))
(sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
-2
#s(literal -2 binary64)
0
#s(literal 0 binary64)
(* eps (* x (* 1/6 (* x x))))
(.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x (.f64 x x))))
eps
(* x (* 1/6 (* x x)))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
x
(* 1/6 (* x x))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
1/6
#s(literal 1/6 binary64)
(* x x)
(*.f64 x x)
(* eps (* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
eps
(* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal -1 binary64)) eps)))))
(+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)) eps))))
-1/2
#s(literal -1/2 binary64)
(* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))
(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)) eps)))
x
(+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))
(+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal -1 binary64)) eps))
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(/ (+ -1 (* 1/6 (* x x))) eps)
(/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64)) eps)
(+ -1 (* 1/6 (* x x)))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(* 1/6 (* x x))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
1/6
#s(literal 1/6 binary64)
(* x x)
(*.f64 x x)
(+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 x (.f64 eps #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))))
(* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))))
(.f64 (+.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal -1/36 binary64)) #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps (*.f64 x x)))
x
(* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))
(.f64 (+.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal -1/36 binary64)) #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps x))
(* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))
(.f64 eps (+.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal -1/36 binary64)) #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64))))
eps
(+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))
(+.f64 (.f64 x (-.f64 (.f64 (.f64 eps eps) #s(literal -1/36 binary64)) #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))
(* (+ -1 (* 1/6 (* eps eps))) (* x -1/6))
(.f64 x (-.f64 (.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal -1/6 binary64)))
(+ -1 (* 1/6 (* eps eps)))
(+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))
-1
#s(literal -1 binary64)
(* 1/6 (* eps eps))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
1/6
#s(literal 1/6 binary64)
(* eps eps)
(*.f64 eps eps)
(* x -1/6)
(*.f64 x #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(* eps 1/4)
(*.f64 eps #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2)))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/6 binary64))))) x))
(+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))
(-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 eps #s(literal 1/6 binary64))))) x)
(* x (+ -1 (* 1/6 (* eps eps))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 eps eps))))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)

localize499.0ms (1.4%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	99.7%	(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
✓	accuracy	99.5%	(*.f64 x #s(literal -1/6 binary64))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
✓	accuracy	99.7%	(.f64 #s(literal 1/6 binary64) (.f64 x x))
✓	accuracy	99.6%	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x))) eps)))))
✓	accuracy	99.6%	(.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
✓	accuracy	99.9%	(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓	accuracy	99.7%	(.f64 #s(literal 1/6 binary64) (.f64 x x))
✓	accuracy	100.0%	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
✓	accuracy	99.9%	(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))

Results

314.0ms	252×	0	valid
11.0ms	3×	2	valid
5.0ms	1×	3	valid

Compiler

Compiled 411 to 47 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-mult: 98.0ms (59.9% of total)

ival-add: 27.0ms (16.5% of total)

...c/correct-round.rkt:119:19: 13.0ms (7.9% of total)

ival-div: 13.0ms (7.9% of total)

ival-sin: 8.0ms (4.9% of total)

const: 2.0ms (1.2% of total)

backward-pass: 2.0ms (1.2% of total)

series80.0ms (0.2%)

Counts

21 → 420

Calls

Call 1

Inputs
#<alt (* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)>
#<alt (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (/ (+ eps 0) 2)>
#<alt (* eps (* x (* 1/6 (* x x))))>
#<alt (* x (* 1/6 (* x x)))>
#<alt (* 1/6 (* x x))>
#<alt (* x x)>
#<alt (* eps (* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))))>
#<alt (* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))))>
#<alt (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))>
#<alt (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))>
#<alt (+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))>
#<alt (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))))>
#<alt (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))>
#<alt (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))>
#<alt (sin (/ (+ eps (* x 2)) 2))>
#<alt (* x -1/6)>
#<alt (* 1/6 (* eps eps))>
#<alt (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))>
#<alt (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2)))>

Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))>
#<alt -1/2>
#<alt (- (* -1 (/ x eps)) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)>
#<alt (* 1/6 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) (pow x 2))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))>
#<alt (* 1/6 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))) x)) (* 1/6 (/ 1 eps)))))>
#<alt (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)>
#<alt (/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)>
#<alt (* -1 (/ x eps))>
#<alt (* x (- (* 1/4 x) (/ 1 eps)))>
#<alt (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps)))>
#<alt (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps)))>
#<alt (* 1/6 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))>
#<alt (* 1/6 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))>
#<alt (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)>
#<alt (/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))>
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* eps (+ (* -1 x) (* 1/6 (pow x 3))))>
#<alt (* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (* 1/4 (pow x 2)) 1/2)))))>
#<alt (* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* -1/36 (pow x 3)) (* 1/6 x)))) 1/2)))))>
#<alt (* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* -1/36 (pow x 3)) (* 1/6 x)))) 1/2)))))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 3)) (* 1/6 x)))>
#<alt (* (pow eps 3) (- (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))) (* 1/2 (/ 1 eps))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/36 (pow x 3)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* -1/6 (pow x 3))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* -1/6 (pow x 3))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* eps (+ (* 1/6 (pow x 3)) (* 1/4 (* eps (pow x 2)))))>
#<alt (* eps (+ (* 1/6 (pow x 3)) (* eps (+ (* -1/36 (* eps (pow x 3))) (* 1/4 (pow x 2))))))>
#<alt (* eps (+ (* 1/6 (pow x 3)) (* eps (+ (* -1/36 (* eps (pow x 3))) (* 1/4 (pow x 2))))))>
#<alt (* -1/36 (* (pow eps 3) (pow x 3)))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 3)) (* 1/4 (/ (pow x 2) eps))))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 3)) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 3)) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))>
#<alt (* -1/36 (* (pow eps 3) (pow x 3)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/4 (/ (pow x 2) eps)) (* 1/36 (pow x 3)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 3) eps)) (* 1/4 (pow x 2))) eps)) (* 1/36 (pow x 3)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 3) eps)) (* 1/4 (pow x 2))) eps)) (* 1/36 (pow x 3)))))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))>
#<alt (* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* eps (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))))>
#<alt (* eps (+ (* 1/6 (pow x 2)) (* eps (+ (* -1/36 (* eps (pow x 2))) (* 1/4 x)))))>
#<alt (* eps (+ (* 1/6 (pow x 2)) (* eps (+ (* -1/36 (* eps (pow x 2))) (* 1/4 x)))))>
#<alt (* -1/36 (* (pow eps 3) (pow x 2)))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps))))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps)))))>
#<alt (* (pow eps 3) (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps)))))>
#<alt (* -1/36 (* (pow eps 3) (pow x 2)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2)))))>
#<alt (* 1/6 (* eps x))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))>
#<alt (* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))>
#<alt (* -1/36 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))>
#<alt (* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* -1/36 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))>
#<alt (* 1/4 (pow eps 2))>
#<alt (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))>
#<alt (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))>
#<alt (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))>
#<alt (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (* -1/36 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* -1/36 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))>
#<alt (* 1/4 eps)>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))>

Calls

105 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
2.0ms	eps	@	0	(* eps (* x (* 1/6 (* x x))))
2.0ms	eps	@	inf	(+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))
2.0ms	eps	@	-inf	(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
2.0ms	eps	@	-inf	(+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))

rewrite873.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

5670×	`-lowering-.f32`
5670×	`-lowering-.f64`
2912×	`/-lowering-/.f32`
2912×	`/-lowering-/.f64`
2358×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	259
1	262	242
2	2969	238
0	9951	238

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 402

Calls

Call 1

Inputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(* eps (* x (* 1/6 (* x x))))
(* x (* 1/6 (* x x)))
(* 1/6 (* x x))
(* x x)
(* eps (* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))))
(* eps (+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))))
(+ -1/2 (* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps))))
(* x (+ (* x 1/4) (/ (+ -1 (* 1/6 (* x x))) eps)))
(+ (* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))) (* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2))))
(* x (* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))))
(* x (* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))))
(* eps (+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4)))
(sin (/ (+ eps (* x 2)) 2))
(* x -1/6)
(* 1/6 (* eps eps))
(+ (* (+ -1 (* 1/6 (* eps eps))) (* x -1/6)) (* eps 1/4))
(* eps (+ (* x (+ -1 (* 1/6 (* eps eps)))) (* eps -1/2)))

Outputs
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal -2 binary64)) #s(literal 2 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) #s(literal 2 binary64)))
(/.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
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(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))) (.f64 (.f64 eps (*.f64 eps eps)) eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 eps (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 eps eps))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 eps (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 eps (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (*.f64 eps eps)) eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 eps eps))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps eps)))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))))) (.f64 (.f64 eps (*.f64 eps eps)) eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps (.f64 eps eps))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (*.f64 eps eps)) eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps eps)))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))))) (.f64 (.f64 eps (*.f64 eps eps)) eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) eps) (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))))) (.f64 eps (.f64 eps eps)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))) eps) (.f64 eps (.f64 (.f64 eps eps) (.f64 eps #s(literal -1/2 binary64))))) (*.f64 eps eps))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))) eps)

simplify782.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

6484×	`-lowering-.f32`
6484×	`-lowering-.f64`
3084×	`+-lowering-+.f64`
3084×	`+-lowering-+.f32`
1816×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	568	5329
1	2064	5121
2	7465	5118
0	8528	5118

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (* eps (pow x 3)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)
(* 1/6 (/ (pow x 3) eps))
(* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))
(* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))
(* (pow x 3) (+ (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) (pow x 2))) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x)))))
(* 1/6 (/ (pow x 3) eps))
(* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x))) x)) (* 1/6 (/ 1 eps)))))
(/ (* x (- (* 1/6 (pow x 2)) 1)) eps)
(/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(/ (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(- (* 1/4 (pow x 2)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)
(* -1 (/ x eps))
(* x (- (* 1/4 x) (/ 1 eps)))
(* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps)))
(* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps)))
(* 1/6 (/ (pow x 3) eps))
(* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))
(* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))
(* (pow x 3) (- (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))) (/ 1 (* eps (pow x 2)))))
(* 1/6 (/ (pow x 3) eps))
(* (pow x 3) (+ (* 1/6 (/ 1 eps)) (* 1/4 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- 1/4 (/ 1 (* eps x))) x)) (* 1/6 (/ 1 eps)))))
(/ (* x (- (* 1/6 (pow x 2)) 1)) eps)
(/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(/ (+ (* 1/4 (* eps (pow x 2))) (* x (- (* 1/6 (pow x 2)) 1))) eps)
(* 1/4 (pow x 2))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(* 1/4 (pow x 2))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* eps (+ (* -1 x) (* 1/6 (pow x 3))))
(* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (* 1/4 (pow x 2)) 1/2)))))
(* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* -1/36 (pow x 3)) (* 1/6 x)))) 1/2)))))
(* eps (+ (* -1 x) (+ (* 1/6 (pow x 3)) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* -1/36 (pow x 3)) (* 1/6 x)))) 1/2)))))
(* (pow eps 3) (+ (* -1/36 (pow x 3)) (* 1/6 x)))
(* (pow eps 3) (- (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (+ (* -1/36 (pow x 3)) (+ (* 1/6 x) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))) (* 1/2 (/ 1 eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/36 (pow x 3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* -1/6 (pow x 3))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* -1/6 (pow x 3))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (+ (* -1/6 x) (* 1/36 (pow x 3))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* 1/6 (* eps (pow x 3)))
(* eps (+ (* 1/6 (pow x 3)) (* 1/4 (* eps (pow x 2)))))
(* eps (+ (* 1/6 (pow x 3)) (* eps (+ (* -1/36 (* eps (pow x 3))) (* 1/4 (pow x 2))))))
(* eps (+ (* 1/6 (pow x 3)) (* eps (+ (* -1/36 (* eps (pow x 3))) (* 1/4 (pow x 2))))))
(* -1/36 (* (pow eps 3) (pow x 3)))
(* (pow eps 3) (+ (* -1/36 (pow x 3)) (* 1/4 (/ (pow x 2) eps))))
(* (pow eps 3) (+ (* -1/36 (pow x 3)) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))
(* (pow eps 3) (+ (* -1/36 (pow x 3)) (+ (* 1/6 (/ (pow x 3) (pow eps 2))) (* 1/4 (/ (pow x 2) eps)))))
(* -1/36 (* (pow eps 3) (pow x 3)))
(* -1 (* (pow eps 3) (+ (* -1/4 (/ (pow x 2) eps)) (* 1/36 (pow x 3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 3) eps)) (* 1/4 (pow x 2))) eps)) (* 1/36 (pow x 3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 3) eps)) (* 1/4 (pow x 2))) eps)) (* 1/36 (pow x 3)))))
(* 1/4 (* (pow eps 2) x))
(* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* 1/6 (* eps (pow x 2)))
(* eps (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))))
(* eps (+ (* 1/6 (pow x 2)) (* eps (+ (* -1/36 (* eps (pow x 2))) (* 1/4 x)))))
(* eps (+ (* 1/6 (pow x 2)) (* eps (+ (* -1/36 (* eps (pow x 2))) (* 1/4 x)))))
(* -1/36 (* (pow eps 3) (pow x 2)))
(* (pow eps 3) (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps))))
(* (pow eps 3) (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps)))))
(* (pow eps 3) (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps)))))
(* -1/36 (* (pow eps 3) (pow x 2)))
(* -1 (* (pow eps 3) (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2)))))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* -1/36 (* (pow eps 3) x))
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* -1/36 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))
(* 1/4 (pow eps 2))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
(* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* 1/6 (* (pow eps 3) x))
(* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))

Outputs
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))
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(+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 x (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (+.f64 (/.f64 (.f64 eps #s(literal 1/4 binary64)) x) (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (+.f64 (/.f64 (.f64 eps #s(literal 1/4 binary64)) x) (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (+.f64 (/.f64 (.f64 eps #s(literal 1/4 binary64)) x) (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 x (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) eps) x) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) eps) x) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) eps) x) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) #s(literal -1/6 binary64))))
(* -1 (* eps x))
(*.f64 eps (-.f64 #s(literal 0 binary64) x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/6 binary64))))) x))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps #s(literal 1/6 binary64))))) x))
(* 1/6 (* (pow eps 3) x))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps)))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps)))
(* 1/6 (* (pow eps 3) x))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 x #s(literal -1/6 binary64)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 x #s(literal -1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 x #s(literal -1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x)))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x)))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps eps) x)) (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps eps) x)) (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps eps) x)) (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))

eval264.0ms (0.7%)

Compiler: Compiled 32218 to 2527 computations (92.2% saved)

prune253.0ms (0.7%)

Pruning

32 alts after pruning (27 fresh and 5 done)

	Pruned	Kept	Total
New	867	13	880
Fresh	9	14	23
Picked	3	2	5
Done	0	3	3
Total	879	32	911

Accuracy

100.0%

Counts

911 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	79.5%	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
	95.7%	(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
	98.0%	(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
	81.9%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
	99.6%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.6%	(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
	77.8%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
	98.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
	98.7%	(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
	97.0%	(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
	99.7%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	52.1%	(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
	99.6%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
	81.3%	(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
	98.9%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
	98.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
	98.1%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.1%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
✓	99.7%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
✓	98.6%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
	98.6%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
	21.8%	(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
	98.0%	(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
	98.4%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
✓	98.5%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
	53.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	51.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	53.4%	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
✓	52.3%	#s(literal 0 binary64)

Compiler

Compiled 1764 to 707 computations (59.9% saved)

regimes79.0ms (0.2%)

Counts

61 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (sin.f64 x)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))

Outputs
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))

Calls

3 calls:

22.0ms	x
21.0ms	eps
18.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes78.0ms (0.2%)

Counts

60 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (sin.f64 x)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))

Outputs
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Calls

3 calls:

22.0ms	x
20.0ms	eps
18.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`
99.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes73.0ms (0.2%)

Counts

58 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (sin.f64 x)))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))

Outputs

(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))

Calls

3 calls:

20.0ms	eps
20.0ms	x
17.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`
99.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes44.0ms (0.1%)

Counts

43 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))) (sin.f64 x)))

Outputs
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))

Calls

2 calls:

16.0ms	eps
15.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes45.0ms (0.1%)

Counts

40 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))

Outputs
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))

Calls

2 calls:

17.0ms	eps
14.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`eps`
99.3%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes42.0ms (0.1%)

Counts

39 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))

Outputs
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))

Calls

2 calls:

14.0ms	x
14.0ms	eps

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes36.0ms (0.1%)

Counts

37 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) x))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) eps))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))

Outputs

(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))

Calls

2 calls:

14.0ms	eps
13.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes27.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (.f64 x (.f64 x (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) (.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 (-.f64 (.f64 eps #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (/.f64 (+.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal 1/2 binary64))) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (.f64 x #s(literal -1/6 binary64))) (*.f64 eps #s(literal 1/4 binary64)))))))))

Outputs

(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))

Calls

2 calls:

11.0ms	x
11.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps)))) (.f64 eps eps))
(+.f64 (.f64 (.f64 x x) (.f64 eps (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) eps))))) (*.f64 eps eps)) eps)

Outputs
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))

Calls

2 calls:

10.0ms	eps
10.0ms	x

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0%)

Counts

18 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 eps (+.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) eps)))))
(.f64 eps (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x))))

Outputs
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))

Calls

2 calls:

8.0ms	x
8.0ms	eps

Results

Accuracy	Segments	Branch
98.6%	1	`eps`
98.6%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0%)

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(.f64 eps (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps x) (.f64 x #s(literal 1/6 binary64))) x)
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 eps x))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) eps))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 eps x))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) x))

Outputs
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))

Calls

2 calls:

6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))

Outputs
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
55.2%	2	`x`
53.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))

Outputs
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
53.4%	1	`eps`
53.4%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))

Outputs
#s(literal 0 binary64)

Calls

2 calls:

3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
52.3%	1	`x`
52.3%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch75.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
70.0ms	-1.8244037240027e-147	-7.289796534023081e-150

Results

52.0ms	78×	2	valid
8.0ms	34×	1	valid

Compiler

Compiled 126 to 94 computations (25.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-cos: 32.0ms (72.4% of total)

backward-pass: 5.0ms (11.3% of total)

ival-add: 4.0ms (9.1% of total)

ival-sub: 3.0ms (6.8% of total)

const: 0.0ms (0% of total)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

128×	`*-commutative_binary64`
84×	`+-commutative_binary64`
52×	`sub-neg_binary64`
42×	`neg-sub0_binary64`
42×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	216
1	161	216
2	184	216
3	203	216
4	231	216
5	260	216
6	277	216
7	304	216
8	323	216
9	341	216
10	348	216
11	351	216
12	352	216

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(if (<=.f64 x #s(literal -6478435864142203/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
#s(literal 0 binary64)

Outputs
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 eps #s(literal 1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(if (<=.f64 x #s(literal -6478435864142203/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
#s(literal 0 binary64)

soundness4.8s (13.4%)

Rules

6484×	`-lowering-.f32`
6484×	`-lowering-.f64`
5702×	`-lowering-.f32`
5702×	`-lowering-.f64`
4150×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	481
1	304	464
2	776	463
3	2952	463
0	8504	463
0	373	4539
1	1318	4397
2	4566	4236
0	8531	4236
0	311	3344
1	994	3223
2	3164	3151
0	8116	3151
0	37	172
1	240	163
2	2356	163
0	8229	163
0	568	5329
1	2064	5121
2	7465	5118
0	8528	5118
0	39	195
1	219	187
2	2093	186
0	8825	186
0	6	16
1	50	16
2	408	16
3	5232	16
0	9160	16

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 664 to 404 computations (39.2% saved)

preprocess211.0ms (0.6%)

Compiler: Compiled 484 to 206 computations (57.4% saved)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	88	216
1	161	216
2	184	216
3	203	216
4	231	216
5	260	216
6	277	216
7	304	216
8	323	216
9	341	216
10	348	216
11	351	216
12	352	216

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	88	216
1	161	216
2	184	216
3	203	216
4	231	216
5	260	216
6	277	216
7	304	216
8	323	216
9	341	216
10	348	216
11	351	216
12	352	216

analyze150.0ms (0.4%)

sample17.4s (48.1%)

preprocess128.0ms (0.4%)

explain498.0ms (1.4%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify33.0ms (0.1%)

localize194.0ms (0.5%)

series9.0ms (0%)

rewrite800.0ms (2.2%)

simplify478.0ms (1.3%)

eval85.0ms (0.2%)

prune105.0ms (0.3%)

simplify467.0ms (1.3%)

localize1.4s (3.8%)

series85.0ms (0.2%)

rewrite982.0ms (2.7%)

simplify793.0ms (2.2%)

eval396.0ms (1.1%)

prune237.0ms (0.7%)

simplify492.0ms (1.4%)

localize468.0ms (1.3%)

series84.0ms (0.2%)

rewrite846.0ms (2.3%)

simplify698.0ms (1.9%)

eval285.0ms (0.8%)

prune237.0ms (0.7%)

simplify406.0ms (1.1%)

localize499.0ms (1.4%)

series80.0ms (0.2%)

rewrite873.0ms (2.4%)

simplify782.0ms (2.2%)

eval264.0ms (0.7%)

prune253.0ms (0.7%)

regimes79.0ms (0.2%)

regimes78.0ms (0.2%)

regimes73.0ms (0.2%)

regimes44.0ms (0.1%)

regimes45.0ms (0.1%)

regimes42.0ms (0.1%)

regimes36.0ms (0.1%)

regimes27.0ms (0.1%)

regimes24.0ms (0.1%)

regimes18.0ms (0%)

regimes15.0ms (0%)

regimes8.0ms (0%)

regimes7.0ms (0%)

regimes6.0ms (0%)

bsearch75.0ms (0.2%)

simplify53.0ms (0.1%)

soundness4.8s (13.4%)

preprocess211.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	88	216
1	161	216
2	184	216
3	203	216
4	231	216
5	260	216
6	277	216
7	304	216
8	323	216
9	341	216
10	348	216
11	351	216
12	352	216