Metrics for 2cos (problem 3.3.5)

analyze68.0ms (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: 35.0ms

ival-cos: 9.0ms (25.5% of total)

...c/correct-round.rkt:119:19: 8.0ms (22.6% of total)

ival-fabs: 4.0ms (11.3% of total)

ival-mult: 3.0ms (8.5% of total)

ival-<=: 3.0ms (8.5% of total)

ival-<: 3.0ms (8.5% of total)

ival-add: 2.0ms (5.7% of total)

ival-sub: 2.0ms (5.7% of total)

ival-and: 1.0ms (2.8% of total)

const: 0.0ms (0% of total)

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

sample9.2s (55.5%)

Results

3.5s	26135×	0	precondition
3.1s	5779×	2	valid
636.0ms	2402×	1	valid
14.0ms	75×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.9s

ival-cos: 2.5s (42% of total)

...c/correct-round.rkt:119:19: 873.0ms (14.8% of total)

ival-add: 369.0ms (6.3% of total)

ival-<: 363.0ms (6.2% of total)

ival-<=: 350.0ms (5.9% of total)

ival-mult: 349.0ms (5.9% of total)

ival-fabs: 349.0ms (5.9% of total)

backward-pass: 297.0ms (5% of total)

ival-sub: 289.0ms (4.9% of total)

ival-and: 137.0ms (2.3% of total)

const: 47.0ms (0.8% of total)

Bogosity

preprocess50.0ms (0.3%)

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))

explain271.0ms (1.6%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
131	2	(-7.007101074908889e-155 1.2962369067825263e-169)	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	1	(17.548390237198202 1.730297369258955e-9)	`(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

183.0ms	350×	2	valid
48.0ms	162×	1	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-cos: 112.0ms (78.4% of total)

backward-pass: 14.0ms (9.8% of total)

ival-add: 9.0ms (6.3% of total)

ival-sub: 7.0ms (4.9% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (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)

localize107.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.0%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

81.0ms	175×	2	valid
14.0ms	81×	1	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-cos: 51.0ms (75.6% of total)

backward-pass: 8.0ms (11.9% of total)

ival-add: 5.0ms (7.4% of total)

ival-sub: 4.0ms (5.9% of total)

const: 0.0ms (0% of total)

series4.0ms (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
1.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	eps	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	eps	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))

rewrite340.0ms (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)

simplify210.0ms (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)

eval36.0ms (0.2%)

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

prune35.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	272	7	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	7	280

Accuracy

99.8%

Counts

280 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.4%	(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))
▶	52.4%	(-.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)))))))
▶	52.5%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
▶	52.3%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.8%	(.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))
▶	80.3%	(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
▶	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 182 to 132 computations (27.5% saved)

simplify203.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 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 x (.f64 x #s(literal 1/24 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	(-.f64 #s(literal 0 binary64) eps)
✓	cost-diff	(sin.f64 x)
✓	cost-diff	(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
✓	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))) (sin.f64 x))
✓	cost-diff	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Rules

2448×	`sum5-define`
2062×	`fnmsub-define`
1678×	`fnmadd-define`
1248×	`fmsub-define`
1208×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	165
1	71	157
2	190	157
3	495	157
4	1397	157
5	3299	157
6	5829	157
7	6864	157
8	7028	157
9	7066	157
10	7067	157
0	8225	157

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 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)
(+ (cos eps) -1)
(cos eps)
eps
-1
(* (sin x) (- 0 eps))
(sin x)
x
(- 0 eps)
0
eps
(- (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))))))
(cos (+ x eps))
(+ x eps)
x
eps
(+ 1 (* (* x x) (+ -1/2 (* x (* x 1/24)))))
1
(* (* x x) (+ -1/2 (* x (* x 1/24))))
(* x x)
(+ -1/2 (* x (* x 1/24)))
-1/2
(* x (* x 1/24))
(* x 1/24)
1/24

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

localize412.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal 1/24 binary64)))
✓	accuracy	99.6%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	53.5%	(-.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)))))))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.7%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	53.4%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	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)))

Results

278.0ms	175×	2	valid
81.0ms	81×	1	valid

Compiler

Compiled 172 to 31 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 256.0ms

ival-cos: 111.0ms (43.4% of total)

ival-mult: 51.0ms (19.9% of total)

backward-pass: 36.0ms (14.1% of total)

ival-add: 21.0ms (8.2% of total)

ival-sub: 16.0ms (6.3% of total)

...c/correct-round.rkt:119:19: 15.0ms (5.9% of total)

ival-sin: 4.0ms (1.6% of total)

const: 2.0ms (0.8% of total)

series25.0ms (0.1%)

Counts

20 → 336

Calls

Call 1

Inputs
#<alt (* eps (- (* eps (* -1/2 (cos x))) (sin x)))>
#<alt (- (* eps (* -1/2 (cos x))) (sin x))>
#<alt (* eps (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (* (sin x) (- 0 eps))>
#<alt (sin x)>
#<alt (- 0 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))))))>
#<alt (+ 1 (* (* x x) (+ -1/2 (* x (* x 1/24)))))>
#<alt (cos x)>
#<alt (* x -1/2)>
#<alt (* x 1/24)>
#<alt (* x (* x 1/24))>
#<alt (* (* x x) (+ -1/2 (* x (* x 1/24))))>

Outputs
#<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 (* -1/2 (* 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 (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (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 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 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 (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (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) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (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) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (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)>
#<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 (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>

Calls

84 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(* x -1/2)
1.0ms	eps	@	0	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	eps	@	0	(* eps (* -1/2 (cos x)))
1.0ms	x	@	inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	-inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))

rewrite423.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3184×	`-lowering-.f32`
3184×	`-lowering-.f64`
2442×	`/-lowering-/.f32`
2442×	`/-lowering-/.f64`
2140×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	124
1	181	117
2	1697	117
0	8275	117

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 486

Calls

Call 1

Inputs
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
(+ (cos eps) -1)
(cos eps)
(* (sin x) (- 0 eps))
(sin x)
(- 0 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))))))
(+ 1 (* (* x x) (+ -1/2 (* x (* x 1/24)))))
(cos x)
(* x -1/2)
(* x 1/24)
(* x (* x 1/24))
(* (* x x) (+ -1/2 (* x (* x 1/24))))

Outputs
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))) (.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(/.f64 (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.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 #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 (cos.f64 x) eps)) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) eps) (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)))
(/.f64 (neg.f64 (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))))))
(/.f64 (neg.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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (neg.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps)) (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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))))))
(/.f64 (neg.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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) eps)) (neg.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) eps)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))
(-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x))) (/.f64 (-.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 (cos.f64 x) eps)) (sin.f64 x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))) (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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))))))))
(/.f64 #s(literal 1 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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)))) (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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)))))))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #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 #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 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (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 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 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 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 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 (-.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 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) eps) #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 (sin.f64 x) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (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 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))))
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(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))))
(cos.f64 x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/24 binary64)) x)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 x (.f64 #s(literal -1/2 binary64) x) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) x (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/24 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) x) x (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal -1/2 binary64) x) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal -1/2 binary64) x) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64) (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)) x (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)) x (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)) x (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64)))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64))) x (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(/.f64 (+.f64 (.f64 #s(literal -1/8 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 1/13824 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64))) (.f64 x x)) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 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 1/13824 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))))))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (.f64 x x))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64))) (.f64 x x))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 x x))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))) x)
(.f64 (.f64 #s(literal 1 binary64) x) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))) (*.f64 x x))

simplify306.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

3196×	`-lowering-.f32`
3196×	`-lowering-.f64`
2350×	`+-lowering-+.f64`
2350×	`+-lowering-+.f32`
2100×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	2622
1	857	2520
2	2581	2464
3	6818	2449
0	8341	2449

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

Inputs
(* -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))
(* -1/2 (* 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)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (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 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 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)
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (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) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (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)
(* -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)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))

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

eval104.0ms (0.6%)

Compiler: Compiled 28592 to 1906 computations (93.3% saved)

prune97.0ms (0.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	901	21	922
Fresh	2	0	2
Picked	4	1	5
Done	0	0	0
Total	907	22	929

Accuracy

100.0%

Counts

929 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.4%	(-.f64 #s(literal 0 binary64) (*.f64 eps x))
	98.8%	(+.f64 (.f64 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
▶	99.8%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.2%	(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
▶	52.2%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
▶	79.7%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
▶	79.6%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
	99.0%	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
	80.3%	(*.f64 (sin.f64 x) (neg.f64 eps))
	79.8%	(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
	79.7%	(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
	79.6%	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
	99.5%	(.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 #s(literal -1/48 binary64))))))) (sin.f64 x)))
	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 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)))
▶	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	99.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	98.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
	98.2%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 binary64)))))))
	99.7%	(.f64 eps (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
	52.5%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 679 to 457 computations (32.7% saved)

simplify195.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
✓	cost-diff	128	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/6 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
✓	cost-diff	128	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 (cos.f64 x) eps)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))
✓	cost-diff	0	(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps)
✓	cost-diff	256	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))

Rules

2624×	`-lowering-.f32`
2624×	`-lowering-.f64`
1592×	`+-lowering-+.f64`
1592×	`+-lowering-+.f32`
1246×	`fma-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	37	226
1	108	210
2	344	201
3	1057	201
4	3323	201
5	6808	199
0	8426	199

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* -1/2 (* (cos x) eps)) eps) (* (- 0 (sin x)) eps))
(* (* -1/2 (* (cos x) eps)) eps)
(* -1/2 (* (cos x) eps))
-1/2
(* (cos x) eps)
(cos x)
x
eps
(* (- 0 (sin x)) eps)
(- 0 (sin x))
0
(sin x)
(+ 1 -1)
1
-1
(* (* x (+ 1 (* x (* x -1/6)))) (- 0 eps))
(* x (+ 1 (* x (* x -1/6))))
x
(+ 1 (* x (* x -1/6)))
1
(* x (* x -1/6))
(* x -1/6)
-1/6
(- 0 eps)
0
eps
(* (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))) (- 0 eps))
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))
x
(+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))
1
(* (* x x) (+ -1/6 (* (* x x) 1/120)))
(* x x)
(+ -1/6 (* (* x x) 1/120))
-1/6
(* (* x x) 1/120)
1/120
(- 0 eps)
0
eps
(* 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)

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

localize159.0ms (1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
✓	accuracy	100.0%	(+.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	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/120 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal -1/6 binary64)))
✓	accuracy	99.6%	(*.f64 x #s(literal -1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps)
✓	accuracy	100.0%	(*.f64 (cos.f64 x) eps)
✓	accuracy	100.0%	(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) eps)
✓	accuracy	99.8%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))

Results

107.0ms

256×

valid

Compiler

Compiled 242 to 38 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 32.0ms (51.4% of total)

...c/correct-round.rkt:119:19: 12.0ms (19.3% of total)

ival-add: 7.0ms (11.2% of total)

ival-sub: 4.0ms (6.4% of total)

ival-cos: 4.0ms (6.4% of total)

ival-sin: 2.0ms (3.2% of total)

const: 1.0ms (1.6% of total)

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

series39.0ms (0.2%)

Counts

20 → 348

Calls

Call 1

Inputs
#<alt (+ (* (* -1/2 (* (cos x) eps)) eps) (* (- 0 (sin x)) eps))>
#<alt (* (* -1/2 (* (cos x) eps)) eps)>
#<alt (* -1/2 (* (cos x) eps))>
#<alt (* (cos x) eps)>
#<alt (+ 1 -1)>
#<alt (* (* x (+ 1 (* x (* x -1/6)))) (- 0 eps))>
#<alt (* x (+ 1 (* x (* x -1/6))))>
#<alt (+ 1 (* x (* x -1/6)))>
#<alt (* x (* x -1/6))>
#<alt (* (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))) (- 0 eps))>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))>
#<alt (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))>
#<alt (* (* x x) (+ -1/6 (* (* x x) 1/120)))>
#<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 (* (- 0 (sin x)) eps)>
#<alt (* x -1/6)>
#<alt (* (* x x) 1/120)>

Outputs
#<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 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<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 (+ (* -1/2 (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 (* -1/2 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 (* 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 eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<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 (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<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) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (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 x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin 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 (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>

Calls

87 calls:

Time	Variable		Point	Expression
13.0ms	x	@	inf	(* eps (+ -1/2 (* x (* x 1/4))))
5.0ms	x	@	0	(* x -1/6)
1.0ms	eps	@	0	(* (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))) (- 0 eps))
1.0ms	eps	@	0	(* (* x (+ 1 (* x (* x -1/6)))) (- 0 eps))
1.0ms	x	@	inf	(* (* x (+ 1 (* x (* x -1/6)))) (- 0 eps))

rewrite509.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3310×	`-lowering-.f32`
3310×	`-lowering-.f64`
2662×	`fma-lowering-fma.f32`
2662×	`fma-lowering-fma.f64`
2652×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	174
1	204	159
2	1862	150
0	9284	150

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 540

Calls

Call 1

Inputs
(+ (* (* -1/2 (* (cos x) eps)) eps) (* (- 0 (sin x)) eps))
(* (* -1/2 (* (cos x) eps)) eps)
(* -1/2 (* (cos x) eps))
(* (cos x) eps)
(+ 1 -1)
(* (* x (+ 1 (* x (* x -1/6)))) (- 0 eps))
(* x (+ 1 (* x (* x -1/6))))
(+ 1 (* x (* x -1/6)))
(* x (* x -1/6))
(* (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))) (- 0 eps))
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120)))))
(+ 1 (* (* x x) (+ -1/6 (* (* x x) 1/120))))
(* (* x x) (+ -1/6 (* (* x x) 1/120)))
(* 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)))
(* (- 0 (sin x)) eps)
(* x -1/6)
(* (* x x) 1/120)

Outputs
(+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (.f64 (sin.f64 x) eps)))
(+.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)))
(-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 x) eps))
(-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 eps (sin.f64 x)))
(-.f64 (.f64 eps (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))) (.f64 eps (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)))) (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) (.f64 eps eps)) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) eps (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (cos.f64 x) eps) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (neg.f64 (*.f64 (sin.f64 x) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps))))) (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (-.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) (neg.f64 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps))))) (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (+.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (.f64 (sin.f64 x) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))))))
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(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 eps (.f64 eps eps))))) (neg.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps))) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps))))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)))))
(/.f64 (neg.f64 (.f64 eps (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 eps (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) eps)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))) eps)) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 eps (.f64 eps eps))) (.f64 #s(literal -1/8 binary64) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (*.f64 #s(literal -1/2 binary64) eps)))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64)))) eps)
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) x #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/64 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/64 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))))) (neg.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 x #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/64 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(+.f64 #s(literal 0 binary64) (neg.f64 (*.f64 (sin.f64 x) eps)))
(neg.f64 (*.f64 (sin.f64 x) eps))
(neg.f64 (*.f64 eps (sin.f64 x)))
(/.f64 (.f64 eps (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 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 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (sin.f64 x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) eps) (sin.f64 x))
(/.f64 (neg.f64 (.f64 eps (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (.f64 eps (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 (+.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 #s(literal 0 binary64) (neg.f64 (*.f64 (sin.f64 x) eps))))))
(*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps)
(*.f64 (/.f64 eps (sin.f64 x)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (/.f64 eps (sin.f64 x)))
(*.f64 x #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) x)
(.f64 x (.f64 x #s(literal 1/120 binary64)))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/120 binary64)) x)

simplify328.0ms (2%)

Algorithm

1×	egg-herbie

Rules

4506×	`-lowering-.f32`
4506×	`-lowering-.f64`
2182×	`+-lowering-+.f64`
2182×	`+-lowering-+.f32`
1976×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3326
1	754	3069
2	2578	2989
3	5068	2973
0	8611	2973

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* -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 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(* -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))
(+ (* -1/2 (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)))
(* -1/2 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 (* 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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -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))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
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) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (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 x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin 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)
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))

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

eval101.0ms (0.6%)

Compiler: Compiled 28735 to 2301 computations (92% saved)

prune125.0ms (0.8%)

Pruning

31 alts after pruning (28 fresh and 3 done)

	Pruned	Kept	Total
New	873	15	888
Fresh	3	13	16
Picked	3	2	5
Done	0	1	1
Total	879	31	910

Accuracy

100.0%

Counts

910 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))
	99.8%	(-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 x) eps))
	79.4%	(-.f64 #s(literal 0 binary64) (*.f64 eps x))
	99.5%	(+.f64 (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal 1/1440 binary64) (.f64 x x))))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.8%	(+.f64 (.f64 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
	99.3%	(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.2%	(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
	79.6%	(.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
	79.6%	(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
	79.7%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
✓	79.6%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
	98.6%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
	80.3%	(*.f64 (sin.f64 x) (neg.f64 eps))
	79.8%	(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
	79.7%	(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
	79.6%	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
	99.5%	(.f64 eps (-.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)))) (sin.f64 x)))
	99.5%	(.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 #s(literal -1/48 binary64))))))) (sin.f64 x)))
	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 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)))
✓	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
▶	99.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	98.2%	(.f64 eps (+.f64 (-.f64 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
▶	98.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
	52.0%	(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
	99.4%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
	52.5%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	79.7%	(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
▶	79.6%	(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
▶	52.2%	#s(literal 0 binary64)

Compiler

Compiled 1066 to 675 computations (36.7% saved)

simplify159.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 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 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 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 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
✓	cost-diff	0	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps)
✓	cost-diff	64	(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
✓	cost-diff	0	(.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (sin.f64 x))
✓	cost-diff	6528	(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))

Rules

2026×	`fnmsub-define`
1788×	`-lowering-.f32`
1788×	`-lowering-.f64`
1636×	`fnmadd-define`
1220×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	194
1	102	185
2	313	178
3	905	176
4	2645	176
5	5574	176
6	7157	176
0	8120	176

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize140.0ms (0.8%)

Localize:

Found 16 expressions of interest:

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

Results

89.0ms	252×	0	valid
11.0ms	4×	5	exit

Compiler

Compiled 209 to 34 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 32.0ms (48.7% of total)

...c/correct-round.rkt:119:19: 9.0ms (13.7% of total)

ival-add: 7.0ms (10.6% of total)

compiled-spec: 7.0ms (10.6% of total)

ival-sub: 3.0ms (4.6% of total)

ival-cos: 2.0ms (3% of total)

ival-sin: 2.0ms (3% of total)

const: 1.0ms (1.5% of total)

backward-pass: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

series17.0ms (0.1%)

Counts

20 → 384

Calls

Call 1

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

Outputs
#<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 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))>
#<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 x)>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (sin x))>
#<alt (* -1 (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 (* -1/2 (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 (* eps x))>
#<alt (* x (- (* 1/6 (* eps (pow x 2))) eps))>
#<alt (* x (- (* 1/6 (* eps (pow x 2))) eps))>
#<alt (* x (- (* 1/6 (* eps (pow x 2))) eps))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))>
#<alt (* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))>
#<alt (* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))>
#<alt (* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))>
#<alt (* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* -1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))>
#<alt (* -1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (* eps (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<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)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) 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) (* 1/6 (* eps (pow x 2))))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<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)>
#<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 (* 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 (* 1/4 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 (* 1/6 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 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)))))>

Calls

96 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* x 1/6) (* eps 1/4)))))))
1.0ms	eps	@	0	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* x 1/6) (* eps 1/4)))))))
1.0ms	eps	@	-inf	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* x 1/6) (* eps 1/4)))))))
1.0ms	x	@	inf	(* eps (+ (* eps -1/2) (* x (+ -1 (* x (+ (* x 1/6) (* eps 1/4)))))))
0.0ms	x	@	inf	(* eps (- (* eps -1/2) (sin x)))

rewrite317.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4680×	`-lowering-.f32`
4680×	`-lowering-.f64`
3358×	`/-lowering-/.f32`
3358×	`/-lowering-/.f64`
1608×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	152
1	185	144
2	1723	137
0	8518	137

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 407

Calls

Call 1

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

Outputs
(+.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.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)))) (neg.f64 (.f64 (sin.f64 x) eps)))
(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) eps))
(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 eps (sin.f64 x)))
(-.f64 (.f64 (/.f64 (.f64 eps eps) eps) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (.f64 (sin.f64 x) eps)))) (/.f64 (.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 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (.f64 (sin.f64 x) eps)))))
(fma.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps (cos.f64 x)) (.f64 eps #s(literal -1/2 binary64)) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (cos.f64 x))) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (.f64 eps (cos.f64 x)) eps) #s(literal -1/2 binary64) (neg.f64 (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) eps (neg.f64 (*.f64 (sin.f64 x) eps)))
(/.f64 #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 eps eps)) (.f64 (.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)))) (neg.f64 (.f64 (sin.f64 x) eps))))) (+.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.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 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 binary64) (neg.f64 (/.f64 (+.f64 (.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 (.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)))) (neg.f64 (.f64 (sin.f64 x) eps))))) (+.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.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 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (.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 (.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)))) (neg.f64 (.f64 (sin.f64 x) eps))))))
(/.f64 (+.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps eps)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 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 eps eps)) (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.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 (.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)))) (neg.f64 (.f64 (sin.f64 x) eps)))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps eps)) (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.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 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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))))))) (neg.f64 (.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 eps eps))) (-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (.f64 (.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 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))))) (.f64 (.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))))) (.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.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 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))))) (.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (.f64 (+.f64 (pow.f64 (neg.f64 (.f64 (sin.f64 x) eps)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (neg.f64 (.f64 (sin.f64 x) eps)) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) #s(literal 6 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) #s(literal 3 binary64)))) (+.f64 (.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 (.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)))) (neg.f64 (*.f64 (sin.f64 x) eps)))))))
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(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))))))
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(/.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 #s(literal -1/4 binary64) eps))))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) (.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps)))))
(/.f64 (neg.f64 (-.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 x #s(literal 1/6 binary64)))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/4 binary64) eps))))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 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 (.f64 x (.f64 x #s(literal 1/6 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 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))))))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 x (.f64 eps #s(literal 1/4 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 eps (.f64 #s(literal 1/4 binary64) x) (.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 #s(literal 1/6 binary64) (.f64 x x) (.f64 x (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) 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 eps) #s(literal 1/4 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/4 binary64)) eps (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 x (.f64 x x)))) (+.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 (-.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 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 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (.f64 x (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))) (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/4 binary64) eps)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))) x) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) x) (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/4 binary64) eps)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 x (.f64 x x))))) (neg.f64 (+.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 (neg.f64 (-.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 eps #s(literal 1/4 binary64)))))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 eps #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
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(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64))) x)) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) x)) (neg.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal -1/4 binary64) eps))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.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 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))
(.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))) x)

simplify268.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

4746×	`-lowering-.f32`
4746×	`-lowering-.f64`
3112×	`+-lowering-+.f64`
3112×	`+-lowering-+.f32`
1148×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	3425
1	1063	3230
2	3608	3085
3	7992	3085
0	8113	3085

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

Inputs
(* -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 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(+ (* -1 (* eps (sin x))) (* -1/2 (* (pow eps 2) (cos x))))
(* -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 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (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)
(* -1/2 (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 (* eps x))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))
(* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))
(* (pow x 3) (- (* -1 (/ eps (pow x 2))) (* -1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))
(* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))
(* -1 (* (pow x 3) (- (/ eps (pow x 2)) (* 1/6 eps))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* -1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))
(* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))
(* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2))))
(* -1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
(* eps (* x (+ 1 (* -1/6 (pow x 2)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* 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)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* -1 (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(* -1/2 eps)
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
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)
(* -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))
(* 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))
(+ (* 1/6 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)))
(* 1/6 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 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)))))

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

eval88.0ms (0.5%)

Compiler: Compiled 21255 to 2015 computations (90.5% saved)

prune94.0ms (0.6%)

Pruning

32 alts after pruning (27 fresh and 5 done)

	Pruned	Kept	Total
New	814	14	828
Fresh	10	13	23
Picked	2	3	5
Done	1	2	3
Total	827	32	859

Accuracy

100.0%

Counts

859 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	83.6%	(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
	99.8%	(-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 x) eps))
	99.5%	(+.f64 (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal 1/1440 binary64) (.f64 x x))))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
	98.8%	(+.f64 (.f64 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
	98.7%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
	79.7%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
	97.9%	(.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)))))
	80.3%	(*.f64 (sin.f64 x) (neg.f64 eps))
	79.8%	(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
	79.7%	(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
	79.6%	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
	52.0%	(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
	99.5%	(.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 #s(literal -1/48 binary64))))))) (sin.f64 x)))
	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 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)))
✓	99.5%	(.f64 eps (-.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
✓	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	99.0%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 #s(literal -1/2 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)))))))))
✓	99.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
✓	98.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
	98.8%	(.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)))))))
	79.6%	(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
	98.7%	(.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))))))
	52.5%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	79.6%	(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
	79.6%	(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
	79.7%	(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
	79.6%	(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
	79.4%	(neg.f64 (*.f64 x eps))
✓	52.2%	#s(literal 0 binary64)

Compiler

Compiled 1498 to 658 computations (56.1% saved)

regimes51.0ms (0.3%)

Counts

58 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(-.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 x (.f64 x #s(literal -1/48 binary64))))))) (sin.f64 x)))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 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 (+.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 (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal 1/1440 binary64) (.f64 x x))))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 eps (-.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)))) (sin.f64 x)))
(-.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 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 x) eps))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.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))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps (.f64 (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps)))

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

Calls

3 calls:

16.0ms	eps
15.0ms	x
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Counts

57 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(-.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 x (.f64 x #s(literal -1/48 binary64))))))) (sin.f64 x)))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 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 (+.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 (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal 1/1440 binary64) (.f64 x x))))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 eps (-.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)))) (sin.f64 x)))
(-.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 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 x) eps))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.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 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Calls

3 calls:

15.0ms	x
14.0ms	eps
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`
99.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes41.0ms (0.2%)

Counts

51 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(-.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 x (.f64 x #s(literal -1/48 binary64))))))) (sin.f64 x)))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 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 (+.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 (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal -1/48 binary64) (.f64 #s(literal 1/1440 binary64) (.f64 x x))))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(.f64 eps (-.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)) (.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps)))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (sin.f64 eps)))

Outputs

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

Calls

3 calls:

14.0ms	x
13.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Counts

46 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(-.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 x (.f64 x #s(literal -1/48 binary64))))))) (sin.f64 x)))
(fma.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))))) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))

Outputs
(.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 #s(literal -1/48 binary64))))))) (sin.f64 x)))

Calls

2 calls:

12.0ms	eps
12.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes27.0ms (0.2%)

Counts

44 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(-.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)))))))

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:

12.0ms	eps
11.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts

40 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.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:

11.0ms	x
10.0ms	eps

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes23.0ms (0.1%)

Counts

37 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(neg.f64 (*.f64 x eps))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 x (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 x x))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) eps))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/6 binary64)) x))) eps))
(neg.f64 (.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x))) x) (-.f64 #s(literal 0 binary64) eps))
(neg.f64 (+.f64 (.f64 x eps) (.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) eps)))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 x #s(literal 1/4 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 #s(literal 0 binary64) x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64)))))))
(.f64 x (-.f64 (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps (.f64 eps x)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x))) (-.f64 #s(literal 0 binary64) eps))
(.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 eps (-.f64 (.f64 eps #s(literal -1/2 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 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 (.f64 eps (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)) (.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 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 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))) eps) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps))

Outputs

(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 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:

10.0ms	eps
10.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts

31 → 1

Calls

Call 1

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

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

9.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	x
7.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

23 → 1

Calls

Call 1

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

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:

7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	eps
5.0ms	x

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(neg.f64 (*.f64 x eps))

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
79.4%	1	`x`
79.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (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:

1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
52.2%	1	`eps`
52.2%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

140×	`*-commutative_binary64`
100×	`+-commutative_binary64`
62×	`sub-neg_binary64`
46×	`neg-mul-1_binary64`
44×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	201
1	183	201
2	216	201
3	237	201
4	265	201
5	294	201
6	311	201
7	338	201
8	357	201
9	375	201
10	382	201
11	385	201
12	386	201

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.7s (10.4%)

Rules

4746×	`-lowering-.f32`
4746×	`-lowering-.f64`
3310×	`-lowering-.f32`
3310×	`-lowering-.f64`
3196×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	174
1	204	159
2	1862	150
0	9284	150
0	30	124
1	181	117
2	1697	117
0	8275	117
0	105	481
1	304	464
2	776	463
3	2952	463
0	8504	463
0	272	2622
1	857	2520
2	2581	2464
3	6818	2449
0	8341	2449
0	315	3425
1	1063	3230
2	3608	3085
3	7992	3085
0	8113	3085

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

Compiler

Compiled 658 to 410 computations (37.7% saved)

preprocess84.0ms (0.5%)

Compiler: Compiled 458 to 214 computations (53.3% 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	93	201
1	183	201
2	216	201
3	237	201
4	265	201
5	294	201
6	311	201
7	338	201
8	357	201
9	375	201
10	382	201
11	385	201
12	386	201

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	93	201
1	183	201
2	216	201
3	237	201
4	265	201
5	294	201
6	311	201
7	338	201
8	357	201
9	375	201
10	382	201
11	385	201
12	386	201

analyze68.0ms (0.4%)

sample9.2s (55.5%)

preprocess50.0ms (0.3%)

explain271.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize107.0ms (0.6%)

series4.0ms (0%)

rewrite340.0ms (2%)

simplify210.0ms (1.3%)

eval36.0ms (0.2%)

prune35.0ms (0.2%)

simplify203.0ms (1.2%)

localize412.0ms (2.5%)

series25.0ms (0.1%)

rewrite423.0ms (2.5%)

simplify306.0ms (1.8%)

eval104.0ms (0.6%)

prune97.0ms (0.6%)

simplify195.0ms (1.2%)

localize159.0ms (1%)

series39.0ms (0.2%)

rewrite509.0ms (3.1%)

simplify328.0ms (2%)

eval101.0ms (0.6%)

prune125.0ms (0.8%)

simplify159.0ms (1%)

localize140.0ms (0.8%)

series17.0ms (0.1%)

rewrite317.0ms (1.9%)

simplify268.0ms (1.6%)

eval88.0ms (0.5%)

prune94.0ms (0.6%)

regimes51.0ms (0.3%)

regimes46.0ms (0.3%)

regimes41.0ms (0.2%)

regimes27.0ms (0.2%)

regimes27.0ms (0.2%)

regimes24.0ms (0.1%)

regimes23.0ms (0.1%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify23.0ms (0.1%)

soundness1.7s (10.4%)

preprocess84.0ms (0.5%)

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	93	201
1	183	201
2	216	201
3	237	201
4	265	201
5	294	201
6	311	201
7	338	201
8	357	201
9	375	201
10	382	201
11	385	201
12	386	201