Metrics for 2cos (problem 3.3.5)

analyze80.0ms (0.5%)

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: 40.0ms

...c/correct-round.rkt:119:19: 14.0ms (35.3% of total)

ival-cos: 9.0ms (22.7% of total)

ival-mult: 3.0ms (7.6% of total)

ival-<=: 3.0ms (7.6% of total)

ival-add: 2.0ms (5% of total)

ival-fabs: 2.0ms (5% of total)

ival-sub: 2.0ms (5% of total)

ival-and: 2.0ms (5% of total)

ival-<: 2.0ms (5% of total)

const: 0.0ms (0% of total)

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

sample9.3s (56.1%)

Results

3.6s	5773×	2	valid
3.4s	25981×	0	precondition
676.0ms	2400×	1	valid
12.0ms	83×	0	valid

Precisions

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

ival-cos: 2.4s (40.6% of total)

...c/correct-round.rkt:119:19: 878.0ms (14.9% of total)

backward-pass: 412.0ms (7% of total)

ival-add: 373.0ms (6.3% of total)

ival-mult: 352.0ms (6% of total)

ival-fabs: 332.0ms (5.6% of total)

ival-sub: 312.0ms (5.3% of total)

ival-<: 308.0ms (5.2% of total)

ival-<=: 286.0ms (4.9% of total)

ival-and: 197.0ms (3.3% of total)

const: 49.0ms (0.8% of total)

Bogosity

preprocess51.0ms (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))

explain304.0ms (1.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
142	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
3	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`x`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`eps`

Results

223.0ms	354×	2	valid
35.0ms	156×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

ival-cos: 101.0ms (54.1% of total)

backward-pass: 51.0ms (27.3% of total)

ival-add: 21.0ms (11.2% of total)

ival-sub: 12.0ms (6.4% of total)

const: 1.0ms (0.5% 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
▶	49.4%	(-.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)

localize171.0ms (1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.8%	(cos.f64 (+.f64 x eps))
✓	accuracy	49.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

124.0ms	177×	2	valid
16.0ms	78×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-cos: 80.0ms (80.8% of total)

backward-pass: 10.0ms (10.1% of total)

ival-add: 5.0ms (5% of total)

ival-sub: 4.0ms (4% 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	x	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

rewrite327.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

2774×	`-lowering-.f32`
2774×	`-lowering-.f64`
2148×	`/-lowering-/.f32`
2148×	`/-lowering-/.f64`
1850×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	50	16
2	412	16
3	5247	16
0	8061	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 173

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

simplify225.0ms (1.4%)

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	458
2	777	457
3	2938	457
0	8476	457

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

eval31.0ms (0.2%)

Compiler: Compiled 6681 to 740 computations (88.9% saved)

prune28.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	250	7	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	250	8	258

Accuracy

99.8%

Counts

258 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.9%	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	49.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	79.2%	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
▶	48.8%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.6%	(.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))
▶	99.8%	(.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)))
▶	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Compiler

Compiled 225 to 158 computations (29.8% saved)

simplify168.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	0	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(cos.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 eps (sin.f64 x))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
✓	cost-diff	0	(cos.f64 eps)
✓	cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	cost-diff	0	(.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))))))
✓	cost-diff	0	(.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)))
✓	cost-diff	6272	(-.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))
✓	cost-diff	6400	(+.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)))))

Rules

2588×	`sum4-define`
1784×	`sum3-define`
1624×	`-lowering-.f32`
1624×	`-lowering-.f64`
1450×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	220
1	86	215
2	222	215
3	538	211
4	1342	207
5	4241	207
6	7777	207
0	8216	207

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))) (sin x)))
eps
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x))))))
(+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))
(* -1/2 (cos x))
-1/2
(cos x)
x
(* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x))))
(+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))
(* (* eps (cos x)) 1/24)
(* eps (cos x))
1/24
(* 1/6 (sin x))
1/6
(sin x)
(+ (cos eps) -1)
(cos eps)
eps
-1
(- 0 (* eps (sin x)))
0
(* eps (sin x))
eps
(sin x)
x
(- (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
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(sin x)

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

localize541.0ms (3.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.8%	(cos.f64 (+.f64 x eps))
✓	accuracy	50.3%	(-.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) (*.f64 eps (sin.f64 x)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	50.6%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	99.8%	(.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)))
✓	accuracy	99.7%	(+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
✓	accuracy	99.5%	(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
✓	accuracy	99.4%	(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))

Results

314.0ms	174×	2	valid
155.0ms	79×	1	valid
11.0ms	3×	3	valid

Compiler

Compiled 238 to 34 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 271.0ms

ival-cos: 106.0ms (39.1% of total)

ival-mult: 55.0ms (20.3% of total)

backward-pass: 48.0ms (17.7% of total)

ival-add: 24.0ms (8.8% of total)

...c/correct-round.rkt:119:19: 15.0ms (5.5% of total)

ival-sub: 13.0ms (4.8% of total)

ival-sin: 7.0ms (2.6% of total)

const: 2.0ms (0.7% of total)

series31.0ms (0.2%)

Counts

23 → 444

Calls

Call 1

Inputs
#<alt (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))) (sin x))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))) (sin x)))>
#<alt (* eps (+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x))))))>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (- 0 (* eps (sin x)))>
#<alt (* eps (sin x))>
#<alt (sin x)>
#<alt (- (cos (+ x eps)) (+ 1 (* x (* x -1/2))))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (+ 1 (* x (* x -1/2)))>
#<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 (* (* eps (cos x)) 1/24)>
#<alt (* 1/6 (sin x))>
#<alt (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))>
#<alt (* x -1/2)>
#<alt (* x (* x -1/2))>
#<alt (cos x)>

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

111 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	(* (* eps (cos x)) 1/24)
2.0ms	eps	@	0	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
2.0ms	x	@	inf	(+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))
1.0ms	eps	@	-inf	(+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))
1.0ms	x	@	-inf	(+ (* -1/2 (cos x)) (* eps (+ (* (* eps (cos x)) 1/24) (* 1/6 (sin x)))))

rewrite310.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2966×	`-lowering-.f32`
2966×	`-lowering-.f64`
2960×	`fma-lowering-fma.f32`
2960×	`fma-lowering-fma.f64`
2146×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	177
1	196	172
2	1864	172
0	8587	172

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 430

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/24 binary64) eps)) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(+.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/24 binary64) eps))) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 1/24 binary64) eps) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 (cos.f64 x) eps) eps) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) eps (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (.f64 eps (.f64 (cos.f64 x) eps)) #s(literal 1/24 binary64) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (.f64 eps #s(literal 1/24 binary64)) (.f64 (cos.f64 x) eps) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64)))) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))
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(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/36 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal -1/6 binary64) (sin.f64 x))))))
(/.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)))) #s(literal 1/36 binary64)) (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))))))
(pow.f64 (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64)))))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/36 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (*.f64 eps #s(literal 1/24 binary64))))))))
(.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal 1/24 binary64))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal -1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) x)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(cos.f64 x)

simplify262.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

5202×	`-lowering-.f32`
5202×	`-lowering-.f64`
1882×	`+-lowering-+.f64`
1882×	`+-lowering-+.f32`
1712×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	442	4247
1	1531	3949
2	5087	3905
0	8467	3905

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin 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 (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 x))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* x (- (* (pow x 2) (- (* -1/120 (* eps (pow x 2))) (* -1/6 eps))) eps))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* 1/5040 (* eps (pow x 2))) (* 1/120 eps))) (* -1/6 eps))) eps))
(* -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)))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* 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)
(- (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))
(* -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))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 eps)
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/24 (* eps (cos x)))
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(* 1/24 (* eps (cos x)))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* 1/24 (* eps (cos x)))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* 1/24 eps)
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin 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)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(- (* 1/24 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) (+.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) x)) #s(literal -1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(+.f64 (.f64 x (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(+.f64 (.f64 x (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x (+.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps (.f64 x #s(literal -1/36 binary64))))))) (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(* 1/24 (* (pow eps 2) (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 eps (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (.f64 eps eps) (+.f64 (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps)) (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (.f64 eps eps) (+.f64 (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps)) (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))))
(* 1/24 (* (pow eps 2) (cos x)))
(.f64 #s(literal 1/24 binary64) (.f64 eps (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (/.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/6 binary64)) (*.f64 (cos.f64 x) (/.f64 #s(literal 1/2 binary64) eps))) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (/.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/6 binary64)) (*.f64 (cos.f64 x) (/.f64 #s(literal 1/2 binary64) eps))) eps)))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(.f64 (+.f64 (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps)) (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (*.f64 eps eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps))) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (/.f64 (+.f64 (/.f64 (sin.f64 x) eps) (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps)) eps)) (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
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(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.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 #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 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(+ 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 #s(literal -1/720 binary64) (.f64 x 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)
(cos x)
(cos.f64 x)

eval114.0ms (0.7%)

Compiler: Compiled 25911 to 2225 computations (91.4% saved)

prune85.0ms (0.5%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	933	20	953
Fresh	0	2	2
Picked	4	1	5
Done	0	1	1
Total	937	24	961

Accuracy

100.0%

Counts

961 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	31.4%	(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 eps eps)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps))))))
▶	98.4%	(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
✓	49.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	78.5%	(-.f64 #s(literal 0 binary64) (.f64 eps (.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)))))))))))
▶	78.4%	(-.f64 #s(literal 0 binary64) (.f64 eps (.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)))))))))
	78.4%	(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
	78.3%	(-.f64 #s(literal 0 binary64) (*.f64 eps x))
▶	48.8%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	25.4%	(.f64 (+.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
	99.6%	(.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))
▶	98.4%	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
	78.4%	(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
▶	99.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	99.3%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.4%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	98.5%	(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.5%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
	98.4%	(.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)))))))
	35.1%	(.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (.f64 eps eps)))))))
	49.8%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	49.1%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	79.2%	(neg.f64 (*.f64 eps (sin.f64 x)))

Compiler

Compiled 862 to 553 computations (35.8% saved)

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	128	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 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 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
✓	cost-diff	0	(.f64 eps (.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))))))))
✓	cost-diff	128	(-.f64 #s(literal 0 binary64) (.f64 eps (.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)))))))))
✓	cost-diff	0	(*.f64 eps x)
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	128	(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))
✓	cost-diff	6272	(-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x))

Rules

2494×	`-lowering-.f32`
2494×	`-lowering-.f64`
1544×	`fnmsub-define`
1434×	`+-lowering-+.f64`
1434×	`+-lowering-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	222
1	105	210
2	311	207
3	993	207
4	3054	205
5	7300	205
0	8007	205

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize177.0ms (1.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(/.f64 (sin.f64 x) eps)
✓	accuracy	100.0%	(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
✓	accuracy	98.6%	(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓	accuracy	100.0%	(.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)))))))
✓	accuracy	99.8%	(.f64 x (.f64 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	99.5%	(.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
✓	accuracy	100.0%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps x)
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	99.8%	(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))
✓	accuracy	99.9%	(.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))
✓	accuracy	99.5%	(*.f64 eps #s(literal 1/6 binary64))

Results

123.0ms	254×	0	valid
8.0ms	2×	3	valid

Compiler

Compiled 255 to 37 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 26.0ms (45.6% of total)

...c/correct-round.rkt:119:19: 11.0ms (19.3% of total)

ival-sub: 5.0ms (8.8% of total)

ival-add: 5.0ms (8.8% of total)

ival-sin: 4.0ms (7% of total)

ival-cos: 3.0ms (5.3% of total)

ival-div: 2.0ms (3.5% of total)

const: 1.0ms (1.8% of total)

backward-pass: 1.0ms (1.8% of total)

series27.0ms (0.2%)

Counts

24 → 420

Calls

Call 1

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

Outputs
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
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#<alt (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))>
#<alt (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))>
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
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#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
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#<alt (* 1/6 (* (pow eps 2) (sin x)))>
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#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
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#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
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#<alt -1/2>
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#<alt (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
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#<alt (* -1 (* eps x))>
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#<alt (* eps (- (* -1/2 eps) x))>
#<alt (* eps (- (* -1/2 eps) x))>
#<alt (* -1/2 (pow eps 2))>
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#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (* -1 (* eps x))>
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#<alt (* x (- (* -1/2 (/ (pow eps 2) x)) eps))>
#<alt (* -1 (* eps x))>
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#<alt (* -1 (* x (- (* 1/2 (/ (pow eps 2) x)) (* -1 eps))))>
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#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
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#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
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#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<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 (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
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#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<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))))))>
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#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* -1 (* eps x))>
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#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* (pow x 5) (- (* 1/6 (/ eps (pow x 2))) (* 1/120 eps)))>
#<alt (* (pow x 5) (- (* -1 (/ eps (pow x 4))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
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#<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) (- (/ eps (pow x 4)) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))>
#<alt (* -1 (* (pow x 5) (- (/ eps (pow x 4)) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))>
#<alt (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
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#<alt (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
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#<alt (* eps x)>
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#<alt (* -1 (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))>
#<alt x>
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#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
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#<alt 1>
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#<alt (* 1/120 (pow x 4))>
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#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* -1 (/ x eps)) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (* -1 (/ (sin x) eps))>
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#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
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#<alt (* -1/2 (cos x))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
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#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
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#<alt (* 1/6 eps)>
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#<alt (* 1/6 eps)>
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#<alt (* 1/6 eps)>
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#<alt (* 1/6 eps)>
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#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* -1/6 x)>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 3))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<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))>
#<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 (/ x eps)>
#<alt (* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<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

105 calls:

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

rewrite296.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3058×	`-lowering-.f32`
3058×	`-lowering-.f64`
2854×	`fma-lowering-fma.f32`
2854×	`fma-lowering-fma.f64`
2382×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	186
1	204	175
2	1797	172
0	8539	172

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 548

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (*.f64 (sin.f64 x) eps)) (sin.f64 x)))
(-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (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 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))
(-.f64 (/.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (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 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(fma.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(fma.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 (sin.f64 x) eps)) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 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 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (-.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 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 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 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 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 -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))) #s(literal 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 (sin.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))
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(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))) (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (/.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 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (sin.f64 x) eps) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps eps))))) (neg.f64 (neg.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (sin.f64 x) eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (*.f64 eps eps)))) #s(literal -1 binary64))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (sin.f64 x) eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (/.f64 (sin.f64 x) eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(.f64 #s(literal 1/6 binary64) (.f64 eps (sin.f64 x)))
(.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))
(.f64 (sin.f64 x) (.f64 eps #s(literal 1/6 binary64)))
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))
(+.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal -1/6 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (-.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))))))
(fma.f64 x #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/120 binary64)) (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) x (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x x) (*.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/120 binary64) (*.f64 x #s(literal -1/6 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))))) (-.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))))
(/.f64 (.f64 x (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)))) (-.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(/.f64 (.f64 (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) x) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) x) (-.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/216 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))))) (neg.f64 (-.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) x)) (neg.f64 (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) x)) (neg.f64 (-.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))))
(.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(.f64 (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 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)
(+.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 x (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 (.f64 x x) #s(literal -1/6 binary64)))
(+.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) x) (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x x))) x))
(+.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) (.f64 #s(literal -1/6 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal -1/6 binary64)) (.f64 x (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -1/6 binary64) (.f64 x x) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/120 binary64)) (.f64 (*.f64 x x) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal -1/6 binary64)) x (.f64 (.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x x))) x))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)))) (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))))) (neg.f64 (-.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))
(.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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))
(.f64 (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))) x)
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))) x)
(exp.f64 (*.f64 (log.f64 (/.f64 eps (sin.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(/.f64 (sin.f64 x) eps)
(/.f64 #s(literal 1 binary64) (/.f64 eps (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 eps (sin.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) eps)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps))))
(pow.f64 (/.f64 eps (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) eps))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) eps))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(cos.f64 x)

simplify284.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

5136×	`-lowering-.f32`
5136×	`-lowering-.f64`
3264×	`+-lowering-+.f64`
3264×	`+-lowering-+.f32`
1128×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	3832
1	1143	3512
2	3705	3474
0	8327	3474

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* 1/6 (* eps (sin x)))
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* 1/6 (* eps (sin x)))
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* eps x))
(* eps (- (* -1/2 eps) x))
(* eps (- (* -1/2 eps) x))
(* eps (- (* -1/2 eps) x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(* -1 (* eps x))
(* x (- (* -1/2 (/ (pow eps 2) x)) eps))
(* x (- (* -1/2 (/ (pow eps 2) x)) eps))
(* x (- (* -1/2 (/ (pow eps 2) x)) eps))
(* -1 (* eps x))
(* -1 (* x (- (* 1/2 (/ (pow eps 2) x)) (* -1 eps))))
(* -1 (* x (- (* 1/2 (/ (pow eps 2) x)) (* -1 eps))))
(* -1 (* x (- (* 1/2 (/ (pow eps 2) x)) (* -1 eps))))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -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)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* -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))))))
(* -1 (* eps x))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* x (- (* (pow x 2) (- (* -1/120 (* eps (pow x 2))) (* -1/6 eps))) eps))
(* x (- (* (pow x 2) (- (* -1/120 (* eps (pow x 2))) (* -1/6 eps))) eps))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (- (* 1/6 (/ eps (pow x 2))) (* 1/120 eps)))
(* (pow x 5) (- (* -1 (/ eps (pow x 4))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* (pow x 5) (- (* -1 (/ eps (pow x 4))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (- (* -1/6 (/ eps (pow x 2))) (* -1/120 eps))))
(* -1 (* (pow x 5) (- (/ eps (pow x 4)) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))
(* -1 (* (pow x 5) (- (/ eps (pow x 4)) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* 1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps)))
(* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4)))))
(* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4)))))
(* 1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1 (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))
(* -1 (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))))
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 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1 (/ (sin x) eps))
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* -1/6 x)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 3))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* 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))
(* -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)))))
(/ x eps)
(* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

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

eval112.0ms (0.7%)

Compiler: Compiled 28020 to 2298 computations (91.8% saved)

prune116.0ms (0.7%)

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	979	16	995
Fresh	8	9	17
Picked	4	1	5
Done	0	2	2
Total	991	28	1019

Accuracy

100.0%

Counts

1019 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	27.0%	(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
✓	98.4%	(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
✓	49.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	78.3%	(-.f64 #s(literal 0 binary64) (*.f64 x eps))
	78.5%	(-.f64 #s(literal 0 binary64) (.f64 eps (.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)))))))))))
	78.4%	(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
	98.4%	(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
	99.6%	(.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))
	78.3%	(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
	97.2%	(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
	97.1%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
	51.2%	(.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64))))))
	49.8%	(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
	94.0%	(.f64 (exp.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
	78.4%	(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 binary64) (.f64 x x)))))) eps))
	78.4%	(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
▶	98.4%	(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
▶	99.3%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	98.5%	(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
▶	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
▶	98.5%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
	98.5%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
	98.4%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
	49.1%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	79.2%	(neg.f64 (*.f64 eps (sin.f64 x)))
▶	48.8%	#s(literal 0 binary64)

Compiler

Compiled 865 to 576 computations (33.4% saved)

simplify171.0ms (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 #s(literal 1/6 binary64) x) (.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 #s(literal 1/6 binary64) x) (*.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 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
✓	cost-diff	0	(/.f64 (*.f64 eps eps) x)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 eps eps) x))
✓	cost-diff	0	(-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 eps eps) x)) eps)
✓	cost-diff	256	(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	0	(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Rules

2968×	`-lowering-.f32`
2968×	`-lowering-.f64`
1930×	`fma-define`
1838×	`fma-lowering-fma.f32`
1838×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	208
1	102	200
2	307	200
3	779	197
4	1793	194
5	3721	194
6	6863	194
0	8025	194

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize166.0ms (1%)

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 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
✓	accuracy	99.7%	(.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) x) (*.f64 eps #s(literal 1/4 binary64))))
✓	accuracy	99.6%	(+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	99.5%	(*.f64 #s(literal 1/6 binary64) x)
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 eps eps) x))
✓	accuracy	99.7%	(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
✓	accuracy	58.2%	(/.f64 (*.f64 eps eps) x)
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
✓	accuracy	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
✓	accuracy	99.5%	(*.f64 eps #s(literal 1/6 binary64))

Results

105.0ms	250×	0	valid
12.0ms	4×	5	exit
6.0ms	2×	3	valid

Compiler

Compiled 235 to 34 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 25.0ms (48.8% of total)

ival-add: 6.0ms (11.7% of total)

...c/correct-round.rkt:119:19: 5.0ms (9.8% of total)

ival-sin: 4.0ms (7.8% of total)

ival-cos: 3.0ms (5.9% of total)

ival-div: 2.0ms (3.9% of total)

ival-sub: 2.0ms (3.9% of total)

backward-pass: 2.0ms (3.9% of total)

const: 1.0ms (2% of total)

series21.0ms (0.1%)

Counts

21 → 420

Calls

Call 1

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

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

105 calls:

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

rewrite335.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

3320×	`-lowering-.f32`
3320×	`-lowering-.f64`
2872×	`/-lowering-/.f32`
2872×	`/-lowering-/.f64`
1908×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	155
1	191	150
2	1839	150
0	8217	150

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 437

Calls

Call 1

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

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

5106×	`-lowering-.f32`
5106×	`-lowering-.f64`
3790×	`+-lowering-+.f64`
3790×	`+-lowering-+.f32`
1338×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	346	3758
1	1216	3346
2	4168	3240
0	8155	3240

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1 (* eps x))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1 eps)
(* eps (- (* -1/2 (/ eps x)) 1))
(* eps (- (* -1/2 (/ eps x)) 1))
(* eps (- (* -1/2 (/ eps x)) 1))
(* -1/2 (/ (pow eps 2) x))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1/2 (/ (pow eps 2) x))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 x)) (/ 1 eps))))
(* -1/2 (/ (pow eps 2) x))
(/ (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) x)
(/ (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) x)
(/ (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) x)
(* -1 eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(* -1 eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(- (* -1/2 (/ (pow eps 2) x)) eps)
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(* -1/2 (/ (pow eps 2) x))
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(* 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))
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)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 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 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (sin.f64 x) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) eps))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (sin.f64 x) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) eps))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(* -1/2 (pow eps 2))
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eval92.0ms (0.6%)

Compiler: Compiled 23633 to 2026 computations (91.4% saved)

prune103.0ms (0.6%)

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	871	13	884
Fresh	8	12	20
Picked	2	3	5
Done	0	3	3
Total	881	31	912

Accuracy

100.0%

Counts

912 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))))
	27.0%	(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
✓	98.4%	(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
✓	49.4%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	78.3%	(-.f64 #s(literal 0 binary64) (*.f64 x eps))
	98.6%	(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
	98.4%	(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
	99.6%	(.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))
	35.6%	(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
	78.3%	(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
	97.2%	(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
	97.1%	(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
	49.8%	(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
	78.4%	(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 binary64) (.f64 x x)))))) eps))
	98.4%	(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓	99.6%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.6%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.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))))))))
	98.6%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.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)))))))))))
	98.5%	(.f64 eps (+.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
✓	99.8%	(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.4%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
	38.8%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
	98.5%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
✓	98.5%	(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
	98.5%	(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
	78.4%	(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
	48.6%	(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
	49.7%	(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
	49.1%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
	79.2%	(neg.f64 (*.f64 eps (sin.f64 x)))
✓	48.8%	#s(literal 0 binary64)

Compiler

Compiled 1478 to 663 computations (55.1% saved)

regimes58.0ms (0.3%)

Counts

57 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (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))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))))
(.f64 (exp.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(.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)))
(.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (.f64 eps eps)))))))
(.f64 (+.f64 (+.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps))) (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 eps eps)) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps))))))

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

Calls

3 calls:

26.0ms	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)

regimes43.0ms (0.3%)

Counts

51 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (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))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))

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

Calls

3 calls:

14.0ms	x
13.0ms	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)

regimes42.0ms (0.3%)

Counts

50 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (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))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)))))

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

Calls

3 calls:

15.0ms	x
13.0ms	eps
10.0ms	(-.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)

regimes39.0ms (0.2%)

Counts

47 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (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:

13.0ms	eps
12.0ms	x
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes37.0ms (0.2%)

Counts

44 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) eps (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

Calls

3 calls:

12.0ms	eps
12.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts

39 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(.f64 eps (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 eps (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(.f64 x (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps eps) x)) eps))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 eps (*.f64 eps #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 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 x (-.f64 (.f64 x (.f64 x (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/120 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 (.f64 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.f64 x 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 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x)))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -1/120 binary64))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.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 (.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)))))))))))
(/.f64 (.f64 (.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 eps x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64))))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps #s(literal -1/36 binary64)))) (.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))) (*.f64 x #s(literal -1/6 binary64)))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))) (*.f64 x x)))) x)))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/36 binary64)))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))

Outputs

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

Calls

2 calls:

11.0ms	x
10.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

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

Outputs
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	x
7.0ms	eps

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(-.f64 #s(literal 0 binary64) (*.f64 eps x))

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
78.3%	1	`x`
78.3%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
49.8%	1	`eps`
52.1%	2	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

3 → 2

Calls

Call 1

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

Outputs
(.f64 #s(literal 1/2 binary64) (.f64 x x))
#s(literal 0 binary64)

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
49.1%	1	`eps`
50.8%	2	`x`

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	x
1.0ms	eps

Results

Accuracy	Segments	Branch
48.8%	1	`eps`
48.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch59.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
57.0ms	-3.287703410415866e-143	-1.5747760279408768e-150

Results

47.0ms	108×	2	valid
5.0ms	36×	1	valid

Compiler

Compiled 158 to 118 computations (25.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-cos: 30.0ms (75.7% of total)

backward-pass: 5.0ms (12.6% of total)

ival-add: 3.0ms (7.6% of total)

ival-sub: 2.0ms (5% of total)

const: 0.0ms (0% of total)

bsearch59.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
57.0ms	-3.287703410415866e-143	-1.5747760279408768e-150

Results

47.0ms	112×	2	valid
4.0ms	32×	1	valid

Compiler

Compiled 122 to 100 computations (18% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-cos: 31.0ms (77.8% of total)

backward-pass: 5.0ms (12.5% of total)

ival-add: 2.0ms (5% of total)

ival-sub: 2.0ms (5% of total)

const: 0.0ms (0% of total)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

126×	`*-commutative_binary64`
88×	`+-commutative_binary64`
58×	`sub-neg_binary64`
44×	`neg-mul-1_binary64`
42×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	226
1	163	226
2	197	226
3	219	226
4	249	226
5	279	226
6	307	226
7	325	226
8	337	226
9	350	226
10	355	226
11	358	226
12	359	226

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.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)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (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 (.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)))))))))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.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 (.f64 x 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 #s(literal 1/6 binary64) x) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 eps (+.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 0 binary64))
#s(literal 0 binary64)

Outputs
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps))))
(fma.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) eps (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (*.f64 eps #s(literal 1/6 binary64))))) (sin.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)))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (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 (.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)))))))))))
(.f64 eps (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.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)))))))))))
(+.f64 (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (.f64 x (.f64 x x)) (.f64 eps (+.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 (.f64 x 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 (.f64 x 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 #s(literal 1/6 binary64) x) (.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 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))))
(.f64 eps (+.f64 (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(-.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (*.f64 x eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 x (-.f64 #s(literal 0 binary64) eps))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 0 binary64))
(if (<=.f64 x #s(literal -439347050248359/13729595320261219429963801598162786434538870600286610818788926918371086366795312104245119281322909109954592622782961716074243975999433287625148056582230114304 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 0 binary64))
#s(literal 0 binary64)

soundness1.7s (10.1%)

Rules

5202×	`-lowering-.f32`
5202×	`-lowering-.f64`
5106×	`-lowering-.f32`
5106×	`-lowering-.f64`
3790×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	155
1	191	150
2	1839	150
0	8217	150
0	105	481
1	304	458
2	777	457
3	2938	457
0	8476	457
0	36	186
1	204	175
2	1797	172
0	8539	172
0	442	4247
1	1531	3949
2	5087	3905
0	8467	3905
0	346	3758
1	1216	3346
2	4168	3240
0	8155	3240

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 639 to 377 computations (41% saved)

preprocess74.0ms (0.4%)

Compiler: Compiled 506 to 200 computations (60.5% 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	85	226
1	163	226
2	197	226
3	219	226
4	249	226
5	279	226
6	307	226
7	325	226
8	337	226
9	350	226
10	355	226
11	358	226
12	359	226

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	85	226
1	163	226
2	197	226
3	219	226
4	249	226
5	279	226
6	307	226
7	325	226
8	337	226
9	350	226
10	355	226
11	358	226
12	359	226

analyze80.0ms (0.5%)

sample9.3s (56.1%)

preprocess51.0ms (0.3%)

explain304.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize171.0ms (1%)

series4.0ms (0%)

rewrite327.0ms (2%)

simplify225.0ms (1.4%)

eval31.0ms (0.2%)

prune28.0ms (0.2%)

simplify168.0ms (1%)

localize541.0ms (3.3%)

series31.0ms (0.2%)

rewrite310.0ms (1.9%)

simplify262.0ms (1.6%)

eval114.0ms (0.7%)

prune85.0ms (0.5%)

simplify137.0ms (0.8%)

localize177.0ms (1.1%)

series27.0ms (0.2%)

rewrite296.0ms (1.8%)

simplify284.0ms (1.7%)

eval112.0ms (0.7%)

prune116.0ms (0.7%)

simplify171.0ms (1%)

localize166.0ms (1%)

series21.0ms (0.1%)

rewrite335.0ms (2%)

simplify268.0ms (1.6%)

eval92.0ms (0.6%)

prune103.0ms (0.6%)

regimes58.0ms (0.3%)

regimes43.0ms (0.3%)

regimes42.0ms (0.3%)

regimes39.0ms (0.2%)

regimes37.0ms (0.2%)

regimes24.0ms (0.1%)

regimes18.0ms (0.1%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

bsearch59.0ms (0.4%)

bsearch59.0ms (0.4%)

simplify23.0ms (0.1%)

soundness1.7s (10.1%)

preprocess74.0ms (0.4%)

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	85	226
1	163	226
2	197	226
3	219	226
4	249	226
5	279	226
6	307	226
7	325	226
8	337	226
9	350	226
10	355	226
11	358	226
12	359	226