Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze95.0ms (0.8%)

Memory

-7.4MiB live, 85.7MiB allocated

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%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.0s (58%)

Memory

-89.5MiB live, 7 621.5MiB allocated

Samples

3.8s	26 234×	0	invalid
630.0ms	5 506×	0	valid
552.0ms	2 750×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.8s

ival-<=: 793.0ms (21.1% of total)

const: 728.0ms (19.4% of total)

ival-sin: 659.0ms (17.5% of total)

ival-fabs: 328.0ms (8.7% of total)

ival-mult: 305.0ms (8.1% of total)

ival-add: 247.0ms (6.6% of total)

ival-sub: 213.0ms (5.7% of total)

ival-<: 164.0ms (4.4% of total)

adjust: 153.0ms (4.1% of total)

ival-and: 107.0ms (2.8% of total)

exact: 47.0ms (1.3% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

explain129.0ms (1.1%)

Memory

-33.2MiB live, 167.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
226	2	(2.5597576384510625e-185 1.3010497316487213e-187)	4	(-1.553883838835655e-302 2.8067307261804276e-304)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	224	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	223	4
-	2	27

Precision

0.9911111111111112

Recall

0.9823788546255506

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	223	4	0
-	2	5	22

Precision?

0.9700854700854701

Recall?

1.0

Freqs

test

number	freq
0	31
1	224
2	1

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

21.0ms	184×	1	valid
16.0ms	324×	0	valid
1.0ms	2×	2	valid
1.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sin: 10.0ms (42% of total)

ival-add: 6.0ms (25.2% of total)

adjust: 4.0ms (16.8% of total)

ival-sub: 3.0ms (12.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess43.0ms (0.4%)

Memory

-0.9MiB live, 45.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	22	43
2	29	43
3	37	43
4	49	43
5	71	43
6	93	43
7	147	43
8	231	43
9	385	43
10	1010	43
11	4371	43
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sin.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	11	18
0	11	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

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

localize32.0ms (0.3%)

Memory

4.2MiB live, 55.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.09878096184362353	(sin.f64 (+.f64 x eps))
accuracy	25.197090487111463	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

12.0ms	92×	1	valid
12.0ms	162×	0	valid
1.0ms	1×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sin: 12.0ms (69.5% of total)

adjust: 2.0ms (11.6% of total)

ival-add: 2.0ms (11.6% of total)

ival-sub: 2.0ms (11.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

-35.2MiB live, 10.4MiB allocated

Counts

4 → 31

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))

simplify209.0ms (1.7%)

Memory

33.5MiB live, 213.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite202.0ms (1.7%)

Memory

-17.6MiB live, 222.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Counts

4 → 154

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)

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

eval23.0ms (0.2%)

Memory: 6.7MiB live, 53.0MiB allocated
Compiler: Compiled 5 510 to 734 computations (86.7% saved)

prune5.0ms (0%)

Memory

15.7MiB live, 15.7MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	6	178

Accuracy

100.0%

Counts

178 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
✓	60.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 145 to 110 computations (24.1% saved)

simplify161.0ms (1.3%)

Memory

13.1MiB live, 164.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	176
0	54	166
1	99	166
2	225	166
3	615	163
4	1490	163
5	2995	163
6	6678	163
0	8331	162

Stop Event

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

Calls

Call 1

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

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

localize201.0ms (1.7%)

Memory

0.7MiB live, 321.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.0	(cos.f64 eps)
accuracy	0.00390625	(*.f64 (cos.f64 eps) (sin.f64 x))
accuracy	20.263299791818742	(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
accuracy	0.0	(cos.f64 x)
accuracy	0.0078125	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.01171875	(*.f64 (sin.f64 x) eps)
accuracy	0.1497393065589549	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.4059730394746403	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	1.0288452754261794	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	0.0	(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy	0.00390625	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.06723542336420314	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

160.0ms	237×	1	valid
10.0ms	14×	2	valid
1.0ms	5×	0	valid

Compiler

Compiled 166 to 33 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

adjust: 33.0ms (31.9% of total)

ival-mult: 26.0ms (25.1% of total)

ival-sin: 16.0ms (15.5% of total)

ival-cos: 10.0ms (9.7% of total)

ival-add: 10.0ms (9.7% of total)

ival-sub: 5.0ms (4.8% of total)

ival-div: 3.0ms (2.9% of total)

exact: 1.0ms (1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series53.0ms (0.4%)

Memory

-20.9MiB live, 24.7MiB allocated

Counts

19 → 100

Calls

Call 1

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

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 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)))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* x (cos eps))
(* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos eps))))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (* (cos eps) (sin x)) (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos eps) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin x)
(+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))
(+ 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)))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(sin (* 1/2 eps))
(cos eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	eps	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (cos eps) (sin x)) (cos eps))
6.0ms	eps	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (cos eps) (sin x)) (cos eps))
5.0ms	x	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (cos eps) (sin x)) (cos eps))
4.0ms	eps	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (cos eps) (sin x)) (cos eps))
4.0ms	x	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (cos eps) (sin x)) (cos eps))

simplify143.0ms (1.2%)

Memory

16.7MiB live, 110.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	395	1371
1	1480	1304
2	5477	1275
0	8393	1159

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 99

Calls

Call 1

Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 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)))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* x (cos eps))
(* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos eps))))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (* (cos eps) (sin x)) (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos eps) (sin x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin x)
(+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))
(+ 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)))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(sin (* 1/2 eps))
(cos eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x)) x)) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) x) x (.f64 #s(literal -1/6 binary64) eps)) (.f64 x eps))
(* x (- (cos eps) 1))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(.f64 (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (cos.f64 eps)) #s(literal 1/120 binary64)) x) x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64))) (.f64 x x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (cos.f64 eps) #s(literal 1/5040 binary64)) x) x (-.f64 (.f64 #s(literal 1/120 binary64) (cos.f64 eps)) #s(literal 1/120 binary64))) (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64))) (*.f64 x x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x)
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* x (cos eps))
(*.f64 (cos.f64 eps) x)
(* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (cos.f64 eps)) x)
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (cos.f64 eps) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))) (*.f64 (cos.f64 eps) x))
(* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos eps))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (cos.f64 eps) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (cos.f64 eps) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
(- (* (cos eps) (sin x)) (sin x))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* (cos eps) (sin x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) eps) eps) #s(literal 1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64))))) (.f64 eps eps))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(sin x)
(sin.f64 x)
(+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 x))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 eps eps) (sin.f64 x))
(+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 x) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(cos eps)
(cos.f64 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite138.0ms (1.1%)

Memory

22.9MiB live, 115.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	144
0	54	136
1	202	130
2	1704	130
0	8155	130

Stop Event

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

Counts

19 → 379

Calls

Call 1

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

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

eval111.0ms (0.9%)

Memory: -8.8MiB live, 91.4MiB allocated
Compiler: Compiled 14 972 to 2 062 computations (86.2% saved)

prune19.0ms (0.2%)

Memory

-16.9MiB live, 31.0MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	502	15	517
Fresh	0	0	0
Picked	3	2	5
Done	1	0	1
Total	506	17	523

Accuracy

100.0%

Counts

523 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
	99.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))

Compiler

Compiled 760 to 540 computations (28.9% saved)

simplify124.0ms (1%)

Memory

10.8MiB live, 100.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
cost-diff	5	(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
cost-diff	3	(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	430
0	92	415
1	164	407
2	402	407
3	1374	407
4	3819	407
5	7945	407
0	8035	400

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
(sin.f64 eps)
eps
(cos.f64 x)
x
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(sin.f64 x)
(fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(*.f64 eps eps)
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+.f64 x eps)
x
eps
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))
(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
(neg.f64 x)
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
eps

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

localize273.0ms (2.3%)

Memory

-11.8MiB live, 271.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
accuracy	0.01171875	(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.06912538348029634	(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.4059730394746403	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
accuracy	0.16015625	(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
accuracy	0.35546875	(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	0.4059730394746403	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.5804119463469561	#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.0078125	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
accuracy	0.1497393065589549	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
accuracy	0.6244619811232539	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy	0.00390625	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	0.4059730394746403	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	1.040193879594606	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
accuracy	0.10546875	(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
accuracy	0.34765625	(.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))

Samples

211.0ms	237×	1	valid
17.0ms	14×	2	valid
2.0ms	5×	0	valid

Compiler

Compiled 283 to 51 computations (82% saved)

Precisions

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

ival-sin: 55.0ms (29.4% of total)

ival-mult: 52.0ms (27.8% of total)

adjust: 25.0ms (13.4% of total)

ival-add: 22.0ms (11.8% of total)

const: 10.0ms (5.3% of total)

ival-cos: 9.0ms (4.8% of total)

ival-sub: 8.0ms (4.3% of total)

ival-div: 3.0ms (1.6% of total)

ival-pi: 2.0ms (1.1% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series33.0ms (0.3%)

Memory

13.2MiB live, 57.8MiB allocated

Counts

24 → 110

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
(sin.f64 eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)

Outputs
(* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos 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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* x (+ 1/24 (* -1/720 (pow eps 2))))
(* x (+ 1/24 (+ (* -1/6 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* -1/720 (pow eps 2)))))
(* x (+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (+ 1/24 (* -1/720 (pow eps 2)))) (* 1/120 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))))))))
(* x (+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* 1/120 (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* (pow eps 2) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))) (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos x)
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(sin (- (* 1/2 (PI)) x))
(* eps (sin (- (* 1/2 (PI)) x)))
(* -1 x)
(* x (- (* 1/2 (/ (PI) x)) 1))
(* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(- (* (cos eps) (sin x)) (sin x))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(sin (+ (* -1 x) (* 1/2 (PI))))
(* eps (sin (+ (* -1 x) (* 1/2 (PI)))))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* 1/24 (sin x))
(+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(* -1/720 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/720 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* -1/720 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* x x)) 1) (sin (+ (neg x) (/ (PI) 2))) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (+ (neg x) (/ (PI) 2)) (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* (+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (* eps eps)) (- (* (cos eps) (sin x)) (sin x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
6.0ms	eps	@	inf	((+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* x x)) 1) (sin (+ (neg x) (/ (PI) 2))) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (+ (neg x) (/ (PI) 2)) (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* (+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (* eps eps)) (- (* (cos eps) (sin x)) (sin x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
5.0ms	x	@	inf	((+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* x x)) 1) (sin (+ (neg x) (/ (PI) 2))) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (+ (neg x) (/ (PI) 2)) (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* (+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (* eps eps)) (- (* (cos eps) (sin x)) (sin x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
5.0ms	x	@	-inf	((+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* x x)) 1) (sin (+ (neg x) (/ (PI) 2))) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (+ (neg x) (/ (PI) 2)) (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* (+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (* eps eps)) (- (* (cos eps) (sin x)) (sin x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))
4.0ms	x	@	0	((+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* x x)) 1) (sin (+ (neg x) (/ (PI) 2))) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (+ (neg x) (/ (PI) 2)) (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* (+ (* (* (sin x) (+ (* (* eps eps) -1/720) 1/24)) (* eps eps)) (* -1/2 (sin x))) (* eps eps)) (- (* (cos eps) (sin x)) (sin x)) (* (+ (* -1/720 (* x x)) 1/24) x) (* (* (+ (* -1/720 (* x x)) 1/24) x) x))

simplify147.0ms (1.2%)

Memory

29.5MiB live, 125.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	402	1763
1	1456	1703
2	5925	1687
0	8206	1545

Stop Event

1×	iter limit
1×	node limit

Counts

110 → 109

Calls

Call 1

Inputs
(* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos 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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* x (+ 1/24 (* -1/720 (pow eps 2))))
(* x (+ 1/24 (+ (* -1/6 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* -1/720 (pow eps 2)))))
(* x (+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (+ 1/24 (* -1/720 (pow eps 2)))) (* 1/120 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))))))))
(* x (+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* 1/120 (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* (pow eps 2) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))) (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))))))))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos x)
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(sin (- (* 1/2 (PI)) x))
(* eps (sin (- (* 1/2 (PI)) x)))
(* -1 x)
(* x (- (* 1/2 (/ (PI) x)) 1))
(* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(- (* (cos eps) (sin x)) (sin x))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(sin (+ (* -1 x) (* 1/2 (PI))))
(* eps (sin (+ (* -1 x) (* 1/2 (PI)))))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* 1/24 (sin x))
(+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(* -1/720 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/720 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* -1/720 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))

Outputs
(* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64))) x)
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 eps eps) #s(literal -1/144 binary64)) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64)))) x)
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2))
(.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/86400 binary64) (.f64 eps eps) #s(literal 1/2880 binary64)) (.f64 eps eps)) #s(literal 1/240 binary64)) (.f64 x x) (fma.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 eps eps) #s(literal -1/144 binary64)) (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64)))) x)
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/5040 binary64) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) #s(literal 1/10080 binary64)) (.f64 x x) (-.f64 (.f64 (fma.f64 #s(literal -1/86400 binary64) (.f64 eps eps) #s(literal 1/2880 binary64)) (.f64 eps eps)) #s(literal 1/240 binary64))) (.f64 x x) (fma.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 eps eps) #s(literal -1/144 binary64)) (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps (-.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64)))) x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64) (.f64 (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/12 binary64)) x)) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(sin (* 1/2 (PI)))
(sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(fma.f64 (neg.f64 x) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(* eps (sin (* 1/2 (PI))))
(.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(.f64 (neg.f64 eps) (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
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(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)

rewrite200.0ms (1.7%)

Memory

-39.6MiB live, 195.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	360
0	92	345
1	347	337
2	2585	337
0	8279	330

Stop Event

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

Counts

24 → 257

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
(sin.f64 eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)

Outputs
(.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps)))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64)))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (*.f64 eps eps)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) #s(literal 2 binary64))) (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)))) (neg.f64 (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (*.f64 eps eps)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64))) (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (*.f64 eps eps)) #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (neg.f64 eps)) (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (neg.f64 eps) (.f64 (neg.f64 eps) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)))
(fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)) (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (sin.f64 x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal -1/2 binary64)))))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1/2 binary64)))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps (sin.f64 x)))) eps))
(-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x))) (*.f64 eps eps)))
(-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (neg.f64 (.f64 eps eps)) (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (*.f64 eps eps)) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
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(+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)) (*.f64 eps eps))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x)
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)) x) (-.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) x) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (.f64 x (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) x (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 #s(literal 1/24 binary64) x (.f64 (.f64 (*.f64 x x) #s(literal -1/720 binary64)) x))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 x #s(literal 1/24 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) x) (.f64 #s(literal 1/24 binary64) x))
(+.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) x))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))) (.f64 x #s(literal 1/24 binary64)))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 x (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)) (.f64 x x)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))

eval49.0ms (0.4%)

Memory: 35.8MiB live, 80.9MiB allocated
Compiler: Compiled 14 274 to 1 729 computations (87.9% saved)

prune48.0ms (0.4%)

Memory

-21.6MiB live, 26.0MiB allocated

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	319	5	324
Fresh	2	8	10
Picked	2	3	5
Done	0	2	2
Total	323	18	341

Accuracy

100.0%

Counts

341 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
	99.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.7%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
▶	5.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))

Compiler

Compiled 784 to 556 computations (29.1% saved)

simplify104.0ms (0.9%)

Memory

0.2MiB live, 98.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	0	#s(approx (* (sin x) eps) (*.f64 x eps))
cost-diff	0	(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
cost-diff	0	#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
cost-diff	0	#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	488
0	100	482
1	191	482
2	636	482
3	3342	479
4	5852	479
0	8102	470

Stop Event

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

Calls

Call 1

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

Outputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
(fma.f64 (cos.f64 x) (sin.f64 eps) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (sin.f64 x))))
(sin.f64 eps)
eps
(cos.f64 x)
x
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (sin.f64 x)))
(.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)
(.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (sin.f64 x))
(.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) eps)
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) (sin.f64 x))
(.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))
(sin.f64 x)
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 eps eps)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps)
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))
(.f64 (.f64 eps x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 x eps))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(-.f64 (/.f64 eps #s(literal -2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)

localize289.0ms (2.4%)

Memory

-1.7MiB live, 278.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 eps eps)
accuracy	0.00390625	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.06406085290397268	#s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.06723542336420314	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.0	(cos.f64 x)
accuracy	0.0078125	(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.1497393065589549	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.9833463951328292	#s(approx (* (sin x) eps) (*.f64 x eps))
accuracy	0.00390625	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
accuracy	0.12890625	(*.f64 eps (+.f64 x eps))
accuracy	0.1497393065589549	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
accuracy	0.6180523388223389	#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps))
accuracy	0.0078125	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps)
accuracy	0.1497393065589549	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
accuracy	0.6244619811232539	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64))))
accuracy	61.597809906961594	#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps))
accuracy	0.015625	(.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) eps)
accuracy	0.109375	(.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)

Samples

224.0ms	237×	1	valid
15.0ms	14×	2	valid
2.0ms	5×	0	valid

Compiler

Compiled 317 to 58 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 201.0ms

ival-mult: 55.0ms (27.3% of total)

adjust: 53.0ms (26.3% of total)

ival-cos: 29.0ms (14.4% of total)

ival-add: 27.0ms (13.4% of total)

ival-sin: 16.0ms (8% of total)

const: 13.0ms (6.5% of total)

ival-sub: 5.0ms (2.5% of total)

ival-div: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory

-7.9MiB live, 45.3MiB allocated

Counts

25 → 128

Calls

Call 1

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

Outputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos 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)))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 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)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* -1/6 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
(* eps (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos x)
(- (* (cos eps) (sin x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* eps (sin x))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (pow eps 2) (* (sin x) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* eps (* (sin x) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ eps (/ (pow eps 2) x)))
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* eps (+ eps x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/720 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* -1/720 (* (pow eps 5) (sin x)))
(* (pow eps 5) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 5) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* (pow eps 2) (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (* 1/720 (sin x)))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (+ (* 1/720 (sin x)) (* 1/2 (/ (sin x) (pow eps 4)))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (* (cos eps) (sin x)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) eps) (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) (* eps (+ x eps)) (cos (/ (+ (* 2 x) eps) -2)) (* eps eps))
5.0ms	x	@	inf	((+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (* (cos eps) (sin x)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) eps) (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) (* eps (+ x eps)) (cos (/ (+ (* 2 x) eps) -2)) (* eps eps))
4.0ms	x	@	-inf	((+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (* (cos eps) (sin x)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) eps) (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) (* eps (+ x eps)) (cos (/ (+ (* 2 x) eps) -2)) (* eps eps))
3.0ms	eps	@	inf	((+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (* (cos eps) (sin x)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) eps) (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) (* eps (+ x eps)) (cos (/ (+ (* 2 x) eps) -2)) (* eps eps))
3.0ms	x	@	0	((+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (cos x) (- (* (cos eps) (sin x)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ x eps))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) eps) (* (* (sin x) (+ (* (+ (* -1/720 (* eps eps)) 1/24) (* eps eps)) -1/2)) eps) (* eps (+ x eps)) (cos (/ (+ (* 2 x) eps) -2)) (* eps eps))

simplify164.0ms (1.4%)

Memory

32.0MiB live, 166.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	494	2036
1	1844	1986
2	6944	1962
0	8270	1807

Stop Event

1×	iter limit
1×	node limit

Counts

128 → 127

Calls

Call 1

Inputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos 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)))
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 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)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* -1/6 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
(* eps (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos x)
(- (* (cos eps) (sin x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* eps (sin x))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* (pow eps 2) (* (sin x) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* eps (* (sin x) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* x (+ eps (/ (pow eps 2) x)))
(cos (* -1/2 (+ eps (* 2 x))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* eps (+ eps x))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* -1/720 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* -1/720 (* (pow eps 5) (sin x)))
(* (pow eps 5) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(* (pow eps 5) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(* (pow eps 2) (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (* 1/720 (sin x)))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (+ (* 1/720 (sin x)) (* 1/2 (/ (sin x) (pow eps 4)))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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1
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(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
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(* x (- (cos eps) 1))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))
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(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))
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eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
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(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
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(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
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(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
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(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x eps) x) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
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(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
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(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
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(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) x))
(* x (+ (* -1/6 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
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(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
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(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* (pow eps 2) (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
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(* eps (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 x eps))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) eps (.f64 (.f64 (.f64 (.f64 x eps) x) #s(literal -1/6 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)))) x)
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 #s(literal -1/6 binary64) eps) (.f64 (.f64 (.f64 (.f64 x eps) x) #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)))) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 x eps)))
(* x (+ (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) (* 1/120 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64))) eps (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/120 binary64) eps) (.f64 (.f64 (.f64 (.f64 x eps) x) #s(literal -1/5040 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)))) (.f64 x x))) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 x eps)))
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow eps 2))
(*.f64 (+.f64 x eps) eps)
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
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(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(cos x)
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(- (sin (+ eps x)) (sin x))
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(* -1/2 (pow x 2))
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(cos (* -1/2 (+ eps (* 2 x))))
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(- (sin (- eps (* -1 x))) (sin x))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64))))) (.f64 eps eps))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) eps)
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))) eps)
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
(* eps (+ eps x))
(*.f64 (+.f64 x eps) eps)
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1/2 (* eps x))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(* -1/2 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x)
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1/720 (* (pow eps 6) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/720 binary64)) (sin.f64 x))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/720 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 (sin.f64 x) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/720 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 6 binary64)))
(* -1/720 (* (pow eps 5) (sin x)))
(.f64 (.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/720 binary64)) (sin.f64 x))
(* (pow eps 5) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/720 binary64) (sin.f64 x))))
(* (pow eps 5) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 (sin.f64 x) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (sin.f64 x) eps) (.f64 #s(literal -1/720 binary64) (sin.f64 x)))))
(* (pow eps 2) (+ 1 (/ x eps)))
(.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)) (neg.f64 eps))) eps) eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (* 1/720 (sin x)))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 5 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 #s(literal -1/24 binary64) eps) (.f64 #s(literal 1/720 binary64) (sin.f64 x))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin x) (pow eps 2))) (+ (* 1/720 (sin x)) (* 1/2 (/ (sin x) (pow eps 4)))))))
(.f64 (neg.f64 (pow.f64 eps #s(literal 5 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 #s(literal -1/24 binary64) eps) (fma.f64 #s(literal 1/720 binary64) (sin.f64 x) (.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64)))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite250.0ms (2.1%)

Memory

-35.9MiB live, 177.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	398
0	100	392
1	368	392
2	3173	392
0	9179	383

Stop Event

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

Counts

25 → 479

Calls

Call 1

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

Outputs
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (fma.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (-.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (.f64 (cos.f64 x) (sin.f64 eps))) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (.f64 (fma.f64 #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (-.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (.f64 (cos.f64 x) (sin.f64 eps))) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (pow.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) #s(literal 3 binary64)))) (.f64 (fma.f64 #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (-.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (.f64 (cos.f64 x) (sin.f64 eps))) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (fma.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (-.f64 #s(approx (- ( (cos eps) (sin x)) (sin x)) (.f64 (.f64 (sin.f64 x) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps))) (.f64 (cos.f64 x) (sin.f64 eps))) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)))))
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(fabs.f64 (*.f64 eps eps))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))

eval183.0ms (1.5%)

Memory: 24.6MiB live, 122.5MiB allocated
Compiler: Compiled 29 878 to 3 619 computations (87.9% saved)

prune35.0ms (0.3%)

Memory

3.4MiB live, 46.9MiB allocated

Pruning

19 alts after pruning (11 fresh and 8 done)

	Pruned	Kept	Total
New	716	4	720
Fresh	1	7	8
Picked	2	3	5
Done	0	5	5
Total	719	19	738

Accuracy

100.0%

Counts

738 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
	99.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (PI.f64)) #s(literal 2 binary64))))
	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
✓	5.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))

Compiler

Compiled 1 229 to 557 computations (54.7% saved)

regimes52.0ms (0.4%)

Memory

-12.2MiB live, 31.9MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))

Outputs

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

Calls

3 calls:

36.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))

Outputs

(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.3%)

Memory

-48.4MiB live, 11.9MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) (PI.f64)) #s(literal 2 binary64))))

Outputs

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

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

18.9MiB live, 19.0MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
99.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

-28.6MiB live, 16.4MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

Calls

3 calls:

4.0ms	eps
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
99.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

4.0ms	eps
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
99.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.1%	1	`x`
99.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

-26.4MiB live, 17.9MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (+.f64 x eps) (.f64 (.f64 #s(literal -1/2 binary64) x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 #s(literal 1/24 binary64) x)) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))

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

Calls

3 calls:

15.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.0%	1	`eps`
99.0%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))

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

Calls

3 calls:

2.0ms	eps
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

8.9MiB live, 8.9MiB allocated

Accuracy

Total -59.8b remaining (-5812%)

Threshold costs -59.8b (-5812%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

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

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

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

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify72.0ms (0.6%)

Memory

-6.0MiB live, 40.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	256
1	147	256
2	256	256
3	656	256
4	1738	256
5	2737	256
6	3652	256
7	5175	256
8	7123	256

Stop Event

1×	node limit

Calls

Call 1

Inputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

Outputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))) eps) eps)))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 x eps)) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

derivations1.1s (9.3%)

Memory

21.3MiB live, 739.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	144
0	54	136
1	202	130
2	1704	130
0	8155	130
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267
0	395	1371
1	1480	1304
2	5477	1275
0	8393	1159
0	494	2036
1	1844	1986
2	6944	1962
0	8270	1807
0	55	360
0	92	345
1	347	337
2	2585	337
0	8279	330
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Compiler

Compiled 262 to 109 computations (58.4% saved)

preprocess139.0ms (1.2%)

Memory: -2.7MiB live, 208.4MiB allocated
Compiler: Compiled 568 to 256 computations (54.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze95.0ms (0.8%)

sample7.0s (58%)

explain129.0ms (1.1%)

preprocess43.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize32.0ms (0.3%)

series10.0ms (0.1%)

simplify209.0ms (1.7%)

rewrite202.0ms (1.7%)

eval23.0ms (0.2%)

prune5.0ms (0%)

simplify161.0ms (1.3%)

localize201.0ms (1.7%)

series53.0ms (0.4%)

simplify143.0ms (1.2%)

rewrite138.0ms (1.1%)

eval111.0ms (0.9%)

prune19.0ms (0.2%)

simplify124.0ms (1%)

localize273.0ms (2.3%)

series33.0ms (0.3%)

simplify147.0ms (1.2%)

rewrite200.0ms (1.7%)

eval49.0ms (0.4%)

prune48.0ms (0.4%)

simplify104.0ms (0.9%)

localize289.0ms (2.4%)

series29.0ms (0.2%)

simplify164.0ms (1.4%)

rewrite250.0ms (2.1%)

eval183.0ms (1.5%)

prune35.0ms (0.3%)

regimes52.0ms (0.4%)

regimes21.0ms (0.2%)

regimes20.0ms (0.2%)

regimes39.0ms (0.3%)

regimes15.0ms (0.1%)

regimes15.0ms (0.1%)

regimes25.0ms (0.2%)

regimes12.0ms (0.1%)

regimes22.0ms (0.2%)

regimes5.0ms (0%)

regimes5.0ms (0%)

simplify72.0ms (0.6%)

derivations1.1s (9.3%)

preprocess139.0ms (1.2%)

end0.0ms (0%)

Profiling