Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze50.0ms (0.4%)

Memory

10.9MiB live, 55.3MiB allocated; 19ms collecting garbage

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)

sample7.2s (59.6%)

Memory

-221.5MiB live, 7 849.7MiB allocated; 2.6s collecting garbage

Samples

4.1s	26 528×	0	invalid
1.0s	5 086×	1	valid
457.0ms	3 170×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.7s

const: 889.0ms (23.8% of total)

ival-sin: 765.0ms (20.5% of total)

ival-fabs: 346.0ms (9.3% of total)

ival-add: 310.0ms (8.3% of total)

ival-<: 294.0ms (7.9% of total)

ival-mult: 263.0ms (7% of total)

ival-<=: 260.0ms (7% of total)

ival-sub: 234.0ms (6.3% of total)

adjust: 214.0ms (5.7% of total)

ival-and: 107.0ms (2.9% of total)

exact: 43.0ms (1.2% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

explain144.0ms (1.2%)

Memory

1.7MiB live, 104.0MiB allocated; 17ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
234	1	(-3.692215190050818e-132 4.881890957351281e-135)	3	(-2.241789272906105e-113 2.3450670030255927e-115)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	1	(-94.74254507487623 6.216247652961803e-11)	`(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	232	4

Confusion

	Predicted +	Predicted -
+	231	3
-	1	21

Precision

0.9956896551724138

Recall

0.9871794871794872

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	231	2	1
-	1	2	19

Precision?

0.9872881355932204

Recall?

0.9957264957264957

Freqs

test

number	freq
0	24
1	232

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

91.0ms	340×	1	valid
8.0ms	170×	0	valid
1.0ms	2×	2	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-add: 35.0ms (57.3% of total)

adjust: 11.0ms (18% of total)

ival-sin: 11.0ms (18% of total)

ival-sub: 4.0ms (6.5% of total)

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

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

preprocess74.0ms (0.6%)

Memory

-1.5MiB live, 42.9MiB allocated; 6ms collecting garbage

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; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

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)

localize38.0ms (0.3%)

Memory

-33.1MiB live, 55.5MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.05332442066866769	(sin.f64 (+.f64 x eps))
accuracy	25.065542306916374	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

22.0ms	170×	1	valid
7.0ms	85×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

adjust: 5.0ms (33.7% of total)

ival-sin: 5.0ms (33.7% of total)

ival-add: 2.0ms (13.5% of total)

ival-sub: 2.0ms (13.5% of total)

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

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

series4.0ms (0%)

Memory

8.3MiB live, 8.4MiB allocated; 0ms collecting garbage

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
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	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
0.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))

simplify157.0ms (1.3%)

Memory

-15.5MiB live, 181.7MiB allocated; 23ms collecting garbage

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)))

rewrite222.0ms (1.8%)

Memory

39.7MiB live, 185.5MiB allocated; 13ms collecting garbage

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)

eval25.0ms (0.2%)

Memory: -13.9MiB live, 31.9MiB allocated; 2ms collecting garbage
Compiler: Compiled 5 510 to 734 computations (86.7% saved)

prune6.0ms (0%)

Memory

12.2MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	7	178

Accuracy

100.0%

Counts

178 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.2%	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
	100.0%	(.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))))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin 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))
▶	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))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 201 to 150 computations (25.4% saved)

simplify98.0ms (0.8%)

Memory

-8.3MiB live, 44.2MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	232
0	53	232
1	85	232
2	165	232
3	386	232
4	898	232
5	1843	232
6	3296	232
7	5480	232
0	8123	232

Stop Event

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

Calls

Call 1

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

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

localize136.0ms (1.1%)

Memory

11.7MiB live, 103.3MiB allocated; 5ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))
accuracy	0.04551192066866769	(sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))))
accuracy	0.2421875	(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
accuracy	25.033286885655855	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
accuracy	0.00390625	(*.f64 (sin.f64 x) eps)
accuracy	0.0078125	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.01171875	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy	0.13826762924542052	#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	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.3474628598739669	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	0.9733491425521613	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0078125	(.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)
accuracy	0.01171875	(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(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))

Samples

74.0ms	169×	1	valid
24.0ms	3×	5	exit
17.0ms	84×	0	valid

Compiler

Compiled 175 to 29 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

adjust: 25.0ms (27.7% of total)

ival-add: 23.0ms (25.5% of total)

ival-mult: 20.0ms (22.2% of total)

ival-sin: 7.0ms (7.8% of total)

const: 4.0ms (4.4% of total)

ival-sub: 3.0ms (3.3% of total)

ival-cos: 3.0ms (3.3% of total)

ival-div: 2.0ms (2.2% of total)

ival-neg: 2.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series32.0ms (0.3%)

Memory

-17.6MiB live, 28.2MiB allocated; 4ms collecting garbage

Counts

18 → 87

Calls

Call 1

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

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)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 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))))))
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)))))))
(+ (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 x)
(* -1 (/ eps x))
(/ (+ (* -1 eps) (* -1 x)) x)
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
-1
(- (* -1 (/ eps x)) 1)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1/2 (sin x))
(* 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))))
(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))))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (- (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 (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (/ (neg eps) x) 1))
5.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (- (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 (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (/ (neg eps) x) 1))
3.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (- (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 (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (/ (neg eps) x) 1))
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (- (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 (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (/ (neg eps) x) 1))
3.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (- (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 (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (* (neg x) (- (/ (neg eps) x) 1)) (- (/ (neg eps) x) 1))

simplify190.0ms (1.6%)

Memory

26.9MiB live, 119.7MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	268	1033
1	1003	1004
2	3700	985
0	8172	890

Stop Event

1×	iter limit
1×	node limit

Counts

87 → 85

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)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 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))))))
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)))))))
(+ (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 x)
(* -1 (/ eps x))
(/ (+ (* -1 eps) (* -1 x)) x)
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
-1
(- (* -1 (/ eps x)) 1)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1/2 (sin x))
(* 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))))
(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))))))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (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))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+.f64 eps (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (.f64 eps (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) x)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/2 x) (* -1/6 eps))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) #s(literal 1/12 binary64)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.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 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps 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 #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 (.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64)) x eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 eps eps) x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64))) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 eps x) #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 (.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))
(* eps x)
(*.f64 eps x)
(* 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 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.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 #s(literal -1/5040 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (.f64 eps x))
(+ (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 x)
(+.f64 eps x)
(* -1 (/ eps x))
(/.f64 (neg.f64 eps) x)
(/ (+ (* -1 eps) (* -1 x)) x)
(-.f64 #s(literal -1 binary64) (/.f64 eps x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* 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 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (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 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
x
(* x (+ 1 (/ eps x)))
(fma.f64 (/.f64 eps x) x x)
-1
#s(literal -1 binary64)
(- (* -1 (/ eps x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 eps 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 #s(literal -1 binary64) (/.f64 eps x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps)
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* 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)
(sin x)
(sin.f64 x)
(+ (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 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (.f64 eps eps))
(* -1/6 (* eps (cos x)))
(.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 (sin.f64 x) eps) #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 (sin.f64 x) eps) #s(literal -1/2 binary64))
(* 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)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1 (* eps (+ (/ 1 eps) (/ 1 x))))
(-.f64 #s(literal -1 binary64) (/.f64 eps x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (.f64 eps eps))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)
(* -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)
(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)))

rewrite280.0ms (2.3%)

Memory

-26.9MiB live, 123.7MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	193
0	53	193
1	189	193
2	1361	193
0	8882	193

Stop Event

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

Counts

18 → 244

Calls

Call 1

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

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

eval70.0ms (0.6%)

Memory: 15.3MiB live, 60.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 16 728 to 1 740 computations (89.6% saved)

prune35.0ms (0.3%)

Memory

-13.7MiB live, 32.8MiB allocated; 2ms collecting garbage

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	366	14	380
Fresh	0	1	1
Picked	2	3	5
Done	0	1	1
Total	368	19	387

Accuracy

100.0%

Counts

387 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	100.0%	(.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))))
	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin 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))
	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #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))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
▶	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))

Compiler

Compiled 855 to 590 computations (31% saved)

simplify160.0ms (1.3%)

Memory

-25.7MiB live, 74.9MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
cost-diff	1	(-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
cost-diff	0	(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #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 #s(literal -1/2 binary64) x) eps #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	(*.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	58	443
0	90	433
1	188	433
2	600	433
3	2546	430
4	6220	430
0	8159	416

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)) (*.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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)
(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
eps
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
x
#s(literal -1/2 binary64)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(*.f64 x x)
x
(-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64))
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

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)) (*.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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps) eps))
(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)
(fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps) eps)
(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps)
eps
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
x
#s(literal -1/2 binary64)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))
(*.f64 x x)
x
(-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64))
(.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps))
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 eps x)
(+.f64 x eps)
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize203.0ms (1.7%)

Memory

12.2MiB live, 245.2MiB allocated; 24ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
accuracy	0.109375	(*.f64 eps (+.f64 eps x))
accuracy	0.18359375	(.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64))
accuracy	0.6723595454475391	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
accuracy	0.0078125	(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
accuracy	0.3046875	(*.f64 #s(literal 1/24 binary64) x)
accuracy	0.3474628598739669	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
accuracy	0.442716578589028	#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.0078125	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps)
accuracy	0.13826762924542052	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
accuracy	0.9858178371593135	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
accuracy	0.01171875	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	0.3474628598739669	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	0.9881063507584185	#s(approx (cos x) #s(literal 1 binary64))
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	0.0078125	(.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	0.02204631324130752	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

129.0ms	169×	1	valid
30.0ms	86×	0	valid
2.0ms	1×	5	exit

Compiler

Compiled 295 to 58 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 122.0ms

ival-mult: 39.0ms (32% of total)

adjust: 36.0ms (29.5% of total)

ival-add: 18.0ms (14.8% of total)

const: 9.0ms (7.4% of total)

ival-sin: 7.0ms (5.7% of total)

ival-cos: 5.0ms (4.1% of total)

ival-div: 3.0ms (2.5% of total)

ival-sub: 3.0ms (2.5% of total)

exact: 1.0ms (0.8% of total)

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

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

series36.0ms (0.3%)

Memory

18.7MiB live, 64.1MiB allocated; 4ms collecting garbage

Counts

25 → 127

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)) (*.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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)
(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
(-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 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 #s(literal -1/2 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64))
(*.f64 eps (+.f64 eps x))

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)))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(- (* 1/12 (pow eps 2)) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(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))))))
(* -1/2 x)
(* 1/24 x)
(* 1/12 (pow eps 2))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(* -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))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ 1 x)))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* 1/12 (* eps x))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(* eps x)
(* x (+ eps (/ (pow eps 2) 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))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow 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)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (- (* 1/24 (pow x 2)) 1/2))
-1/2
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(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))))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x 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)))))
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	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)) (* (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)) (+ (* (* -1/2 x) eps) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* 1/24 x) x) -1/2)) (* x x)) eps) (* eps (+ (* (* 1/24 x) x) -1/2)) (- (* (* eps (+ eps x)) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (* 1/24 x) (* (* eps (+ eps x)) 1/12) (* eps (+ eps x)))
7.0ms	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)) (* (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)) (+ (* (* -1/2 x) eps) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* 1/24 x) x) -1/2)) (* x x)) eps) (* eps (+ (* (* 1/24 x) x) -1/2)) (- (* (* eps (+ eps x)) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (* 1/24 x) (* (* eps (+ eps x)) 1/12) (* eps (+ eps x)))
5.0ms	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)) (* (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)) (+ (* (* -1/2 x) eps) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* 1/24 x) x) -1/2)) (* x x)) eps) (* eps (+ (* (* 1/24 x) x) -1/2)) (- (* (* eps (+ eps x)) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (* 1/24 x) (* (* eps (+ eps x)) 1/12) (* eps (+ eps x)))
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)) (* (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)) (+ (* (* -1/2 x) eps) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* 1/24 x) x) -1/2)) (* x x)) eps) (* eps (+ (* (* 1/24 x) x) -1/2)) (- (* (* eps (+ eps x)) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (* 1/24 x) (* (* eps (+ eps x)) 1/12) (* eps (+ eps x)))
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)) (* (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)) (+ (* (* -1/2 x) eps) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* 1/24 x) x) -1/2)) (* x x)) eps) (* eps (+ (* (* 1/24 x) x) -1/2)) (- (* (* eps (+ eps x)) 1/12) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (* 1/24 x) (* (* eps (+ eps x)) 1/12) (* eps (+ eps x)))

simplify154.0ms (1.3%)

Memory

-8.9MiB live, 178.6MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	420	1570
1	1555	1512
2	5494	1502
0	8370	1378

Stop Event

1×	iter limit
1×	node limit

Counts

127 → 126

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)))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(- (* 1/12 (pow eps 2)) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(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))))))
(* -1/2 x)
(* 1/24 x)
(* 1/12 (pow eps 2))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(* -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))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ 1 x)))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* 1/12 (* eps x))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(* eps x)
(* x (+ eps (/ (pow eps 2) 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))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow 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)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (- (* 1/24 (pow x 2)) 1/2))
-1/2
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(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))))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(* eps (+ eps x))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(sin (* 1/2 eps))
(* (pow eps 2) (+ 1 (/ x 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)))))
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos 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 (cos.f64 eps) #s(literal -1/6 binary64) #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 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) 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 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64)) #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 (.f64 #s(literal -1/2 binary64) eps) (+.f64 x 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 #s(literal -1/2 binary64) eps) (+.f64 x eps) (.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))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))
(- (* 1/12 (pow eps 2)) 1/2)
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(-.f64 (.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) eps) #s(literal 1/2 binary64))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 #s(literal 1/12 binary64) (.f64 (.f64 eps eps) x))) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) eps (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) eps) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(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)))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* 1/12 (pow eps 2))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))
(.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow eps 2))
(*.f64 (+.f64 x eps) eps)
(* -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))
(* -1/2 (* eps x))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(* x (+ (* -1/2 eps) (/ 1 x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* 1/24 (* eps (pow x 4)))
(.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(* 1/24 (* eps (pow x 2)))
(.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps)) x) x)
(* 1/12 (* eps x))
(.f64 #s(literal 1/12 binary64) (.f64 x eps))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))
(.f64 (.f64 #s(literal 1/12 binary64) x) (fma.f64 eps (/.f64 eps x) eps))
(* eps x)
(*.f64 x eps)
(* x (+ eps (/ (pow eps 2) x)))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) 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))
(* -1 (* x (- (* 1/2 eps) (/ 1 x))))
(.f64 (neg.f64 x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(*.f64 (fma.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))
(.f64 (.f64 #s(literal 1/12 binary64) x) (fma.f64 eps (/.f64 eps x) eps))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) 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 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.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) (sin.f64 x)) eps (.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)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.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 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (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)
(* eps (- (* 1/24 (pow x 2)) 1/2))
(.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) eps)
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x eps)) #s(literal 1/2 binary64))
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(-.f64 (.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) eps) #s(literal 1/2 binary64))
(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))
(* eps (+ (* 1/12 eps) (* 1/12 x)))
(.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) eps)
(* eps (+ eps x))
(*.f64 (+.f64 x 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 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal -1/2 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)) (/ (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)
(* eps (+ (* -1/2 x) (/ 1 eps)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps) eps)
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) eps) (*.f64 (cos.f64 x) eps))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (.f64 eps eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* (pow eps 2) (+ 1 (/ x eps)))
(.f64 (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) 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)))
(- (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)
(* -1 (* eps (- (* 1/2 x) (/ 1 eps))))
(.f64 (neg.f64 eps) (-.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 (neg.f64 x) x) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))) (neg.f64 eps))) eps) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite180.0ms (1.5%)

Memory

16.7MiB live, 209.6MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	357
0	90	349
1	379	349
2	3461	349
0	8174	340

Stop Event

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

Counts

25 → 286

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)) (*.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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps))
(fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)
(.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
(-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 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 #s(literal -1/2 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64))
(*.f64 eps (+.f64 eps x))

Outputs
(pow.f64 eps #s(literal 1 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 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (/.f64 (*.f64 eps eps) (neg.f64 eps)))
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
(/.f64 (-.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64)))
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64)))
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
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(+.f64 (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) eps))
(+.f64 (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) eps) (.f64 #s(literal 0 binary64) #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))))))
(+.f64 (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) eps) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))) #s(literal 0 binary64)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps)) #s(literal 1/2 binary64)) x) x (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))))
(fma.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.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 (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)))))
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #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 #s(literal -2 binary64)) (/.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 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 x eps))
(.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps)
(.f64 #s(literal 1/12 binary64) (.f64 (+.f64 x eps) eps))
(.f64 (.f64 (+.f64 x eps) eps) #s(literal 1/12 binary64))
(.f64 (+.f64 x eps) (.f64 eps #s(literal 1/12 binary64)))
(.f64 eps (.f64 #s(literal 1/12 binary64) (+.f64 x eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (*.f64 #s(literal 1/12 binary64) (+.f64 x eps))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 1/12 binary64) (+.f64 x eps))) (*.f64 eps eps))
(fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (.f64 (*.f64 x eps) #s(literal 1/12 binary64)))
(fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x eps)))
(+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(+.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
(*.f64 (+.f64 x eps) eps)
(*.f64 eps (+.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) eps) (-.f64 eps x))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) eps) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (+.f64 x eps)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 x eps)) (.f64 eps eps))
(/.f64 (.f64 (+.f64 x eps) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (+.f64 x eps) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (.f64 eps (.f64 (+.f64 x eps) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 eps (.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 eps (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 eps (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 x eps) #s(literal 2 binary64))) (.f64 eps (-.f64 eps x)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 x eps) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (*.f64 x eps)))))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 eps x) (neg.f64 eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (-.f64 eps x) (.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (.f64 eps eps))) (.f64 (-.f64 x eps) (neg.f64 eps)))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (neg.f64 eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (neg.f64 eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 eps eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 eps x))) (.f64 (neg.f64 eps) (-.f64 eps x)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 (neg.f64 eps) (-.f64 x eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (neg.f64 eps) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (neg.f64 eps) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (+.f64 x eps) (-.f64 eps x))) (.f64 (.f64 eps eps) (-.f64 eps x)))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 (.f64 eps eps) (-.f64 x eps)))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(fma.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)) (*.f64 x eps))
(fma.f64 (fabs.f64 (fabs.f64 eps)) (fabs.f64 (fabs.f64 eps)) (*.f64 x eps))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (*.f64 x eps))
(fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x eps))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 x eps))
(fma.f64 (+.f64 x eps) eps (*.f64 #s(literal 0 binary64) (+.f64 x eps)))
(fma.f64 (+.f64 x eps) eps (*.f64 (+.f64 x eps) #s(literal 0 binary64)))
(fma.f64 (+.f64 x eps) #s(literal 0 binary64) (*.f64 (+.f64 x eps) eps))
(fma.f64 x eps (*.f64 eps eps))
(fma.f64 eps (-.f64 eps #s(literal 0 binary64)) (*.f64 x eps))
(fma.f64 eps (+.f64 x eps) (*.f64 #s(literal 0 binary64) (+.f64 x eps)))
(fma.f64 eps (+.f64 x eps) (*.f64 (+.f64 x eps) #s(literal 0 binary64)))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x eps))
(fma.f64 #s(literal 0 binary64) (+.f64 x eps) (*.f64 (+.f64 x eps) eps))
(-.f64 (.f64 eps eps) (.f64 (neg.f64 eps) x))
(-.f64 (.f64 eps eps) (.f64 (neg.f64 x) eps))
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 x eps)) (.f64 (+.f64 x eps) eps))
(+.f64 (.f64 (+.f64 x eps) #s(literal 0 binary64)) (.f64 (+.f64 x eps) eps))
(+.f64 (.f64 x eps) (.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 x eps))
(+.f64 (.f64 (+.f64 x eps) eps) (.f64 #s(literal 0 binary64) (+.f64 x eps)))
(+.f64 (.f64 (+.f64 x eps) eps) (.f64 (+.f64 x eps) #s(literal 0 binary64)))

eval64.0ms (0.5%)

Memory: 17.1MiB live, 116.4MiB allocated; 8ms collecting garbage
Compiler: Compiled 15 376 to 2 052 computations (86.7% saved)

prune49.0ms (0.4%)

Memory

-9.5MiB live, 35.8MiB allocated; 4ms collecting garbage

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	391	7	398
Fresh	4	6	10
Picked	2	3	5
Done	1	3	4
Total	398	19	417

Accuracy

100.0%

Counts

417 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.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) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	100.0%	(.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))))
▶	99.8%	(.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))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin 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))
✓	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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
	98.8%	#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))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #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))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
▶	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))

Compiler

Compiled 868 to 610 computations (29.7% saved)

simplify142.0ms (1.2%)

Memory

-7.9MiB live, 168.3MiB allocated; 53ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
cost-diff	0	(.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))))
cost-diff	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	1	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	0	(fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
cost-diff	0	(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
cost-diff	0	(.f64 (.f64 x x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
cost-diff	0	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff	0	(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
cost-diff	0	(.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)))
cost-diff	0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	526
0	91	516
1	188	516
2	563	516
3	2096	513
4	5052	511
5	7724	511
0	8031	494

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
(.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)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
eps
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(*.f64 x x)
x
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
(.f64 #s(literal 1/12 binary64) (.f64 x eps))
#s(literal 1/12 binary64)
(*.f64 x eps)
eps
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.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 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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 (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
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
(.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)))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps eps))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps eps)
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(*.f64 x x)
x
#s(literal -1/2 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))
eps
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64))) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64))) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 #s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64))) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64))) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(*.f64 x x)
x
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(.f64 #s(literal 1/12 binary64) (.f64 x eps))
(.f64 (.f64 x eps) #s(literal 1/12 binary64))
#s(literal 1/12 binary64)
(*.f64 x eps)
eps
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.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 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)

localize296.0ms (2.4%)

Memory

-6.8MiB live, 394.5MiB allocated; 125ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.0078125	(.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))))
accuracy	0.02204631324130752	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.12336527302836162	#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
accuracy	0.19921875	(.f64 #s(literal 1/12 binary64) (.f64 x eps))
accuracy	0.6723595454475391	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
accuracy	61.60407714230292	#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
accuracy	0.0078125	(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
accuracy	0.9858178371315651	#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal -1/2 binary64))
accuracy	0.3474628598739669	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
accuracy	0.6632264004209038	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
accuracy	0.0078125	(.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)))
accuracy	0.02204631324130752	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

189.0ms	169×	1	valid
47.0ms	86×	0	valid
2.0ms	1×	5	exit

Compiler

Compiled 332 to 56 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-mult: 36.0ms (27.6% of total)

adjust: 29.0ms (22.2% of total)

const: 24.0ms (18.4% of total)

ival-add: 19.0ms (14.6% of total)

ival-sin: 8.0ms (6.1% of total)

ival-cos: 6.0ms (4.6% of total)

ival-div: 3.0ms (2.3% of total)

ival-sub: 3.0ms (2.3% of total)

exact: 1.0ms (0.8% of total)

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

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

series34.0ms (0.3%)

Memory

19.4MiB live, 65.0MiB allocated; 7ms collecting garbage

Counts

26 → 145

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
(.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)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(.f64 (.f64 x x) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 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))
(.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 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
(.f64 #s(literal 1/12 binary64) (.f64 x eps))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)

Outputs
(* 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* 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))))))
(* -1/2 (pow x 2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* -1/2 x)
(- (* 1/12 (pow eps 2)) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(* 1/12 (* eps x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (+ (* -1/6 (/ (pow eps 2) x)) (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -1 x)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* 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 (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (pow x 3))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (+ (* 1/12 (pow x 3)) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(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))))))
(* 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
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* 1/12 (/ (pow x 3) eps)) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (/ (pow x 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/12 (pow x 3)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (+ (* -1/12 (pow x 3)) (* 1/2 x))) eps)) (* 1/12 (pow x 2))) 1/6))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) -1/2) eps) eps) (* (* x x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (* 1/2 eps)) (* -1/2 x) (- (* (* eps (+ eps x)) 1/12) 1/2) (* 1/12 (* x eps)) (sin (/ (+ 0 eps) 2)) (* 1/2 eps))
5.0ms	eps	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) -1/2) eps) eps) (* (* x x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (* 1/2 eps)) (* -1/2 x) (- (* (* eps (+ eps x)) 1/12) 1/2) (* 1/12 (* x eps)) (sin (/ (+ 0 eps) 2)) (* 1/2 eps))
5.0ms	x	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) -1/2) eps) eps) (* (* x x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (* 1/2 eps)) (* -1/2 x) (- (* (* eps (+ eps x)) 1/12) 1/2) (* 1/12 (* x eps)) (sin (/ (+ 0 eps) 2)) (* 1/2 eps))
5.0ms	eps	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) -1/2) eps) eps) (* (* x x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (* 1/2 eps)) (* -1/2 x) (- (* (* eps (+ eps x)) 1/12) 1/2) (* 1/12 (* x eps)) (sin (/ (+ 0 eps) 2)) (* 1/2 eps))
4.0ms	eps	@	0	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) -1/2) eps) eps) (* (* x x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (* 1/2 eps)) (* -1/2 x) (- (* (* eps (+ eps x)) 1/12) 1/2) (* 1/12 (* x eps)) (sin (/ (+ 0 eps) 2)) (* 1/2 eps))

simplify182.0ms (1.5%)

Memory

14.9MiB live, 153.5MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	562	2170
1	2050	2076
2	7580	2061
0	8638	1878

Stop Event

1×	iter limit
1×	node limit

Counts

145 → 144

Calls

Call 1

Inputs
(* 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))))))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (cos (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* 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))))))
(* -1/2 (pow x 2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(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))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* -1/2 x)
(- (* 1/12 (pow eps 2)) 1/2)
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)
(* 1/12 (* eps x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (+ (* -1/6 (/ (pow eps 2) x)) (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -1 x)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))
(* 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 (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (pow x 3))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (+ (* 1/12 (pow x 3)) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(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))))))
(* 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
(- (* 1/12 (* eps x)) 1/2)
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* 1/12 (/ (pow x 3) eps)) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (/ (pow x 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(* 1/12 (pow eps 2))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/12 (pow x 3)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (+ (* -1/12 (pow x 3)) (* 1/2 x))) eps)) (* 1/12 (pow x 2))) 1/6))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.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 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x) (cos.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 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
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(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))
(+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) eps #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 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (pow x 3))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) x)) eps (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (+ (* 1/12 (pow x 3)) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) x))) eps (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.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 1/48 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* 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
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
(-.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)
(-.f64 (.f64 (.f64 eps (+.f64 x eps)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(* -1/6 (* (pow eps 3) (cos x)))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/6))
(.f64 (.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps) eps)
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (/ 1 (pow eps 2))) 1/6))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) #s(literal 1/6 binary64)) (.f64 eps eps))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps) eps)
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* 1/12 (/ (pow x 3) eps)) (* 1/12 (pow x 2)))) 1/6))
(.f64 (fma.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) eps)) #s(literal 1/12 binary64) (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (/ (pow x 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) eps)) #s(literal 1/12 binary64) (/.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps) eps))) #s(literal 1/6 binary64)) (*.f64 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))
(* 1/12 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))
(.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/12 binary64)) eps) eps)
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))
(* 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)))
(* 2 (* (cos (- x (* -1/2 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)))
(* 2 (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(.f64 (neg.f64 eps) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))) (neg.f64 eps))) eps) eps)
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6))
(.f64 (-.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)) (neg.f64 eps)) #s(literal 1/6 binary64)) (*.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1/12 (pow x 3)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) x (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 eps))) #s(literal 1/6 binary64)) (.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (+ (* -1/12 (pow x 3)) (* 1/2 x))) eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps)))) (neg.f64 eps)) (fma.f64 (.f64 #s(literal -1/12 binary64) x) x #s(literal 1/6 binary64))) (.f64 eps eps))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps)) (.f64 eps eps))

rewrite331.0ms (2.7%)

Memory

-30.0MiB live, 308.0MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	459
0	91	451
1	360	451
2	3122	451
0	9930	439

Stop Event

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

Counts

26 → 343

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
(.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)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)
(.f64 (.f64 x x) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 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))
(.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 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps)))
(.f64 #s(literal 1/12 binary64) (.f64 x eps))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(.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)))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)))))
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(+.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #s(literal 1/2 binary64) eps)))
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(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(approx (- (* (* eps (+ eps x)) 1/12) 1/2) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(.f64 (.f64 #s(literal 1/12 binary64) eps) x)
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(fma.f64 (.f64 #s(literal 1/12 binary64) x) eps (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
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(fma.f64 x (.f64 eps #s(literal 1/12 binary64)) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 eps (.f64 #s(literal 1/12 binary64) x) (.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)))
(fma.f64 eps (.f64 #s(literal 1/12 binary64) x) (.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x) (.f64 (*.f64 x eps) #s(literal 1/12 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x)) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(+.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)) (.f64 (.f64 x eps) #s(literal 1/12 binary64)))
(+.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) (.f64 #s(literal 0 binary64) (.f64 #s(literal 1/12 binary64) x)))
(+.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) (.f64 (.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)))
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/2 binary64)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) eps))

eval124.0ms (1%)

Memory: 20.8MiB live, 112.2MiB allocated; 7ms collecting garbage
Compiler: Compiled 24 701 to 2 561 computations (89.6% saved)

prune27.0ms (0.2%)

Memory

3.8MiB live, 50.1MiB allocated; 1ms collecting garbage

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	515	6	521
Fresh	4	4	8
Picked	3	2	5
Done	0	6	6
Total	522	18	540

Accuracy

100.0%

Counts

540 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin 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))
✓	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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))
	46.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps)))) (neg.f64 eps)) (fma.f64 (.f64 #s(literal -1/12 binary64) x) x #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
	98.8%	#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))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps #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))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
✓	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	100.0%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))

Compiler

Compiled 1 626 to 656 computations (59.7% saved)

regimes67.0ms (0.6%)

Memory

-10.4MiB live, 45.4MiB allocated; 12ms collecting garbage

Counts

34 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps)))) (neg.f64 eps)) (fma.f64 (.f64 #s(literal -1/12 binary64) x) x #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
(-.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))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) 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) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin 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))

Outputs
#s(approx (- (sin (+ x eps)) (sin 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))

Calls

3 calls:

49.0ms	eps
8.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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)

regimes47.0ms (0.4%)

Memory

-15.0MiB live, 28.2MiB allocated; 8ms collecting garbage

Counts

33 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps)))) (neg.f64 eps)) (fma.f64 (.f64 #s(literal -1/12 binary64) x) x #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
(-.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))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.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))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) 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) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))

Outputs

#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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))))

Calls

3 calls:

29.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	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)

regimes20.0ms (0.2%)

Memory

25.1MiB live, 25.1MiB allocated; 0ms collecting garbage

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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 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)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) (neg.f64 eps)))) (neg.f64 eps)) (fma.f64 (.f64 #s(literal -1/12 binary64) x) x #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
(-.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))

Outputs

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

Calls

3 calls:

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

regimes42.0ms (0.3%)

Memory

-19.1MiB live, 26.9MiB allocated; 4ms collecting garbage

Counts

20 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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)) #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))

Outputs
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 #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:

31.0ms	eps
5.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes19.0ms (0.2%)

Memory

-14.2MiB live, 32.7MiB allocated; 2ms collecting garbage

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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 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 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

26.3MiB live, 26.3MiB allocated; 0ms collecting garbage

Counts

17 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) 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))

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)

regimes20.0ms (0.2%)

Memory

-27.9MiB live, 25.5MiB allocated; 3ms collecting garbage

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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #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 (.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

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

Calls

3 calls:

10.0ms	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	`eps`
99.1%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

9 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) 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 (*.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) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x x) #s(approx (- ( (* eps (+ eps x)) 1/12) 1/2) (.f64 #s(literal 1/12 binary64) (.f64 x eps))) #s(approx (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1) #s(literal 1 binary64)))) eps))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Counts

5 → 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)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 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 #s(literal -1/2 binary64) x) eps #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (* x x) (- (* (* eps (+ eps x)) 1/12) 1/2)) (+ (* eps (+ (* -1/6 eps) (* -1/2 x))) 1)) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))) eps))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.8%	1	`eps`
98.8%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 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	x
1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps

Results

Accuracy	Segments	Branch
98.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify68.0ms (0.6%)

Memory

-16.2MiB live, 30.3MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	237
1	117	237
2	215	237
3	539	237
4	1201	237
5	2011	237
6	3029	237
7	5478	237
8	7765	237

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations946.0ms (7.8%)

Memory

62.3MiB live, 611.3MiB allocated; 93ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	420	1570
1	1555	1512
2	5494	1502
0	8370	1378
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267
0	562	2170
1	2050	2076
2	7580	2061
0	8638	1878
0	268	1033
1	1003	1004
2	3700	985
0	8172	890
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×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 243 to 85 computations (65% saved)

preprocess81.0ms (0.7%)

Memory: -32.8MiB live, 101.9MiB allocated; 22ms collecting garbage
Compiler: Compiled 530 to 208 computations (60.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze50.0ms (0.4%)

sample7.2s (59.6%)

explain144.0ms (1.2%)

preprocess74.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize38.0ms (0.3%)

series4.0ms (0%)

simplify157.0ms (1.3%)

rewrite222.0ms (1.8%)

eval25.0ms (0.2%)

prune6.0ms (0%)

simplify98.0ms (0.8%)

localize136.0ms (1.1%)

series32.0ms (0.3%)

simplify190.0ms (1.6%)

rewrite280.0ms (2.3%)

eval70.0ms (0.6%)

prune35.0ms (0.3%)

simplify160.0ms (1.3%)

localize203.0ms (1.7%)

series36.0ms (0.3%)

simplify154.0ms (1.3%)

rewrite180.0ms (1.5%)

eval64.0ms (0.5%)

prune49.0ms (0.4%)

simplify142.0ms (1.2%)

localize296.0ms (2.4%)

series34.0ms (0.3%)

simplify182.0ms (1.5%)

rewrite331.0ms (2.7%)

eval124.0ms (1%)

prune27.0ms (0.2%)

regimes67.0ms (0.6%)

regimes47.0ms (0.4%)

regimes20.0ms (0.2%)

regimes42.0ms (0.3%)

regimes19.0ms (0.2%)

regimes14.0ms (0.1%)

regimes20.0ms (0.2%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

regimes3.0ms (0%)

simplify68.0ms (0.6%)

derivations946.0ms (7.8%)

preprocess81.0ms (0.7%)

end0.0ms (0%)

Profiling