Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze109.0ms (1.5%)

Memory

23.1MiB live, 136.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.0s (27.8%)

Memory

43.5MiB live, 1 683.5MiB allocated

Samples

695.0ms	2 280×	2	valid
479.0ms	4 189×	0	valid
308.0ms	577×	3	valid
140.0ms	1 206×	1	valid
4.0ms	4×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 783.0ms (60.4% of total)

ival-sin: 178.0ms (13.7% of total)

ival-div: 125.0ms (9.6% of total)

adjust: 111.0ms (8.6% of total)

ival-sub: 85.0ms (6.6% of total)

ival-true: 7.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain182.0ms (2.5%)

Memory

-25.1MiB live, 136.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
78	0	-	7	(2.767639969231121e-157)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
77	1	(-2.4439125162464226e-162)	2	(3.0618241236825145e+288)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	76	4
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	71	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	71

Confusion

	Predicted +	Predicted -
+	146	1
-	1	108

Precision

0.9931972789115646

Recall

0.9931972789115646

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	1	0
-	1	3	105

Precision?

0.9735099337748344

Recall?

1.0

Freqs

test

number	freq
0	109
1	147

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

60.0ms	232×	0	valid
55.0ms	176×	2	valid
12.0ms	32×	3	valid
8.0ms	72×	1	valid

Compiler

Compiled 62 to 28 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-cos: 47.0ms (40.5% of total)

ival-sub: 39.0ms (33.6% of total)

ival-sin: 12.0ms (10.3% of total)

adjust: 10.0ms (8.6% of total)

ival-div: 6.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess70.0ms (1%)

Memory

-6.1MiB live, 31.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	181	8
4	448	8
5	683	8
6	708	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	317	4
9	534	4
10	590	4
11	593	4
12	601	4
13	607	4
14	611	4
15	618	4
16	625	4
17	626	4
0	626	4

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify23.0ms (0.3%)

Memory

17.7MiB live, 17.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	6592	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	317	14
9	534	14
10	590	14
11	593	14
12	601	14
13	607	14
14	611	14
15	618	14
16	625	14
17	626	14
0	626	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

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

localize83.0ms (1.2%)

Memory

-20.8MiB live, 62.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	15.71878246837175	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	17.34888569217625	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

37.0ms	116×	0	valid
26.0ms	88×	2	valid
6.0ms	16×	3	valid
4.0ms	36×	1	valid

Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-cos: 26.0ms (41.1% of total)

ival-div: 25.0ms (39.5% of total)

ival-sin: 5.0ms (7.9% of total)

adjust: 4.0ms (6.3% of total)

ival-sub: 3.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

4 → 20

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)

Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
x
(* 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))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)

Calls

3 calls:

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

simplify220.0ms (3%)

Memory

21.8MiB live, 175.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	202
1	224	202
2	555	196
3	1661	196
4	3002	196
5	4256	196
6	4608	196
7	5339	196
8	6812	196
0	8041	172

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
x
(* 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))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
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)) (fma.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 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)

rewrite224.0ms (3.1%)

Memory

-25.6MiB live, 260.6MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	247	12
3	2387	11
0	9106	11

Stop Event

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

Counts

4 → 645

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)

Outputs
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (sin.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x))) #s(literal -1 binary64)))
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(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)))) (-.f64 #s(literal -1 binary64) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (cos.f64 x))) (pow.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 x))) (-.f64 #s(literal -1 binary64) (cos.f64 x)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)))))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 (cos.f64 x) (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x))))))
(neg.f64 (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(cos.f64 x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) (sin.f64 x))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64))) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64)))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (sin.f64 x)))
(sin.f64 x)
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) (sin.f64 x)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 x))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sin.f64 x)))

eval105.0ms (1.5%)

Memory: 38.2MiB live, 111.0MiB allocated
Compiler: Compiled 14 961 to 1 738 computations (88.4% saved)

prune15.0ms (0.2%)

Memory

6.7MiB live, 41.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	658	6	664
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	659	6	665

Accuracy

100.0%

Counts

665 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.6%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
▶	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	56.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 162 to 118 computations (27.2% saved)

simplify66.0ms (0.9%)

Memory

-27.8MiB live, 60.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	204
0	44	192
1	82	192
2	142	192
3	294	192
4	649	192
5	969	192
6	1023	192
7	1101	192
8	1230	192
9	1448	192
10	1504	192
11	1507	192
12	1515	192
13	1521	192
14	1525	192
15	1532	192
16	1707	192
17	1942	192
18	1948	192
0	1948	192

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize201.0ms (2.8%)

Memory

-7.0MiB live, 144.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0546875	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
accuracy	0.27383839434154217	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	28.319675554521595	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.046875	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.05078125	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.2749785930262207	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	28.29821840178657	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.30443174318534627	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	28.24666682055248	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	27.98590381948989	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

84.0ms	88×	2	valid
57.0ms	116×	0	valid
15.0ms	36×	1	valid
13.0ms	16×	3	valid

Compiler

Compiled 380 to 56 computations (85.3% saved)

Precisions

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

ival-cos: 48.0ms (39.4% of total)

ival-mult: 22.0ms (18.1% of total)

adjust: 13.0ms (10.7% of total)

const: 13.0ms (10.7% of total)

ival-add: 10.0ms (8.2% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

16 → 44

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
3.0ms	x	@	inf	((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))
2.0ms	x	@	0	((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

Time

Variable

Point

Expression

4.0ms

-inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

3.0ms

inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

2.0ms

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

simplify137.0ms (1.9%)

Memory

29.1MiB live, 99.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	445
1	319	445
2	843	441
3	2234	439
4	4873	439
0	8278	406

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* 1/240 (pow x 2))
(.f64 #s(literal 1/240 binary64) (.f64 x x))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 17/40320 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/240 binary64) (.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) x) x)
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 2))
(.f64 #s(literal 17/40320 binary64) (.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) x) x) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) x) x) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))

rewrite226.0ms (3.1%)

Memory

-29.6MiB live, 255.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	179
0	44	167
1	177	167
2	1220	167
0	8528	167

Stop Event

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

Counts

16 → 503

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

Outputs
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(.f64 (pow.f64 (.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x))))))
(.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (+.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (-.f64 (.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))) (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (sin.f64 x) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (sin.f64 x) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
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eval91.0ms (1.3%)

Memory: 28.3MiB live, 213.0MiB allocated
Compiler: Compiled 20 344 to 2 427 computations (88.1% saved)

prune42.0ms (0.6%)

Memory

-3.1MiB live, 48.3MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	585	2	587
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	585	8	593

Accuracy

100.0%

Counts

593 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.6%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	56.1%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	56.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 124 to 89 computations (28.2% saved)

simplify415.0ms (5.8%)

Memory

-35.4MiB live, 153.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	155
0	37	127
1	68	127
2	130	127
3	356	127
4	910	127
5	1682	127
6	1865	127
7	1949	127
8	2060	127
9	2224	127
10	2263	127
11	2276	127
12	2298	127
13	2321	127
14	2327	127
15	2337	127
16	2513	127
17	2850	127
18	3200	127
19	4004	127
20	4666	127
21	6076	127
22	6785	127
23	7611	127
24	7655	127
25	7659	127
26	7723	127
27	7733	127
28	7733	127
29	7733	127
0	8456	127

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize168.0ms (2.3%)

Memory

-23.7MiB live, 135.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0.0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
accuracy	27.98590381948989	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
accuracy	0.0546875	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
accuracy	0.1424950342849023	(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
accuracy	0.27383839434154217	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	28.319675554521595	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))

Samples

51.0ms	88×	2	valid
34.0ms	116×	0	valid
13.0ms	36×	1	valid
11.0ms	16×	3	valid

Compiler

Compiled 296 to 52 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-cos: 26.0ms (29.1% of total)

const: 13.0ms (14.5% of total)

ival-mult: 13.0ms (14.5% of total)

ival-div: 12.0ms (13.4% of total)

adjust: 10.0ms (11.2% of total)

ival-add: 5.0ms (5.6% of total)

ival-sin: 5.0ms (5.6% of total)

ival-sub: 3.0ms (3.4% of total)

ival-pow: 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)

series5.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

11 → 38

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 2 binary64) x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))

Outputs
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(/ 2 x)
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
24
(+ 24 (* -12/5 (pow x 2)))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(/ 40320/17 (pow x 4))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ (- 1 (cos x)) (sin x)) (* (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) x) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (pow 1 -1/2) (+ (* 17/40320 (* x x)) 1/240) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))

1.0ms

-inf

((/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ (- 1 (cos x)) (sin x)) (* (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) x) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (pow 1 -1/2) (+ (* 17/40320 (* x x)) 1/240) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))

1.0ms

((/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ (- 1 (cos x)) (sin x)) (* (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) x) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (pow 1 -1/2) (+ (* 17/40320 (* x x)) 1/240) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))

simplify154.0ms (2.1%)

Memory

-2.3MiB live, 107.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	416
1	319	415
2	814	413
3	2118	409
4	4654	409
0	8466	381

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 38

Calls

Call 1

Inputs
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(/ 2 x)
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
24
(+ 24 (* -12/5 (pow x 2)))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(/ 40320/17 (pow x 4))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))

Outputs
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
24
#s(literal 24 binary64)
(+ 24 (* -12/5 (pow x 2)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 43/1750 binary64) (.f64 x x) #s(literal -1/350 binary64)) (.f64 x x) #s(literal -12/5 binary64)) (*.f64 x x) #s(literal 24 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) x) x)
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal -17/40320 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/240 binary64) (.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* 17/40320 (pow x 2))
(.f64 #s(literal 17/40320 binary64) (.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ 40320/17 (pow x 4))
(/.f64 #s(literal 40320/17 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/.f64 (-.f64 #s(literal 40320/17 binary64) (/.f64 #s(literal 6773760/289 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/.f64 (-.f64 (-.f64 #s(literal 40320/17 binary64) (/.f64 #s(literal 13547520/4913 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 6773760/289 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 195734568960/83521 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 40320/17 binary64)) (-.f64 (/.f64 #s(literal 13547520/4913 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -6773760/289 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))

rewrite232.0ms (3.2%)

Memory

22.6MiB live, 226.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	141
0	37	113
1	162	113
2	987	113
0	8749	113

Stop Event

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

Counts

11 → 573

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 2 binary64) x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))

Outputs
(.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x)) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x)) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) (neg.f64 x) #s(literal 1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x)) x)))))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (.f64 (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x)) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))))))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x)) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)))
(pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x) #s(literal 4 binary64)) #s(literal 1/331776 binary64)) (pow.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)))
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(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64) #s(literal 1/24 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64)) (fma.f64 (.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64)) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64) #s(literal 1/24 binary64)))
(+.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))))
(+.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (neg.f64 (.f64 (.f64 (neg.f64 x) x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 (.f64 (neg.f64 x) x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1 binary64)))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1 binary64) (.f64 (.f64 (neg.f64 x) x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x))
(exp.f64 (.f64 (log.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))

eval107.0ms (1.5%)

Memory: -2.5MiB live, 157.9MiB allocated
Compiler: Compiled 19 418 to 2 337 computations (88% saved)

prune39.0ms (0.5%)

Memory

-12.3MiB live, 26.6MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	475	3	478
Fresh	0	0	0
Picked	3	0	3
Done	1	4	5
Total	479	7	486

Accuracy

100.0%

Counts

486 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	56.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	7.6%	#s(literal 1 binary64)

Compiler

Compiled 136 to 95 computations (30.1% saved)

simplify223.0ms (3.1%)

Memory

29.5MiB live, 67.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	320	(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	320	(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	356
0	49	350
1	92	344
2	158	344
3	325	344
4	478	344
5	506	344
6	539	344
7	613	344
8	744	344
9	961	344
10	1017	344
11	1023	344
12	1040	344
13	1049	344
14	1052	344
15	1059	344
16	1174	344
17	1350	344
18	1429	344
19	1633	344
20	1799	344
21	1995	344
22	2745	344
23	3792	344
24	4427	344
25	4662	344
26	4738	344
27	4770	344
28	4792	344
29	5031	344
30	5121	344
31	5122	344
32	5122	344
33	5134	344
0	5134	318

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
#s(literal 1 binary64)
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
#s(literal -12/5 binary64)
(*.f64 x x)
x
#s(literal 24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
#s(literal 1 binary64)
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
(fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))
#s(literal -1/350 binary64)
(*.f64 x x)
x
#s(literal -12/5 binary64)
#s(literal 24 binary64)
#s(literal 1/2 binary64)

Outputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))))))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))))
#s(literal 1 binary64)
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))
#s(literal -12/5 binary64)
(*.f64 x x)
x
#s(literal 24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))))
(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
#s(literal 1 binary64)
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
(fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))
#s(literal -1/350 binary64)
(*.f64 x x)
x
#s(literal -12/5 binary64)
#s(literal 24 binary64)
#s(literal 1/2 binary64)

localize248.0ms (3.4%)

Memory

-15.8MiB live, 175.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.046875	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
accuracy	0.2599117980385215	(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))
accuracy	28.319675554521595	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	28.48877727477674	#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
accuracy	0.046875	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
accuracy	0.09375	(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
accuracy	28.319675554521595	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	28.438323325676237	#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))

Samples

149.0ms	88×	2	valid
33.0ms	116×	0	valid
24.0ms	16×	3	valid
16.0ms	36×	1	valid

Compiler

Compiled 577 to 65 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

adjust: 65.0ms (32.4% of total)

const: 37.0ms (18.5% of total)

ival-div: 34.0ms (17% of total)

ival-cos: 25.0ms (12.5% of total)

ival-mult: 21.0ms (10.5% of total)

ival-add: 10.0ms (5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

10 → 33

Calls

Call 1

Inputs
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))

Outputs
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
24
(+ 24 (* -12/5 (pow x 2)))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
-12/5
(- (* -1/350 (pow x 2)) 12/5)
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(/ 40320/17 (pow x 4))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(* -12/5 (pow x 2))
(* (pow x 2) (- (* 24 (/ 1 (pow x 2))) 12/5))
(* -1/350 (pow x 2))
(* -1 (* (pow x 2) (+ 1/350 (* 12/5 (/ 1 (pow x 2))))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* -12/5 (* x x)) 24) (+ (* -1/350 (* x x)) -12/5))

1.0ms

-inf

((+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* -12/5 (* x x)) 24) (+ (* -1/350 (* x x)) -12/5))

1.0ms

((+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (* x x)) 1/2) (/ (- 1 (cos x)) (sin x)) (/ 1 (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24))) (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (+ (* -12/5 (* x x)) 24) (+ (* -1/350 (* x x)) -12/5))

simplify115.0ms (1.6%)

Memory

-4.7MiB live, 118.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	323
1	268	322
2	683	322
3	1679	322
4	3405	322
5	7259	322
0	8239	289

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 33

Calls

Call 1

Inputs
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
24
(+ 24 (* -12/5 (pow x 2)))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
-12/5
(- (* -1/350 (pow x 2)) 12/5)
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(/ 40320/17 (pow x 4))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(* -12/5 (pow x 2))
(* (pow x 2) (- (* 24 (/ 1 (pow x 2))) 12/5))
(* -1/350 (pow x 2))
(* -1 (* (pow x 2) (+ 1/350 (* 12/5 (/ 1 (pow x 2))))))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
24
#s(literal 24 binary64)
(+ 24 (* -12/5 (pow x 2)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(+ 24 (* (pow x 2) (- (* -1/350 (pow x 2)) 12/5)))
(fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))
(+ 24 (* (pow x 2) (- (* (pow x 2) (- (* 43/1750 (pow x 2)) 1/350)) 12/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 43/1750 binary64) (.f64 x x) #s(literal -1/350 binary64)) (.f64 x x) #s(literal -12/5 binary64)) (*.f64 x x) #s(literal 24 binary64))
-12/5
#s(literal -12/5 binary64)
(- (* -1/350 (pow x 2)) 12/5)
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x)
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(/ 40320/17 (pow x 4))
(/.f64 #s(literal 40320/17 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (- 40320/17 (* 6773760/289 (/ 1 (pow x 2)))) (pow x 4))
(/.f64 (-.f64 #s(literal 40320/17 binary64) (/.f64 #s(literal 6773760/289 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 40320/17 (* -1 (/ (+ 6773760/289 (* 13547520/4913 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/.f64 (-.f64 (-.f64 #s(literal 40320/17 binary64) (/.f64 #s(literal 13547520/4913 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 6773760/289 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (+ 40320/17 (* 195734568960/83521 (/ 1 (pow x 6)))) (+ (* 6773760/289 (/ 1 (pow x 2))) (/ 13547520/4913 (pow x 4)))) (pow x 4))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 195734568960/83521 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 40320/17 binary64)) (-.f64 (/.f64 #s(literal 13547520/4913 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -6773760/289 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 4 binary64)))
(* -12/5 (pow x 2))
(.f64 #s(literal -12/5 binary64) (.f64 x x))
(* (pow x 2) (- (* 24 (/ 1 (pow x 2))) 12/5))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(* -1/350 (pow x 2))
(.f64 #s(literal -1/350 binary64) (.f64 x x))
(* -1 (* (pow x 2) (+ 1/350 (* 12/5 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))

rewrite175.0ms (2.4%)

Memory

20.5MiB live, 172.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	260
0	49	254
1	222	250
2	1518	250
0	8282	234

Stop Event

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

Counts

10 → 226

Calls

Call 1

Inputs
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))))
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64))))
#s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))

Outputs
(.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))))))))
(.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 (-.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 2 binary64)) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))))))))
(.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 (pow.f64 #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))))) #s(literal -1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 576 binary64) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 144/25 binary64)) (.f64 (*.f64 x x) #s(literal -288/5 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64) #s(literal 13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))))
(fma.f64 (*.f64 #s(literal -12/5 binary64) x) x #s(literal 24 binary64))
(fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64))
(fma.f64 #s(literal -12/5 binary64) (*.f64 x x) #s(literal 24 binary64))
(fma.f64 x (*.f64 #s(literal -12/5 binary64) x) #s(literal 24 binary64))
(-.f64 (/.f64 #s(literal 576 binary64) (-.f64 #s(literal 24 binary64) (.f64 (.f64 x x) #s(literal -12/5 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 144/25 binary64)) (-.f64 #s(literal 24 binary64) (.f64 (*.f64 x x) #s(literal -12/5 binary64)))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 144/25 binary64)) (fma.f64 (.f64 x x) #s(literal -12/5 binary64) #s(literal -24 binary64))) (/.f64 #s(literal 576 binary64) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal -24 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal -12/5 binary64)) #s(literal 24 binary64))
(+.f64 #s(literal 24 binary64) (.f64 (.f64 x x) #s(literal -12/5 binary64)))
(.f64 (-.f64 #s(literal 144/25 binary64) (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (.f64 x x)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -144/25 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (*.f64 x x) #s(literal 6/875 binary64)))))))
(.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -144/25 binary64)) (pow.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 144/25 binary64) (-.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal 6/875 binary64))))))
(.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64)) (pow.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (*.f64 x x) #s(literal 6/875 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 144/25 binary64) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (fma.f64 (/.f64 #s(literal 144/25 binary64) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (/.f64 #s(literal 144/25 binary64) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (/.f64 #s(literal 144/25 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 144/25 binary64) (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -144/25 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (.f64 x x) #s(literal 6/875 binary64)))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/350 binary64) (.f64 x x)) #s(literal 4 binary64)) #s(literal 20736/625 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 144/25 binary64)) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/350 binary64) (.f64 x x)) #s(literal 6 binary64)) #s(literal 2985984/15625 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/350 binary64) (.f64 x x)) #s(literal 4 binary64)) (+.f64 #s(literal 20736/625 binary64) (.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 144/25 binary64)))) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/350 binary64) (.f64 x x)) #s(literal 6 binary64)) #s(literal 2985984/15625 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1728/125 binary64)) (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (*.f64 x x) #s(literal 6/875 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal -1/78815638671875000000000 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal -5159780352/1953125 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/1838265625000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (-.f64 #s(literal 2985984/15625 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 216/669921875 binary64)))) (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (*.f64 x x) #s(literal 6/875 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64)) #s(literal 144/25 binary64))) (.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64)) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))))
(/.f64 (-.f64 #s(literal 144/25 binary64) (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -144/25 binary64))) (neg.f64 (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64))) (neg.f64 (+.f64 #s(literal 144/25 binary64) (-.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 6/875 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64))) (neg.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (.f64 x x) #s(literal 6/875 binary64))))))
(/.f64 (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -144/25 binary64)) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64)))
(/.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64)) (+.f64 #s(literal 144/25 binary64) (-.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 6/875 binary64)))))
(/.f64 (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64)) (fma.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 144/25 binary64) (.f64 (.f64 x x) #s(literal 6/875 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (.f64 x x))) (-.f64 #s(literal 144/25 binary64) (*.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 144/25 binary64) (-.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 6/875 binary64)))) (fma.f64 #s(literal -1/42875000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1728/125 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))))
(fma.f64 (*.f64 #s(literal -1/350 binary64) x) x #s(literal -12/5 binary64))
(fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/350 binary64) #s(literal -12/5 binary64))
(fma.f64 x (*.f64 #s(literal -1/350 binary64) x) #s(literal -12/5 binary64))
(-.f64 (/.f64 #s(literal 144/25 binary64) (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/122500 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal 12/5 binary64))) (/.f64 #s(literal 144/25 binary64) (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal 12/5 binary64))))
(+.f64 (.f64 #s(literal -1/350 binary64) (.f64 x x)) #s(literal -12/5 binary64))
(+.f64 #s(literal -12/5 binary64) (.f64 #s(literal -1/350 binary64) (.f64 x x)))

eval90.0ms (1.3%)

Memory: -9.6MiB live, 84.7MiB allocated
Compiler: Compiled 15 597 to 1 545 computations (90.1% saved)

prune12.0ms (0.2%)

Memory

-17.7MiB live, 19.3MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	253	2	255
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	255	7	262

Accuracy

100.0%

Counts

262 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
	55.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
	55.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
✓	56.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	7.6%	#s(literal 1 binary64)

Compiler

Compiled 430 to 170 computations (60.5% saved)

regimes9.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Calls

2 calls:

4.0ms	x
4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes11.0ms (0.2%)

Memory

-22.3MiB live, 13.8MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (+.f64 (/.f64 (*.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (*.f64 x x) #s(literal -12/5 binary64)) (*.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))

#s(literal 1 binary64)

Calls

2 calls:

7.0ms	x
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
59.6%	2	`x`
59.4%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 #s(literal -12/5 binary64) (.f64 x x) #s(literal 24 binary64)))) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))

Outputs

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (+.f64 (/.f64 (*.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x))

#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
59.6%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
59.5%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
59.5%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
59.5%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
7.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
7.6%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch18.0ms (0.3%)

Memory

-22.3MiB live, 16.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.8683722393706124	50.18739124050979

Samples

11.0ms

112×

valid

Compiler

Compiled 318 to 227 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-cos: 4.0ms (46.6% of total)

ival-sin: 3.0ms (35% of total)

ival-sub: 1.0ms (11.7% of total)

ival-div: 1.0ms (11.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch8.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	1.8683722393706124	50.18739124050979

Samples

4.0ms

48×

valid

Compiler

Compiled 283 to 213 computations (24.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-cos: 1.0ms (28.7% of total)

ival-sin: 1.0ms (28.7% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch14.0ms (0.2%)

Memory

10.3MiB live, 10.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.8683722393706124	50.18739124050979

Samples

9.0ms

96×

valid

Compiler

Compiled 164 to 136 computations (17.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-cos: 3.0ms (42.7% of total)

ival-sin: 3.0ms (42.7% of total)

ival-div: 1.0ms (14.2% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.8683722393706124	50.18739124050979

Compiler

Compiled 129 to 122 computations (5.4% saved)

bsearch19.0ms (0.3%)

Memory

14.3MiB live, 14.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	1.2455519092185206e-11	1.8683722393706124

Samples

12.0ms

160×

valid

Compiler

Compiled 130 to 140 computations (-7.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-cos: 3.0ms (36.2% of total)

ival-sin: 3.0ms (36.2% of total)

ival-sub: 1.0ms (12.1% of total)

ival-div: 1.0ms (12.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify111.0ms (1.5%)

Memory

-33.7MiB live, 51.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	144
1	74	144
2	94	144
3	151	144
4	207	144
5	238	144
6	314	144
7	618	144
8	5573	144
9	7141	144

Stop Event

1×	node limit

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 2871044762448691/281474976710656 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 14 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3152519739159347/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 2871044762448691/281474976710656 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (fma.f64 #s(literal -1/350 binary64) (.f64 x x) #s(literal -12/5 binary64)) (.f64 x x) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 14 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(approx (/ 1 (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24)) (fma.f64 (*.f64 x x) #s(literal -12/5 binary64) #s(literal 24 binary64)))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3152519739159347/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.2s (16.1%)

Memory

22.0MiB live, 648.4MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	202
1	224	202
2	555	196
3	1661	196
4	3002	196
5	4256	196
6	4608	196
7	5339	196
8	6812	196
0	8041	172
0	111	416
1	319	415
2	814	413
3	2118	409
4	4654	409
0	8466	381
0	6	15
0	10	12
1	39	12
2	247	12
3	2387	11
0	9106	11
0	24	141
0	37	113
1	162	113
2	987	113
0	8749	113
0	33	260
0	49	254
1	222	250
2	1518	250
0	8282	234
0	26	179
0	44	167
1	177	167
2	1220	167
0	8528	167

Stop Event

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

Compiler

Compiled 389 to 217 computations (44.2% saved)

preprocess55.0ms (0.8%)

Memory: 10.9MiB live, 48.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 348 to 146 computations (58% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	181	8
4	448	8
5	683	8
6	708	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	317	4
9	534	4
10	590	4
11	593	4
12	601	4
13	607	4
14	611	4
15	618	4
16	625	4
17	626	4
0	626	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	317	14
9	534	14
10	590	14
11	593	14
12	601	14
13	607	14
14	611	14
15	618	14
16	625	14
17	626	14
0	626	14

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	181	8
4	448	8
5	683	8
6	708	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	317	4
9	534	4
10	590	4
11	593	4
12	601	4
13	607	4
14	611	4
15	618	4
16	625	4
17	626	4
0	626	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	317	14
9	534	14
10	590	14
11	593	14
12	601	14
13	607	14
14	611	14
15	618	14
16	625	14
17	626	14
0	626	14

start0.0ms (0%)

analyze109.0ms (1.5%)

sample2.0s (27.8%)

explain182.0ms (2.5%)

preprocess70.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify23.0ms (0.3%)

localize83.0ms (1.2%)

series2.0ms (0%)

simplify220.0ms (3%)

rewrite224.0ms (3.1%)

eval105.0ms (1.5%)

prune15.0ms (0.2%)

simplify66.0ms (0.9%)

localize201.0ms (2.8%)

series10.0ms (0.1%)

simplify137.0ms (1.9%)

rewrite226.0ms (3.1%)

eval91.0ms (1.3%)

prune42.0ms (0.6%)

simplify415.0ms (5.8%)

localize168.0ms (2.3%)

series5.0ms (0.1%)

simplify154.0ms (2.1%)

rewrite232.0ms (3.2%)

eval107.0ms (1.5%)

prune39.0ms (0.5%)

simplify223.0ms (3.1%)

localize248.0ms (3.4%)

series4.0ms (0.1%)

simplify115.0ms (1.6%)

rewrite175.0ms (2.4%)

eval90.0ms (1.3%)

prune12.0ms (0.2%)

regimes9.0ms (0.1%)

regimes11.0ms (0.2%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch18.0ms (0.3%)

bsearch8.0ms (0.1%)

bsearch14.0ms (0.2%)

bsearch1.0ms (0%)

bsearch19.0ms (0.3%)

simplify111.0ms (1.5%)

soundness1.2s (16.1%)

preprocess55.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	181	8
4	448	8
5	683	8
6	708	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	317	4
9	534	4
10	590	4
11	593	4
12	601	4
13	607	4
14	611	4
15	618	4
16	625	4
17	626	4
0	626	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	317	14
9	534	14
10	590	14
11	593	14
12	601	14
13	607	14
14	611	14
15	618	14
16	625	14
17	626	14
0	626	14