Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze110.0ms (2.1%)

Memory

-19.8MiB live, 133.9MiB 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 (36.9%)

Memory

56.9MiB live, 1 699.7MiB allocated

Samples

649.0ms	2 228×	2	valid
582.0ms	4 233×	0	valid
237.0ms	587×	3	valid
127.0ms	1 203×	1	valid
6.0ms	5×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-cos: 865.0ms (62.5% of total)

ival-sin: 199.0ms (14.4% of total)

adjust: 123.0ms (8.9% of total)

ival-div: 100.0ms (7.2% of total)

ival-sub: 82.0ms (5.9% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

explain207.0ms (3.9%)

Memory

-9.6MiB live, 193.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
84	51	(4.1255342195242803e-286)	4	(-8.17673534456649e+270)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51	0	-	51	(-3.7865188957562755e-295)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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	131	8

Confusion

	Predicted +	Predicted -
+	129	4
-	2	121

Precision

0.9847328244274809

Recall

0.9699248120300752

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	2	2
-	2	6	115

Precision?

0.9424460431654677

Recall?

0.9849624060150376

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms	124×	2	valid
29.0ms	270×	0	valid
15.0ms	36×	3	valid
10.0ms	82×	1	valid

Compiler

Compiled 79 to 37 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-cos: 38.0ms (55.6% of total)

ival-sin: 12.0ms (17.5% of total)

adjust: 7.0ms (10.2% of total)

ival-div: 6.0ms (8.8% of total)

ival-sub: 5.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess45.0ms (0.8%)

Memory

14.8MiB live, 14.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	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	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	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: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify72.0ms (1.4%)

Memory

-37.1MiB live, 6.3MiB 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	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	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)

localize53.0ms (1%)

Memory

31.7MiB live, 66.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	11.754539134497968	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	17.454535280143272	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

16.0ms	62×	2	valid
15.0ms	135×	0	valid
5.0ms	18×	3	valid
5.0ms	41×	1	valid

Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-cos: 17.0ms (52.2% of total)

ival-sin: 5.0ms (15.3% of total)

ival-div: 3.0ms (9.2% of total)

adjust: 3.0ms (9.2% of total)

ival-sub: 3.0ms (9.2% 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

2.4MiB live, 2.4MiB 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))

simplify233.0ms (4.4%)

Memory

-8.0MiB live, 148.5MiB 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	3000	196
5	4247	196
6	4597	196
7	5328	196
8	6820	196
0	8376	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)

rewrite179.0ms (3.4%)

Memory

4.7MiB live, 238.2MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

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

eval129.0ms (2.4%)

Memory: -12.4MiB live, 107.8MiB allocated
Compiler: Compiled 13 034 to 1 647 computations (87.4% saved)

prune13.0ms (0.2%)

Memory

-0.2MiB live, 37.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	629	5	634
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	630	5	635

Accuracy

100.0%

Counts

635 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.6%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	49.7%	#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))
▶	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 110 to 86 computations (21.8% saved)

simplify38.0ms (0.7%)

Memory

-12.4MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
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	22	124
0	34	113
1	59	113
2	92	113
3	156	113
4	255	113
5	285	113
6	321	113
7	395	113
8	517	113
9	725	113
10	767	113
11	770	113
12	778	113
13	783	113
14	787	113
15	794	113
16	874	113
17	961	113
18	965	113
0	965	113

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

localize120.0ms (2.2%)

Memory

6.8MiB live, 119.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0.03515625	(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	0.0390625	(.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	0.05859375	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	32.20836428590022	#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	(*.f64 x x)
accuracy	0.05859375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.12890625	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	32.19011265108829	#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	(*.f64 #s(literal 1/2 binary64) x)
accuracy	32.11514131341068	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

37.0ms	135×	0	valid
33.0ms	62×	2	valid
17.0ms	41×	1	valid
11.0ms	18×	3	valid

Compiler

Compiled 230 to 47 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-cos: 17.0ms (21.7% of total)

ival-mult: 14.0ms (17.9% of total)

adjust: 10.0ms (12.8% of total)

ival-sub: 8.0ms (10.2% of total)

const: 8.0ms (10.2% of total)

ival-tan: 6.0ms (7.7% of total)

ival-add: 5.0ms (6.4% of total)

ival-sin: 5.0ms (6.4% of total)

ival-div: 3.0ms (3.8% of total)

ival-pow: 2.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

12 → 25

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))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 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)))
(/ (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)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	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) (pow 1 -1/2))
2.0ms	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) (pow 1 -1/2))
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) (pow 1 -1/2))

Time

Variable

Point

Expression

2.0ms

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) (pow 1 -1/2))

2.0ms

-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) (pow 1 -1/2))

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) (pow 1 -1/2))

simplify211.0ms (4%)

Memory

31.2MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	206
1	188	206
2	480	206
3	1159	206
4	2301	206
5	5530	206
0	8283	185

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 25

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)))
(/ (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)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

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))
(/ (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 #s(literal 1/2 binary64) x))
(* 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)))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (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)
(* 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))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.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)

rewrite216.0ms (4.1%)

Memory

-10.7MiB live, 237.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	105
0	34	94
1	126	94
2	766	94
3	7651	94
0	8234	94

Stop Event

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

Counts

12 → 510

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

Outputs
(*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.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) (pow.f64 (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(.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 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (-.f64 (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(.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)) (tan.f64 (.f64 x #s(literal 1/2 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 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #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 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 (cos.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) (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))))
(.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 -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) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 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 (pow.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.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 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (/.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 -2 binary64))) #s(literal -1 binary64)))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(*.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 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (sin.f64 x)) (sin.f64 x))
(/.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sin.f64 x))) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (sin.f64 x))) (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (sin.f64 x))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (sin.f64 x))) (neg.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (neg.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x))) (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (sin.f64 x)))
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(fma.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) x) (/.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)) (/.f64 #s(literal 1/240 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) (/.f64 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/57600 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/240 binary64) x) (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x)))))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
#s(literal 1 binary64)

eval91.0ms (1.7%)

Memory: 15.1MiB live, 124.7MiB allocated
Compiler: Compiled 15 892 to 1 968 computations (87.6% saved)

prune31.0ms (0.6%)

Memory

-3.8MiB live, 39.3MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	554	3	557
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	555	7	562

Accuracy

100.0%

Counts

562 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
▶	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))
✓	49.7%	#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))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	8.6%	#s(literal 1 binary64)

Compiler

Compiled 94 to 69 computations (26.6% saved)

simplify36.0ms (0.7%)

Memory

-21.8MiB live, 15.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	103
0	28	97
1	57	93
2	100	93
3	157	93
4	269	93
5	317	93
6	353	93
7	427	93
8	550	93
9	760	93
10	802	93
11	805	93
12	813	93
13	819	93
14	823	93
15	830	93
16	910	93
17	1000	93
18	1004	93
0	1004	89

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

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

localize122.0ms (2.3%)

Memory

-11.3MiB live, 127.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.049160009768442016	(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
accuracy	0.05859375	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.19921875	(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	32.20836428590022	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.03515625	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.28515625	(*.f64 #s(literal 1/24 binary64) x)
accuracy	32.19011265108829	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))

Samples

53.0ms	135×	0	valid
33.0ms	62×	2	valid
12.0ms	41×	1	valid
10.0ms	18×	3	valid

Compiler

Compiled 186 to 40 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-cos: 20.0ms (29.3% of total)

ival-mult: 15.0ms (22% of total)

const: 9.0ms (13.2% of total)

adjust: 8.0ms (11.7% of total)

ival-add: 5.0ms (7.3% of total)

ival-sin: 5.0ms (7.3% of total)

ival-div: 3.0ms (4.4% of total)

ival-sub: 3.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

-9.6MiB live, 23.4MiB allocated

Counts

9 → 20

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

-inf

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

3.0ms

inf

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

1.0ms

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

simplify166.0ms (3.1%)

Memory

-1.4MiB live, 198.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	161
1	180	161
2	452	161
3	1055	161
4	2413	161
5	5371	161
0	8115	145

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 20

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))))))))
(pow x 2)
(* 1/24 x)
(* x (+ 1/24 (* 1/240 (pow x 2))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(* 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 3))
(* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))

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

rewrite183.0ms (3.4%)

Memory

36.5MiB live, 154.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	89
0	28	83
1	113	79
2	825	79
0	8487	75

Stop Event

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

Counts

9 → 280

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))) x) (/.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))))
(.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))) (.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 1/24 binary64) x) x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 9 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))) #s(literal 1 binary64)) (.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))) (.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))) (+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (fma.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))))) (neg.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)) x) #s(literal 2 binary64)))) (.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64))) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x)))) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) x) x (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x)))) (.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/576 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
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(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal -1/5760 binary64)))))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (-.f64 #s(literal 1/576 binary64) (*.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal -1/5760 binary64)))) (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/5760 binary64) (.f64 x x)))))))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))

eval45.0ms (0.8%)

Memory: -11.0MiB live, 62.7MiB allocated
Compiler: Compiled 11 930 to 1 318 computations (89% saved)

prune11.0ms (0.2%)

Memory

-27.3MiB live, 22.9MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	322	0	322
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	322	7	329

Accuracy

100.0%

Counts

329 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))
✓	49.7%	#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))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	8.6%	#s(literal 1 binary64)

Compiler

Compiled 198 to 103 computations (48% saved)

regimes7.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

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

3.0ms	x
3.0ms	(/.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)

regimes6.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
54.4%	2	`x`
54.2%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB 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)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #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))

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
54.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

5.7MiB live, 5.7MiB 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)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes5.0ms (0.1%)

Memory

-32.3MiB live, 5.6MiB allocated

Counts

3 → 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))

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:

4.0ms

Results

Accuracy	Segments	Branch
54.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB 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

2 calls:

2.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
53.7%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
53.8%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB 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
8.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
8.6%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch24.0ms (0.4%)

Memory

-6.1MiB live, 31.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	0.003787583980521803	504.1027739590249

Samples

16.0ms

144×

valid

Compiler

Compiled 226 to 181 computations (19.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-cos: 7.0ms (51.8% of total)

ival-sin: 5.0ms (37% of total)

ival-sub: 1.0ms (7.4% of total)

ival-div: 1.0ms (7.4% 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

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.003787583980521803	504.1027739590249

Compiler

Compiled 208 to 172 computations (17.3% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.003787583980521803	504.1027739590249

Compiler

Compiled 181 to 163 computations (9.9% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.003787583980521803	504.1027739590249

Compiler

Compiled 163 to 154 computations (5.5% saved)

bsearch15.0ms (0.3%)

Memory

23.2MiB live, 23.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.003787583980521803	504.1027739590249

Samples

9.0ms

128×

valid

Compiler

Compiled 118 to 127 computations (-7.6% saved)

Precisions

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

ival-cos: 3.0ms (45.6% of total)

ival-sin: 2.0ms (30.4% of total)

ival-sub: 1.0ms (15.2% of total)

ival-div: 1.0ms (15.2% of total)

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

exact: 0.0ms (0% of total)

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

simplify71.0ms (1.3%)

Memory

-40.4MiB live, 52.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	119
1	45	119

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 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 7093169413108531/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 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))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 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 7093169413108531/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 7093169413108531/2251799813685248 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))
(if (<=.f64 x #s(literal 3152519739159347/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness837.0ms (15.7%)

Memory

3.7MiB live, 514.5MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	79	202
1	224	202
2	555	196
3	1661	196
4	3000	196
5	4247	196
6	4597	196
7	5328	196
8	6820	196
0	8376	172
0	22	105
0	34	94
1	126	94
2	766	94
3	7651	94
0	8234	94

Stop Event

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

Compiler

Compiled 236 to 126 computations (46.6% saved)

preprocess49.0ms (0.9%)

Memory: 36.5MiB live, 74.5MiB allocated
Remove: (negabs x)
Compiler: Compiled 276 to 108 computations (60.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	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	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	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	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	22	124
0	34	113
1	59	113
2	92	113
3	156	113
4	255	113
5	285	113
6	321	113
7	395	113
8	517	113
9	725	113
10	767	113
11	770	113
12	778	113
13	783	113
14	787	113
15	794	113
16	874	113
17	961	113
18	965	113
0	965	113

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	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	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	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	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	22	124
0	34	113
1	59	113
2	92	113
3	156	113
4	255	113
5	285	113
6	321	113
7	395	113
8	517	113
9	725	113
10	767	113
11	770	113
12	778	113
13	783	113
14	787	113
15	794	113
16	874	113
17	961	113
18	965	113
0	965	113

start0.0ms (0%)

analyze110.0ms (2.1%)

sample2.0s (36.9%)

explain207.0ms (3.9%)

preprocess45.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify72.0ms (1.4%)

localize53.0ms (1%)

series2.0ms (0%)

simplify233.0ms (4.4%)

rewrite179.0ms (3.4%)

eval129.0ms (2.4%)

prune13.0ms (0.2%)

simplify38.0ms (0.7%)

localize120.0ms (2.2%)

series7.0ms (0.1%)

simplify211.0ms (4%)

rewrite216.0ms (4.1%)

eval91.0ms (1.7%)

prune31.0ms (0.6%)

simplify36.0ms (0.7%)

localize122.0ms (2.3%)

series13.0ms (0.2%)

simplify166.0ms (3.1%)

rewrite183.0ms (3.4%)

eval45.0ms (0.8%)

prune11.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch24.0ms (0.4%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch15.0ms (0.3%)

simplify71.0ms (1.3%)

soundness837.0ms (15.7%)

preprocess49.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	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	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	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	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	22	124
0	34	113
1	59	113
2	92	113
3	156	113
4	255	113
5	285	113
6	321	113
7	395	113
8	517	113
9	725	113
10	767	113
11	770	113
12	778	113
13	783	113
14	787	113
15	794	113
16	874	113
17	961	113
18	965	113
0	965	113