Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze133.0ms (2.4%)

Memory

27.7MiB live, 165.5MiB 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)

sample1.9s (34.5%)

Memory

17.7MiB live, 1 625.3MiB allocated

Samples

708.0ms	2 265×	2	valid
485.0ms	4 238×	0	valid
214.0ms	542×	3	valid
161.0ms	1 206×	1	valid
6.0ms	5×	4	valid

Precisions

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

ival-cos: 762.0ms (57.8% of total)

ival-sin: 174.0ms (13.2% of total)

ival-div: 133.0ms (10.1% of total)

ival-sub: 123.0ms (9.3% of total)

adjust: 112.0ms (8.5% of total)

ival-true: 6.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

explain269.0ms (4.9%)

Memory

-12.1MiB live, 184.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
71	0	-	3	(-9.054609904804236e-162)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
67	1	(-9.054609904804236e-162)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	68	6
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	68	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	68

Confusion

	Predicted +	Predicted -
+	136	1
-	0	119

Precision

1.0

Recall

0.9927007299270073

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	1	0
-	0	5	114

Precision?

0.9647887323943662

Recall?

1.0

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

122.0ms	252×	0	valid
38.0ms	136×	2	valid
19.0ms	50×	3	valid
8.0ms	74×	1	valid

Compiler

Compiled 62 to 28 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-cos: 138.0ms (81.6% of total)

ival-sin: 11.0ms (6.5% of total)

adjust: 7.0ms (4.1% of total)

ival-div: 6.0ms (3.5% of total)

ival-sub: 5.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess42.0ms (0.8%)

Memory

35.3MiB live, 35.3MiB 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, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune39.0ms (0.7%)

Memory

-37.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify25.0ms (0.4%)

Memory

27.6MiB live, 27.6MiB 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)

localize64.0ms (1.2%)

Memory

-22.3MiB live, 58.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.584865981202968	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	16.25843695202075	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

19.0ms	68×	2	valid
13.0ms	126×	0	valid
9.0ms	25×	3	valid
4.0ms	37×	1	valid

Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-cos: 22.0ms (59.8% of total)

ival-sin: 5.0ms (13.6% of total)

adjust: 4.0ms (10.9% of total)

ival-div: 3.0ms (8.2% of total)

ival-sub: 3.0ms (8.2% 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

1.1MiB live, 1.1MiB 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))

simplify228.0ms (4.2%)

Memory

20.1MiB live, 176.6MiB 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)

rewrite196.0ms (3.6%)

Memory

-3.2MiB live, 194.4MiB 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)))

eval81.0ms (1.5%)

Memory: -11.1MiB live, 143.9MiB allocated
Compiler: Compiled 13 034 to 1 647 computations (87.4% saved)

prune15.0ms (0.3%)

Memory

4.9MiB live, 44.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	628	6	634
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	629	6	635

Accuracy

100.0%

Counts

635 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	52.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
▶	52.4%	#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))
▶	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	52.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 162 to 118 computations (27.2% saved)

simplify86.0ms (1.6%)

Memory

3.4MiB live, 41.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	204
0	44	192
1	82	192
2	142	192
3	294	192
4	649	192
5	958	192
6	1012	192
7	1090	192
8	1214	192
9	1422	192
10	1464	192
11	1467	192
12	1475	192
13	1481	192
14	1485	192
15	1492	192
16	1667	192
17	1914	192
18	1920	192
0	1920	192

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize177.0ms (3.2%)

Memory

8.3MiB live, 162.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
accuracy	0.053066259768442016	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
accuracy	0.0859375	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	30.425749690525596	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.0390625	(.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	0.05078125	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.08203125	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	30.431715221253977	#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	0.0703125	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.1015625	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	30.464854208523935	#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	30.337791541107965	#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

59.0ms	126×	0	valid
49.0ms	68×	2	valid
23.0ms	37×	1	valid
20.0ms	25×	3	valid

Compiler

Compiled 380 to 56 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-sin: 27.0ms (22.4% of total)

ival-cos: 26.0ms (21.6% of total)

ival-mult: 21.0ms (17.4% of total)

adjust: 13.0ms (10.8% of total)

const: 12.0ms (10% of total)

ival-add: 9.0ms (7.5% of total)

ival-tan: 5.0ms (4.2% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

16 → 44

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

4.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify194.0ms (3.5%)

Memory

6.0MiB live, 123.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	445
1	319	445
2	843	441
3	2203	439
4	4765	439
0	8114	405

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

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

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

rewrite209.0ms (3.8%)

Memory

0.6MiB live, 204.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	179
0	44	167
1	177	167
2	1218	167
0	8509	167

Stop Event

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

Counts

16 → 503

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(.f64 (pow.f64 (.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (pow.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x))))))
(.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (+.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (-.f64 (.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))) (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (sin.f64 x) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (sin.f64 x) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (.f64 (+.f64 (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 3 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (sin.f64 x) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (neg.f64 (sin.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (tan.f64 x)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (sin.f64 x)) (tan.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 x)) (.f64 (sin.f64 x) (tan.f64 x)))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x)))))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 (sin.f64 x)) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sin.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (+.f64 (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 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
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(/.f64 (neg.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64))) (neg.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)))))
(/.f64 (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/57600 binary64)) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal -1/240 binary64)))
(/.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64)) (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64)) (fma.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x))) (-.f64 #s(literal 1/57600 binary64) (*.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))) (fma.f64 #s(literal 4913/65548320768000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824000 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) x) x #s(literal 1/240 binary64))
(fma.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal -1/240 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal -1/240 binary64)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(fma.f64 x (*.f64 #s(literal 17/40320 binary64) x) #s(literal 1/240 binary64))
(-.f64 (/.f64 #s(literal 1/57600 binary64) (-.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal -1/240 binary64))) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal -1/240 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 289/1625702400 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal -1/240 binary64))) (neg.f64 (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal -1/240 binary64)))))
(+.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) #s(literal 1/240 binary64))
(+.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))

eval108.0ms (2%)

Memory: -16.5MiB live, 219.5MiB allocated
Compiler: Compiled 20 343 to 2 426 computations (88.1% saved)

prune16.0ms (0.3%)

Memory

2.8MiB live, 41.8MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

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

Accuracy

100.0%

Counts

593 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.1%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
▶	52.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	52.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	52.4%	#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))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	52.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 112 to 83 computations (25.9% saved)

simplify26.0ms (0.5%)

Memory

24.3MiB live, 24.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/24 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
cost-diff	320	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize115.0ms (2.1%)

Memory

-7.9MiB live, 144.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.05859375	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.1953125	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	30.464854208523935	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.16796875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
accuracy	30.337791541107965	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

Samples

53.0ms	126×	0	valid
28.0ms	68×	2	valid
14.0ms	25×	3	valid
8.0ms	37×	1	valid

Compiler

Compiled 128 to 40 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-cos: 45.0ms (52.5% of total)

ival-sin: 10.0ms (11.7% of total)

adjust: 7.0ms (8.2% of total)

ival-mult: 7.0ms (8.2% of total)

ival-div: 6.0ms (7% of total)

const: 4.0ms (4.7% of total)

ival-sub: 3.0ms (3.5% of total)

ival-pow: 2.0ms (2.3% of total)

ival-add: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

9 → 10

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify188.0ms (3.4%)

Memory

-39.1MiB live, 112.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	77
1	105	77
2	262	77
3	617	77
4	1010	77
5	1777	77
6	3121	77
7	4292	77
8	5214	77
9	5887	77
10	6746	77
11	7171	77
12	7943	77
0	8069	70

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 10

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

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

rewrite205.0ms (3.7%)

Memory

-4.9MiB live, 153.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	63
0	27	51
1	100	49
2	618	49
3	6439	49
0	8220	47

Stop Event

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

Counts

9 → 213

Calls

Call 1

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

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

eval25.0ms (0.4%)

Memory: 2.2MiB live, 37.7MiB allocated
Compiler: Compiled 5 197 to 673 computations (87.1% saved)

prune5.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	194	7	201

Accuracy

100.0%

Counts

201 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
✓	52.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	52.4%	#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))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	52.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	7.1%	#s(literal 1 binary64)

Compiler

Compiled 97 to 70 computations (27.8% saved)

simplify2.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
1	3	1
0	3	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

localize9.0ms (0.2%)

Memory

-21.6MiB live, 12.9MiB allocated

Samples

4.0ms

256×

valid

Compiler

Compiled 4 to 6 computations (-50% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	()
0.0ms	x	@	inf	()
0.0ms	x	@	-inf	()

simplify2.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite4.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune4.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	6	6
Total	7	7

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
✓	52.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	52.4%	#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))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	52.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	7.1%	#s(literal 1 binary64)

Compiler

Compiled 217 to 111 computations (48.8% saved)

regimes8.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes12.0ms (0.2%)

Memory

-46.4MiB live, 7.3MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

#s(literal 1 binary64)

Calls

2 calls:

4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
55.8%	2	`x`
55.5%	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

2.3MiB live, 2.3MiB allocated

Counts

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

3.0ms

Results

Accuracy	Segments	Branch
55.8%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB 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 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
55.6%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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:

2.0ms

Results

Accuracy	Segments	Branch
55.6%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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
55.2%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
55.4%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
1.0ms	x

Results

Accuracy	Segments	Branch
7.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
7.1%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch16.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.12192133568614906	19.328341563726564

Samples

11.0ms

112×

valid

Compiler

Compiled 199 to 150 computations (24.6% saved)

Precisions

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

ival-cos: 3.0ms (36.3% of total)

ival-sin: 3.0ms (36.3% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch12.0ms (0.2%)

Memory

4.6MiB live, 4.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.12192133568614906	19.328341563726564

Samples

7.0ms

96×

valid

Compiler

Compiled 164 to 136 computations (17.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-cos: 2.0ms (36.3% of total)

ival-sin: 2.0ms (36.3% of total)

ival-sub: 1.0ms (18.1% of total)

ival-div: 1.0ms (18.1% 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

0.5MiB live, 0.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.12192133568614906	19.328341563726564

Compiler

Compiled 143 to 129 computations (9.8% saved)

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.12192133568614906	19.328341563726564

Compiler

Compiled 129 to 122 computations (5.4% saved)

bsearch3.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.12192133568614906	19.328341563726564

Samples

1.0ms

16×

valid

Compiler

Compiled 94 to 101 computations (-7.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

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

simplify58.0ms (1.1%)

Memory

0.9MiB live, 40.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	122
1	49	122

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 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 6980579422424269/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 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 6530219459687219/4503599627370496 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 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 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 6980579422424269/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 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 6530219459687219/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness897.0ms (16.3%)

Memory

1.3MiB live, 478.0MiB 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	19	63
0	27	51
1	100	49
2	618	49
3	6439	49
0	8220	47
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	26	179
0	44	167
1	177	167
2	1218	167
0	8509	167

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

Compiler

Compiled 223 to 119 computations (46.6% saved)

preprocess96.0ms (1.7%)

Memory: -19.2MiB live, 56.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 282 to 118 computations (58.2% 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	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

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	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

start0.0ms (0%)

analyze133.0ms (2.4%)

sample1.9s (34.5%)

explain269.0ms (4.9%)

preprocess42.0ms (0.8%)

eval0.0ms (0%)

prune39.0ms (0.7%)

simplify25.0ms (0.4%)

localize64.0ms (1.2%)

series2.0ms (0%)

simplify228.0ms (4.2%)

rewrite196.0ms (3.6%)

eval81.0ms (1.5%)

prune15.0ms (0.3%)

simplify86.0ms (1.6%)

localize177.0ms (3.2%)

series10.0ms (0.2%)

simplify194.0ms (3.5%)

rewrite209.0ms (3.8%)

eval108.0ms (2%)

prune16.0ms (0.3%)

simplify26.0ms (0.5%)

localize115.0ms (2.1%)

series5.0ms (0.1%)

simplify188.0ms (3.4%)

rewrite205.0ms (3.7%)

eval25.0ms (0.4%)

prune5.0ms (0.1%)

simplify2.0ms (0%)

localize9.0ms (0.2%)

series0.0ms (0%)

simplify2.0ms (0%)

rewrite4.0ms (0.1%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes8.0ms (0.1%)

regimes12.0ms (0.2%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch16.0ms (0.3%)

bsearch12.0ms (0.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch3.0ms (0.1%)

simplify58.0ms (1.1%)

soundness897.0ms (16.3%)

preprocess96.0ms (1.7%)

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	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55