Metrics for tanhf (example 3.4)

start0.0ms (0%)

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

analyze118.0ms (2.7%)

Memory

20.2MiB live, 151.7MiB allocated; 57ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.2s (52%)

Memory

62.5MiB live, 1 695.5MiB allocated; 957ms collecting garbage

Samples

734.0ms	4 170×	0	valid
671.0ms	2 227×	2	valid
295.0ms	642×	3	valid
257.0ms	1 211×	1	valid
7.0ms	6×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-cos: 778.0ms (52.9% of total)

adjust: 236.0ms (16% of total)

ival-sin: 172.0ms (11.7% of total)

ival-div: 147.0ms (10% of total)

ival-sub: 125.0ms (8.5% of total)

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

exact: 5.0ms (0.3% of total)

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

Bogosity

explain178.0ms (4.1%)

Memory

-17.3MiB live, 129.8MiB allocated; 22ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
76	1	(-3.4018019826307054e+174)	1	(-6.254215438935449e+28)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
55	0	-	3	(1.3473390336776904e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	76	2
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	52	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	52

Confusion

	Predicted +	Predicted -
+	127	0
-	1	128

Precision

0.9921875

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	127	0	0
-	1	2	126

Precision?

0.9769230769230769

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms	148×	2	valid
28.0ms	266×	0	valid
10.0ms	28×	3	valid
8.0ms	70×	1	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-cos: 53.0ms (62% of total)

ival-sin: 11.0ms (12.9% of total)

adjust: 10.0ms (11.7% of total)

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

ival-sub: 5.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess190.0ms (4.4%)

Memory

-17.0MiB live, 119.4MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	29	9
2	71	8
3	143	8
4	377	8
5	1418	8
0	6	7
0	10	4
1	24	4
2	37	4
3	60	4
4	131	4
5	606	4
0	8288	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify135.0ms (3.1%)

Memory

-7.7MiB live, 139.4MiB allocated; 22ms collecting garbage

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	3	(/.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	24	14
2	37	14
3	60	14
4	131	14
5	606	14
0	8288	14

Stop Event

1×	iter limit
1×	node limit
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)

localize57.0ms (1.3%)

Memory

8.7MiB live, 54.8MiB allocated; 4ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	12.717336334768756	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	16.29599443696264	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

20.0ms	74×	2	valid
14.0ms	133×	0	valid
13.0ms	14×	3	valid
4.0ms	35×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-cos: 27.0ms (63.5% of total)

adjust: 5.0ms (11.8% of total)

ival-sin: 5.0ms (11.8% of total)

ival-div: 3.0ms (7.1% of total)

ival-sub: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

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
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (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))

simplify165.0ms (3.8%)

Memory

13.7MiB live, 114.0MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	282
1	286	282
2	814	276
3	3365	276
4	7632	276
0	8021	252

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 20

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#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)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#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)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) (.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))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (- 1 (cos x)) (.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))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos x) (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)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) x)
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) (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))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (sin x) (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))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (sin x) (sin.f64 x))

rewrite44.0ms (1%)

Memory

0.9MiB live, 46.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	41	12
0	302	12

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 32

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

eval6.0ms (0.1%)

Memory: 11.8MiB live, 11.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 767 to 205 computations (73.3% saved)

prune2.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	4	53

Accuracy

100.0%

Counts

53 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	49.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 60 to 45 computations (25% saved)

simplify149.0ms (3.4%)

Memory

-40.5MiB live, 106.5MiB allocated; 15ms collecting garbage

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	131
0	32	119
1	66	119
2	171	119
3	572	119
4	1746	119
5	3325	119
0	8631	119

Stop Event

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

Calls

Call 1

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

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

localize117.0ms (2.7%)

Memory

32.4MiB live, 121.1MiB allocated; 9ms collecting garbage

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.05859375	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.49727706006807415	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	32.254915243515065	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 x x)
accuracy	0.06640625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.33266851464986186	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	32.29269146645893	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	32.15725910023745	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Samples

45.0ms	73×	2	valid
31.0ms	133×	0	valid
17.0ms	36×	1	valid
10.0ms	14×	3	valid

Compiler

Compiled 108 to 22 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-cos: 24.0ms (28.4% of total)

adjust: 14.0ms (16.5% of total)

const: 13.0ms (15.4% of total)

ival-mult: 13.0ms (15.4% of total)

ival-tan: 5.0ms (5.9% of total)

ival-add: 5.0ms (5.9% of total)

ival-sin: 5.0ms (5.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

12 → 37

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ (- 1 (cos x)) (sin x)) (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))
2.0ms	x	@	-inf	((/ (- 1 (cos x)) (sin x)) (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))
2.0ms	x	@	0	((/ (- 1 (cos x)) (sin x)) (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))

Time

Variable

Point

Expression

2.0ms

inf

((/ (- 1 (cos x)) (sin x)) (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))

2.0ms

-inf

((/ (- 1 (cos x)) (sin x)) (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))

2.0ms

((/ (- 1 (cos x)) (sin x)) (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))

simplify195.0ms (4.5%)

Memory

-25.3MiB live, 160.3MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	672
1	300	672
2	977	671
3	5026	671
0	8189	609

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 37

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

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

rewrite67.0ms (1.5%)

Memory

-5.7MiB live, 54.4MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	114
0	32	102
1	125	102
0	912	102

Stop Event

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

Counts

12 → 122

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 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 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) x) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/48 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/48 binary64))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64) #s(literal 1/8 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 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))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal 1/24 binary64)))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (.f64 #s(literal 1/24 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/48 binary64)))) (/.f64 #s(literal 1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/48 binary64)))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 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)
(.f64 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)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x (.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)))
(fma.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)))
(+.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/2 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (neg.f64 x)) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64))
(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(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 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x)) x))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x))
(/.f64 (-.f64 #s(literal 1/576 binary64) (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))
(fma.f64 (*.f64 #s(literal 1/240 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/240 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 #s(literal 1/240 binary64) x)) x))
(-.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/240 binary64) (.f64 x x)))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal 1/240 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))) (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))

eval20.0ms (0.5%)

Memory: 25.9MiB live, 25.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 4 624 to 715 computations (84.5% saved)

prune12.0ms (0.3%)

Memory

-24.8MiB live, 19.0MiB allocated; 6ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	186	5	191

Accuracy

100.0%

Counts

191 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x (.f64 #s(literal 1/2 binary64) x)))
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	49.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 83 to 61 computations (26.5% saved)

simplify115.0ms (2.7%)

Memory

-4.2MiB live, 83.1MiB allocated; 10ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	72
0	24	67
1	58	67
2	144	67
3	454	67
4	1347	67
5	3192	67
0	8568	65

Stop Event

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

Calls

Call 1

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

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

localize103.0ms (2.4%)

Memory

24.5MiB live, 131.2MiB allocated; 8ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
accuracy	0.2109375	(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
accuracy	0.49727706006807415	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	32.254915243515065	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x (.f64 #s(literal 1/2 binary64) x)))

Samples

34.0ms	73×	2	valid
24.0ms	133×	0	valid
14.0ms	14×	3	valid
9.0ms	36×	1	valid

Compiler

Compiled 63 to 19 computations (69.8% saved)

Precisions

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

ival-cos: 21.0ms (30.7% of total)

adjust: 10.0ms (14.6% of total)

ival-mult: 10.0ms (14.6% of total)

const: 8.0ms (11.7% of total)

ival-div: 7.0ms (10.2% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

-37.4MiB live, 8.7MiB allocated; 3ms collecting garbage

Counts

5 → 24

Calls

Call 1

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

Outputs
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* 1/240 (pow x 3))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify150.0ms (3.5%)

Memory

19.6MiB live, 116.4MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	466
1	265	466
2	885	465
3	4548	465
0	8261	425

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* (+ (* 1/240 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* 1/240 (pow x 3))))
#s(approx (* (+ (* 1/240 (* x x)) 1/24) x) #s(hole binary64 (* (pow x 3) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* (+ (* 1/240 (* x x)) 1/24) x) x) x) (* 1/2 x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

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

rewrite67.0ms (1.6%)

Memory

26.2MiB live, 70.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	62
0	24	57
1	102	57
0	760	55

Stop Event

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

Counts

5 → 73

Calls

Call 1

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

Outputs
(.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x)
(.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal -1/2 binary64)))
(.f64 x (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) (.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 1/2 binary64)) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) (fabs.f64 x)) (fabs.f64 x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) (neg.f64 x)) (neg.f64 x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 x x) x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x))
(fma.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) (.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)) (.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)) x))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x)) (*.f64 x x)))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 x) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(.f64 x (.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (.f64 x x)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x)
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) x) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64))) (-.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) x (*.f64 #s(literal 1/24 binary64) x))
(fma.f64 #s(literal 1/24 binary64) x (.f64 (.f64 (*.f64 x x) #s(literal 1/240 binary64)) x))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/240 binary64)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 x #s(literal 1/24 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) x) (.f64 #s(literal 1/24 binary64) x))
(+.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) x))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/240 binary64))) (.f64 x #s(literal 1/24 binary64)))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/240 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))
(fma.f64 (*.f64 #s(literal 1/240 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/240 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x #s(literal 1/240 binary64)) x #s(literal 1/24 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 x #s(literal 1/240 binary64))) x))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal 1/240 binary64)))
(-.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/240 binary64) (.f64 x x)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))) (/.f64 #s(literal 1/13824 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 2 binary64)) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/240 binary64)))

eval24.0ms (0.5%)

Memory: -20.2MiB live, 21.9MiB allocated; 12ms collecting garbage
Compiler: Compiled 2 947 to 453 computations (84.6% saved)

prune6.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	95	5	100

Accuracy

100.0%

Counts

100 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) x (.f64 #s(literal 1/2 binary64) x)))
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	49.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 173 to 91 computations (47.4% saved)

regimes5.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.4b remaining (-1.2%)

Threshold costs -0.4b (-1.2%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
49.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
49.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify25.0ms (0.6%)

Memory

-17.8MiB live, 27.6MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	25	17
2	38	17
3	66	17
4	140	17
5	685	17

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations86.0ms (2%)

Memory

-4.3MiB live, 49.5MiB allocated; 15ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 11 computations (52.2% saved)

preprocess19.0ms (0.4%)

Memory: 22.1MiB live, 22.1MiB allocated; 0ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 92 to 62 computations (32.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze118.0ms (2.7%)

sample2.2s (52%)

explain178.0ms (4.1%)

preprocess190.0ms (4.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify135.0ms (3.1%)

localize57.0ms (1.3%)

series2.0ms (0.1%)

simplify165.0ms (3.8%)

rewrite44.0ms (1%)

eval6.0ms (0.1%)

prune2.0ms (0.1%)

simplify149.0ms (3.4%)

localize117.0ms (2.7%)

series8.0ms (0.2%)

simplify195.0ms (4.5%)

rewrite67.0ms (1.5%)

eval20.0ms (0.5%)

prune12.0ms (0.3%)

simplify115.0ms (2.7%)

localize103.0ms (2.4%)

series7.0ms (0.2%)

simplify150.0ms (3.5%)

rewrite67.0ms (1.6%)

eval24.0ms (0.5%)

prune6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify25.0ms (0.6%)

derivations86.0ms (2%)

preprocess19.0ms (0.4%)

end0.0ms (0%)

Profiling