Metrics for tanhf (example 3.4)

start0.0ms (0%)

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

analyze113.0ms (2.6%)

Memory

4.9MiB live, 143.3MiB allocated; 10ms 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 (50.5%)

Memory

64.4MiB live, 1 690.9MiB allocated; 963ms collecting garbage

Samples

937.0ms	2 271×	2	valid
508.0ms	4 119×	0	valid
293.0ms	617×	3	valid
156.0ms	1 243×	1	valid
7.0ms	6×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-cos: 752.0ms (44.7% of total)

ival-div: 371.0ms (22.1% of total)

ival-sin: 262.0ms (15.6% of total)

adjust: 192.0ms (11.4% of total)

ival-sub: 91.0ms (5.4% of total)

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

exact: 5.0ms (0.3% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain151.0ms (3.5%)

Memory

7.5MiB live, 110.1MiB allocated; 12ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
81	2	(3.634031037374211e+149)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
60	0	-	2	(-1.8917414770733465e-155)	`(/.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	83	1
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	58	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	58

Confusion

	Predicted +	Predicted -
+	139	0
-	2	115

Precision

0.9858156028368794

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	0
-	2	1	114

Precision?

0.9788732394366197

Recall?

1.0

Freqs

test

number	freq
0	115
1	141

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms	146×	2	valid
34.0ms	244×	0	valid
14.0ms	34×	3	valid
10.0ms	86×	1	valid
2.0ms	2×	4	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-cos: 46.0ms (52.1% of total)

ival-sin: 19.0ms (21.5% of total)

adjust: 11.0ms (12.5% of total)

ival-div: 6.0ms (6.8% of total)

ival-sub: 5.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess175.0ms (4%)

Memory

-6.4MiB live, 131.6MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	40	13
2	78	12
3	152	12
4	392	12
5	1447	12
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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify146.0ms (3.4%)

Memory

-19.9MiB live, 90.3MiB allocated; 15ms 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)

localize55.0ms (1.3%)

Memory

15.9MiB live, 62.0MiB allocated; 2ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	13.84578970539386	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	17.61484979940502	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

21.0ms	73×	2	valid
13.0ms	122×	0	valid
7.0ms	17×	3	valid
6.0ms	43×	1	valid
1.0ms	1×	4	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-cos: 22.0ms (56.5% of total)

adjust: 6.0ms (15.4% of total)

ival-sin: 5.0ms (12.8% of total)

ival-div: 3.0ms (7.7% of total)

ival-sub: 3.0ms (7.7% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB 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))

simplify183.0ms (4.2%)

Memory

8.0MiB live, 107.0MiB allocated; 14ms 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))

rewrite70.0ms (1.6%)

Memory

-28.4MiB live, 59.5MiB allocated; 10ms 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: 6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 767 to 205 computations (73.3% saved)

prune3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB 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
▶	99.4%	(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	53.6%	#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 46 to 37 computations (19.6% saved)

simplify110.0ms (2.5%)

Memory

8.0MiB live, 110.6MiB allocated; 8ms collecting garbage

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(+.f64 (cos.f64 x) #s(literal 1 binary64))
cost-diff	0	(sin.f64 x)
cost-diff	3	(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
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	20	90
0	30	78
1	56	78
2	108	78
3	244	78
4	515	78
5	1155	78
0	8783	78

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

localize103.0ms (2.4%)

Memory

17.5MiB live, 108.1MiB allocated; 6ms collecting garbage

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 x)
accuracy	0.0	(cos.f64 x)
accuracy	0.15625	(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
accuracy	0.33453453711775105	(+.f64 (cos.f64 x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.0546875	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.109375	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	29.807678079451406	#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	29.705254950473293	#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	#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0.00390625	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

37.0ms	73×	2	valid
29.0ms	122×	0	valid
11.0ms	17×	3	valid
11.0ms	43×	1	valid
2.0ms	1×	5	exit

Compiler

Compiled 76 to 18 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-cos: 24.0ms (33.1% of total)

adjust: 14.0ms (19.3% of total)

ival-add: 7.0ms (9.6% of total)

ival-div: 6.0ms (8.3% of total)

ival-mult: 6.0ms (8.3% of total)

ival-tan: 5.0ms (6.9% of total)

ival-sin: 5.0ms (6.9% of total)

const: 4.0ms (5.5% of total)

ival-sub: 3.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.3%)

Memory

-34.4MiB live, 10.7MiB allocated; 9ms collecting garbage

Counts

12 → 40

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)
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 x)
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.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 (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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 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 (+ (cos x) 1) #s(hole binary64 2))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* -1/2 (pow x 2)))))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#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 (/ (- 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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (/ (sin x) (+ 1 (cos x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))

Calls

3 calls:

Time	Variable		Point	Expression
8.0ms	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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))
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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))
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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))

Time

Variable

Point

Expression

8.0ms

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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))

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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))

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) (/ (sin x) (+ (cos x) 1)) (sin x) (+ (cos x) 1) (cos x))

simplify218.0ms (5%)

Memory

40.4MiB live, 135.7MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	557
1	317	551
2	1077	551
3	3597	551
0	8237	505

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 40

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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 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 (+ (cos x) 1) #s(hole binary64 2))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* -1/2 (pow x 2)))))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#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 (/ (- 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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (/ (sin x) (+ 1 (cos x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos 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 (tan (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin 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 (/ (- 1 (cos x)) (sin 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 (/ (- 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 (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 (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 (* 1/2 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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (sin x) (+ (cos x) 1)) #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 (/ (sin x) (+ (cos x) 1)) #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 (/ (sin x) (+ (cos x) 1)) #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 (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)) (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x))
#s(approx (+ (cos x) 1) #s(hole binary64 2))
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* -1/2 (pow x 2)))))
#s(approx (+ (cos x) 1) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (cos x) 1) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 2 binary64)))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (cos x) 1) (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 2 binary64)))
#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 (/ (- 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 (tan (* 1/2 x)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (- 1 (cos x)) (sin 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 (/ (sin x) (+ (cos x) 1)) #s(hole binary64 (/ (sin x) (+ 1 (cos x)))))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (sin x) (sin.f64 x))
#s(approx (+ (cos x) 1) #s(hole binary64 (+ 1 (cos x))))
#s(approx (+ (cos x) 1) (-.f64 (cos.f64 x) #s(literal -1 binary64)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos x) (cos.f64 x))

rewrite50.0ms (1.2%)

Memory

-14.6MiB live, 29.2MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	78
0	30	69
1	101	66
0	672	66

Stop Event

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

Counts

12 → 107

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

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 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 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 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 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 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 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 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 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 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 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)))
(*.f64 (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal -1 binary64))) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.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 (-.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (neg.f64 (sin.f64 x))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (-.f64 (cos.f64 x) #s(literal -1 binary64)))))
(/.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 (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (-.f64 (cos.f64 x) #s(literal -1 binary64))))
(/.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 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 x)) (-.f64 (cos.f64 x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(neg.f64 (/.f64 (sin.f64 x) (neg.f64 (-.f64 (cos.f64 x) #s(literal -1 binary64)))))
(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)))
(sin.f64 x)
(/.f64 (neg.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal -1 binary64))) (neg.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal -1 binary64)) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (cos.f64 x) #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)))))

eval20.0ms (0.5%)

Memory: -7.7MiB live, 33.9MiB allocated; 8ms collecting garbage
Compiler: Compiled 2 370 to 481 computations (79.7% saved)

prune6.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	135	6	141

Accuracy

100.0%

Counts

141 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	4.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
✓	53.6%	#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 87 to 67 computations (23% saved)

simplify128.0ms (3%)

Memory

-19.1MiB live, 135.5MiB allocated; 21ms collecting garbage

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	103
0	27	95
1	63	95
2	138	95
3	318	95
4	625	95
5	1179	95
0	8492	90

Stop Event

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

Calls

Call 1

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

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

localize105.0ms (2.4%)

Memory

23.4MiB live, 122.6MiB allocated; 11ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.046875	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.2265625	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	29.807678079451406	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0546875	(.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x)
accuracy	0.2265625	(.f64 (.f64 x x) #s(literal 1/24 binary64))
accuracy	29.807678079451406	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
accuracy	32.44152224899245	#s(approx (+ (* (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64)))

Samples

44.0ms	73×	2	valid
30.0ms	122×	0	valid
10.0ms	17×	3	valid
10.0ms	43×	1	valid
1.0ms	1×	4	valid

Compiler

Compiled 67 to 18 computations (73.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-cos: 22.0ms (29.2% of total)

ival-sub: 15.0ms (19.9% of total)

adjust: 12.0ms (15.9% of total)

ival-sin: 9.0ms (12% of total)

ival-mult: 8.0ms (10.6% of total)

const: 4.0ms (5.3% of total)

ival-div: 3.0ms (4% of total)

ival-add: 2.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series69.0ms (1.6%)

Memory

-42.3MiB live, 4.6MiB allocated; 3ms collecting garbage

Counts

9 → 21

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

65.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify219.0ms (5%)

Memory

36.9MiB live, 213.1MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	297
1	190	297
2	627	297
3	3153	297
0	8109	273

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 21

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 (* (+ (* (* 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) 1/24) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin 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 (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (+ (* (* 1/24 (* x x)) x) (* 1/2 x)) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))

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

rewrite50.0ms (1.1%)

Memory

-3.7MiB live, 42.9MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	95
0	27	87
1	108	87
0	754	82

Stop Event

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

Counts

9 → 66

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
(.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x)
(.f64 x #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) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(.f64 (.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) x) x)
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1/24 binary64)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/24 binary64) x))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(.f64 x (-.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #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 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/48 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/13824 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) 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 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))) (pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (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 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))) (pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 x x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal -1/2 binary64) x))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/13824 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))) (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #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 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))) (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)))))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(.f64 (.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) x) x)
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1/24 binary64)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/24 binary64) x))
(*.f64 (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)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))

eval9.0ms (0.2%)

Memory: 14.5MiB live, 14.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 989 to 332 computations (83.3% saved)

prune6.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	85	6	91

Accuracy

100.0%

Counts

91 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #s(literal 1/2 binary64) x)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	4.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
✓	53.6%	#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 181 to 102 computations (43.6% saved)

regimes7.0ms (0.2%)

Memory

-37.3MiB live, 9.3MiB allocated; 2ms collecting garbage

Counts

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

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

Calls

2 calls:

4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
2.0ms	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

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Accuracy

Total -31.5b remaining (-106.1%)

Threshold costs -31.5b (-106.1%)

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 #s(approx (+ ( (* x x) 1/24) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 #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
53.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
53.6%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify23.0ms (0.5%)

Memory

21.6MiB live, 21.6MiB allocated; 0ms 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))

derivations84.0ms (1.9%)

Memory

0.8MiB live, 53.9MiB allocated; 13ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 11 computations (52.2% saved)

preprocess23.0ms (0.5%)

Memory: -15.1MiB live, 30.7MiB allocated; 5ms 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%)

analyze113.0ms (2.6%)

sample2.2s (50.5%)

explain151.0ms (3.5%)

preprocess175.0ms (4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify146.0ms (3.4%)

localize55.0ms (1.3%)

series3.0ms (0.1%)

simplify183.0ms (4.2%)

rewrite70.0ms (1.6%)

eval6.0ms (0.1%)

prune3.0ms (0.1%)

simplify110.0ms (2.5%)

localize103.0ms (2.4%)

series13.0ms (0.3%)

simplify218.0ms (5%)

rewrite50.0ms (1.2%)

eval20.0ms (0.5%)

prune6.0ms (0.1%)

simplify128.0ms (3%)

localize105.0ms (2.4%)

series69.0ms (1.6%)

simplify219.0ms (5%)

rewrite50.0ms (1.1%)

eval9.0ms (0.2%)

prune6.0ms (0.1%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

simplify23.0ms (0.5%)

derivations84.0ms (1.9%)

preprocess23.0ms (0.5%)

end0.0ms (0%)

Profiling