Metrics for Hyperbolic secant

analyze2.0ms (0.1%)

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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample752.0ms (41.9%)

Results

741.0ms

8256×

body

256

valid

Bogosity

preprocess214.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

455×	`distribute-lft-neg-in`
436×	`*-commutative`
436×	`fma-def`
362×	`associate-r`
302×	`swap-sqr`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	33	124
2	55	124
3	88	124
4	162	124
5	354	124
6	904	124
7	2673	124
8	3655	124
9	4881	124
10	6693	124

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(abs x)

Compiler

Compiled 34 to 16 computations (52.9% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize33.0ms (1.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 25 to 9 computations (64% saved)

series2.0ms (0.1%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite196.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

58×	`*-un-lft-identity`
55×	`add-cbrt-cube`
53×	`add-exp-log`
53×	`pow1`
52×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2151	20

Stop Event

1×

unsound

Counts

1 → 11

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

simplify81.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def`
609×	`distribute-lft-in`
604×	`distribute-rgt-in`
385×	`associate-+l+`
364×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	253
1	72	249
2	154	245
3	340	241
4	1133	241
5	2479	241
6	3309	241
7	5882	241

Stop Event

1×	node limit

Counts

19 → 24

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (*.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -61/720 (pow.f64 x 6) (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1)))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 5/24 -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4

eval5.0ms (0.3%)

Compiler: Compiled 180 to 149 computations (17.2% saved)

prune6.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Accuracy

100.0%

Counts

25 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize39.0ms (2.2%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 -1/2 (pow.f64 x 2))

Compiler

Compiled 21 to 17 computations (19% saved)

series1.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 -1/2 (pow.f64 x 2))
0.0ms	x	@	inf	(*.f64 -1/2 (pow.f64 x 2))
0.0ms	x	@	-inf	(*.f64 -1/2 (pow.f64 x 2))

rewrite172.0ms (9.6%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`associate-+l+`
557×	`associate-r`
408×	`associate-l`
228×	`+-commutative`
213×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	71	16
2	718	16
3	7485	16

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))

Outputs
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) -1))
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 -1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2) (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))

simplify52.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-+l-`
517×	`distribute-lft-out`
487×	`associate-+r-`
473×	`*-commutative`
426×	`associate-/r*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	807
1	214	795
2	675	782
3	3367	734

Stop Event

1×	node limit

Counts

29 → 40

Calls

Call 1

Inputs
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) -1))
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 -1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2) (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))

Outputs
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) -1))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 -1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (/.f64 1 (exp.f64 (pow.f64 x 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 x 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))))
(+.f64 (log.f64 (cbrt.f64 (/.f64 1 (exp.f64 (pow.f64 x 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 x 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2))
(/.f64 (fma.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -1/2 (pow.f64 x 2) 1) -1) (fma.f64 -1/2 (pow.f64 x 2) 2))
(/.f64 (fma.f64 -1/2 (pow.f64 x 2) 2) (/.f64 (fma.f64 -1/2 (pow.f64 x 2) 2) (*.f64 -1/2 (pow.f64 x 2))))
(.f64 (/.f64 (fma.f64 -1/2 (pow.f64 x 2) 2) (fma.f64 -1/2 (pow.f64 x 2) 2)) (.f64 -1/2 (pow.f64 x 2)))
(/.f64 (*.f64 (pow.f64 x 4) 1/4) (fma.f64 -1/2 (pow.f64 x 2) 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 2) (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) 3) -1) (+.f64 (*.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -1/2 (pow.f64 x 2) 1)) (fma.f64 -1/2 (pow.f64 x 2) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) 3)) (fma.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -1/2 (pow.f64 x 2) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -1/2 (pow.f64 x 2) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) 3)) (+.f64 3 (*.f64 (pow.f64 x 4) 1/4)))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(*.f64 -1/2 (pow.f64 x 2))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(*.f64 -1/2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(*.f64 -1/2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(log.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(*.f64 -1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))
(*.f64 -1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(*.f64 -1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))

eval15.0ms (0.8%)

Compiler: Compiled 604 to 531 computations (12.1% saved)

prune7.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	40	5	45

Accuracy

100.0%

Counts

45 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	0	0
Done	2	2
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune11.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	0	0
Done	2	2
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	48.4%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	48.9%	1
	10.6%	1/2
	53.5%	0

Compiler

Compiled 42 to 36 computations (14.3% saved)

regimes12.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

3 calls:

4.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 37 to 29 computations (21.6% saved)

regimes8.0ms (0.4%)

Counts

4 → 2

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))

Outputs
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes9.0ms (0.5%)

Counts

3 → 2

Calls

Call 1

Inputs
0
1/2
1

Outputs
1
0

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
99.2%	2	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes6.0ms (0.4%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1/2

Outputs
1/2
0

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
60.9%	2	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
53.5%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch17.0ms (0.9%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.15222660471464408	183.4603664343399

Results

15.0ms

128×

body

256

valid

Compiler

Compiled 109 to 98 computations (10.1% saved)

bsearch16.0ms (0.9%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	183.4603664343399	98744.94802489175

Results

14.0ms

128×

body

256

valid

Compiler

Compiled 61 to 58 computations (4.9% saved)

bsearch15.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	183.4603664343399	98744.94802489175

Results

13.0ms

128×

body

256

valid

Compiler

Compiled 61 to 58 computations (4.9% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
3×	`+-commutative`
2×	`*-commutative`
1×	`sub-neg`
1×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	95
1	39	95
2	41	95
3	42	95

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 6530219459687219/4503599627370496) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 6530219459687219/4503599627370496) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Compiler

Compiled 38 to 32 computations (15.8% saved)

soundness64.0ms (3.5%)

Rules

58×	`*-un-lft-identity`
58×	`*-un-lft-identity`
55×	`add-cbrt-cube`
55×	`add-cbrt-cube`
53×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2151	20
0	12	20
1	144	20
2	2151	20

Stop Event

1×	unsound
1×	unsound

end0.0ms (0%)

preprocess47.0ms (2.6%)

Remove: (abs x)
Compiler: Compiled 104 to 84 computations (19.2% saved)

analyze2.0ms (0.1%)

sample752.0ms (41.9%)

preprocess214.0ms (11.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize33.0ms (1.8%)

series2.0ms (0.1%)

rewrite196.0ms (10.9%)

simplify81.0ms (4.5%)

eval5.0ms (0.3%)

prune6.0ms (0.3%)

localize39.0ms (2.2%)

series1.0ms (0.1%)

rewrite172.0ms (9.6%)

simplify52.0ms (2.9%)

eval15.0ms (0.8%)

prune7.0ms (0.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune11.0ms (0.6%)

regimes12.0ms (0.7%)

regimes8.0ms (0.4%)

regimes9.0ms (0.5%)

regimes6.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch17.0ms (0.9%)

bsearch16.0ms (0.9%)

bsearch15.0ms (0.8%)

simplify5.0ms (0.3%)

soundness64.0ms (3.5%)

end0.0ms (0%)

preprocess47.0ms (2.6%)

Profiling