Metrics for Hyperbolic secant

analyze0.0ms (0%)

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)

Precisions

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

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation ival-exp, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

sample1.3s (45.2%)

Results

1.2s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 513.0ms

Operation ival-exp, time spent: 212.0ms, 41.0% of total-time

Operation ival-add, time spent: 143.0ms, 28.0% of total-time

Operation ival-div, time spent: 74.0ms, 14.0% of total-time

Operation ival-neg, time spent: 62.0ms, 12.0% of total-time

Operation const, time spent: 21.0ms, 4.0% of total-time

Bogosity

preprocess189.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

2226×	`fma-neg`
1630×	`times-frac`
824×	`fma-define`
478×	`div-sub`
460×	`associate-*r/`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(exp.f64 (neg.f64 x))`
-	-	`(neg.f64 x)`
-	-	`(exp.f64 x)`
-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
-	-	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
-	-	`2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	35	124
2	67	124
3	119	124
4	247	124
5	653	124
6	2372	124
7	5958	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 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

Operation ival-exp, time spent: 7.0ms, 30.0% of total-time

Operation ival-add, time spent: 7.0ms, 30.0% of total-time

Operation ival-div, time spent: 4.0ms, 17.0% of total-time

Operation const, time spent: 2.0ms, 9.0% of total-time

Operation ival-neg, time spent: 2.0ms, 9.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize39.0ms (1.3%)

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)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

Operation ival-exp, time spent: 4.0ms, 34.0% of total-time

Operation ival-add, time spent: 4.0ms, 34.0% of total-time

Operation ival-div, time spent: 2.0ms, 17.0% of total-time

Operation const, time spent: 1.0ms, 9.0% of total-time

Operation ival-neg, time spent: 1.0ms, 9.0% of total-time

series4.0ms (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))))
1.0ms	x	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite147.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

94×	`associate-r`
62×	`add-exp-log`
62×	`add-log-exp`
62×	`log1p-expm1-u`
62×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2343	20

Stop Event

1×

unsound

Counts

1 → 10

Calls

Call 1

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

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

simplify76.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1434×	`fma-define`
806×	`associate-*l/`
766×	`distribute-lft-out`
760×	`associate-*r/`
676×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	252
1	72	248
2	137	244
3	358	240
4	1256	240
5	3139	240
6	3937	240
7	4829	240

Stop Event

1×	node limit

Counts

18 → 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
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 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (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))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (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
0
1/2
1
3/2
2
3
4

eval6.0ms (0.2%)

Compiler: Compiled 195 to 161 computations (17.4% saved)

prune5.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	3	25

Accuracy

100.0%

Counts

25 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
▶	50.7%	1
▶	52.3%	0

Compiler

Compiled 12 to 11 computations (8.3% saved)

localize49.0ms (1.7%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(pow.f64 x 2)

Compiler

Compiled 23 to 19 computations (17.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

Operation ival-pow, time spent: 9.0ms, 46.0% of total-time

Operation ival-mult, time spent: 4.0ms, 21.0% of total-time

Operation ival-add, time spent: 3.0ms, 15.0% of total-time

Operation const, time spent: 3.0ms, 15.0% of total-time

series8.0ms (0.3%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(pow.f64 x 2)
1.0ms	x	@	-inf	(pow.f64 x 2)
1.0ms	x	@	0	(pow.f64 x 2)

rewrite122.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1350×	`fma-define`
793×	`log1p-expm1-u`
793×	`expm1-log1p-u`
680×	`fma-neg`
448×	`log1p-undefine`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	48	10
2	460	10
3	4331	10

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

Inputs
(pow.f64 x 2)

Outputs
(+.f64 (fma.f64 x x 1) -1)
(+.f64 0 (pow.f64 x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))))
(-.f64 (fma.f64 x x 1) 1)
(*.f64 x x)
(*.f64 (pow.f64 x 2) 1)
(*.f64 (pow.f64 x 2) (log.f64 (E.f64)))
(*.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 5))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (pow.f64 x 3/2)))
(*.f64 (sqrt.f64 x) (pow.f64 x 3/2))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x 8))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (sqrt.f64 x))
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (pow.f64 x 3/2)))
(*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x))
(*.f64 (pow.f64 1 1/3) (pow.f64 x 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 5)) (cbrt.f64 x))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (cbrt.f64 (pow.f64 x 8)))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(.f64 (.f64 (pow.f64 x 3/2) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (.f64 (pow.f64 x 3/2) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 x 1/6)) (pow.f64 x 1/6))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (cbrt.f64 x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x 1) 3) 1) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) (+.f64 1 (fma.f64 x x 1))))
(/.f64 (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) -1) (+.f64 (fma.f64 x x 1) 1))
(sqrt.f64 (pow.f64 x 4))
(fabs.f64 (pow.f64 x 2))
(log.f64 (exp.f64 (pow.f64 x 2)))
(cbrt.f64 (pow.f64 x 6))
(expm1.f64 (log1p.f64 (pow.f64 x 2)))
(log1p.f64 (expm1.f64 (pow.f64 x 2)))
(exp.f64 (log.f64 (pow.f64 x 2)))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 x 6)) 1/3))
(fma.f64 1 (fma.f64 x x 1) -1)
(fma.f64 (fma.f64 x x 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (fma.f64 x x 1))) (cbrt.f64 (fma.f64 x x 1)) -1)
(fma.f64 (hypot.f64 1 x) (hypot.f64 1 x) -1)

simplify94.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1844×	`fma-neg`
1364×	`distribute-lft-in`
1204×	`distribute-rgt-in`
1136×	`log-prod`
710×	`associate-+r+`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	1359
1	263	975
2	600	958
3	2237	933
4	6941	929

Stop Event

1×	node limit

Counts

44 → 70

Calls

Call 1

Inputs
(+.f64 (fma.f64 x x 1) -1)
(+.f64 0 (pow.f64 x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))))
(-.f64 (fma.f64 x x 1) 1)
(*.f64 x x)
(*.f64 (pow.f64 x 2) 1)
(*.f64 (pow.f64 x 2) (log.f64 (E.f64)))
(*.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 5))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (pow.f64 x 3/2)))
(*.f64 (sqrt.f64 x) (pow.f64 x 3/2))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x 8))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (sqrt.f64 x))
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (pow.f64 x 3/2)))
(*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x))
(*.f64 (pow.f64 1 1/3) (pow.f64 x 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 5)) (cbrt.f64 x))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (cbrt.f64 (pow.f64 x 8)))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(.f64 (.f64 (pow.f64 x 3/2) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (.f64 (pow.f64 x 3/2) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 x 1/6)) (pow.f64 x 1/6))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (cbrt.f64 x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x 1) 3) 1) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) (+.f64 1 (fma.f64 x x 1))))
(/.f64 (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) -1) (+.f64 (fma.f64 x x 1) 1))
(sqrt.f64 (pow.f64 x 4))
(fabs.f64 (pow.f64 x 2))
(log.f64 (exp.f64 (pow.f64 x 2)))
(cbrt.f64 (pow.f64 x 6))
(expm1.f64 (log1p.f64 (pow.f64 x 2)))
(log1p.f64 (expm1.f64 (pow.f64 x 2)))
(exp.f64 (log.f64 (pow.f64 x 2)))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 x 6)) 1/3))
(fma.f64 1 (fma.f64 x x 1) -1)
(fma.f64 (fma.f64 x x 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (fma.f64 x x 1))) (cbrt.f64 (fma.f64 x x 1)) -1)
(fma.f64 (hypot.f64 1 x) (hypot.f64 1 x) -1)

Outputs
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(+.f64 0 (pow.f64 x 2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(-.f64 (fma.f64 x x 1) 1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 x 2) 1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 x 2) (log.f64 (E.f64)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 1 (pow.f64 x 2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 5))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (pow.f64 x 3/2)))
(.f64 (.f64 (cbrt.f64 x) (pow.f64 x 1/6)) (pow.f64 x 3/2))
(.f64 (pow.f64 x 3/2) (.f64 (cbrt.f64 x) (pow.f64 x 1/6)))
(*.f64 (pow.f64 x 3/2) (pow.f64 (pow.f64 x 1/6) 3))
(*.f64 (sqrt.f64 x) (pow.f64 x 3/2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (pow.f64 (cbrt.f64 x) 4) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x 8))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x 8))) (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (cbrt.f64 (cbrt.f64 (pow.f64 x 8)))))
(*.f64 (pow.f64 x 3/2) (sqrt.f64 x))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (pow.f64 x 3/2)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 1 1/3) (pow.f64 x 2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2) 1/3) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 x 8)) 2)))
(*.f64 (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 5)) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 5)))
(*.f64 (cbrt.f64 x) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 5/2))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (cbrt.f64 (pow.f64 x 8)))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)))
(.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x 8))) (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (cbrt.f64 (cbrt.f64 (pow.f64 x 8)))))
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (.f64 (pow.f64 (cbrt.f64 x) 4) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (pow.f64 (cbrt.f64 x) 4) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (.f64 (pow.f64 x 3/2) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (.f64 (cbrt.f64 x) (pow.f64 x 1/6)) (pow.f64 x 3/2))
(.f64 (pow.f64 x 3/2) (.f64 (cbrt.f64 x) (pow.f64 x 1/6)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (pow.f64 x 3/2)))
(*.f64 (pow.f64 x 3/2) (pow.f64 (pow.f64 x 1/6) 3))
(.f64 (.f64 (pow.f64 x 3/2) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 x 1/6)) (pow.f64 x 1/6))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(.f64 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (cbrt.f64 x)))
(.f64 (pow.f64 (cbrt.f64 x) 5) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (cbrt.f64 x))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 (cbrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x 1) 3) 1) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) (+.f64 1 (fma.f64 x x 1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x 1) 3) -1) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) (+.f64 1 (fma.f64 x x 1))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x x 1) 3)) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) (+.f64 (pow.f64 x 2) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x x 1) 3)) (+.f64 1 (*.f64 (fma.f64 x x 1) (fma.f64 x x 2))))
(/.f64 (+.f64 -1 (pow.f64 (hypot.f64 1 x) 6)) (+.f64 1 (*.f64 (fma.f64 x x 1) (fma.f64 x x 2))))
(/.f64 (+.f64 -1 (pow.f64 (hypot.f64 1 x) 6)) (fma.f64 (fma.f64 x x 1) (fma.f64 x x 2) 1))
(/.f64 (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) -1) (+.f64 (fma.f64 x x 1) 1))
(/.f64 (fma.f64 (fma.f64 x x 1) (fma.f64 x x 1) -1) (+.f64 1 (fma.f64 x x 1)))
(/.f64 (*.f64 (+.f64 (pow.f64 x 2) 2) (pow.f64 x 2)) (+.f64 (pow.f64 x 2) 2))
(*.f64 (fma.f64 x x 2) (/.f64 (pow.f64 x 2) (fma.f64 x x 2)))
(/.f64 (expm1.f64 (*.f64 2 (log1p.f64 (pow.f64 x 2)))) (fma.f64 x x 2))
(sqrt.f64 (pow.f64 x 4))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(fabs.f64 (pow.f64 x 2))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(log.f64 (exp.f64 (pow.f64 x 2)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(cbrt.f64 (pow.f64 x 6))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(expm1.f64 (log1p.f64 (pow.f64 x 2)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(log1p.f64 (expm1.f64 (pow.f64 x 2)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(exp.f64 (log.f64 (pow.f64 x 2)))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 x))) 3))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(exp.f64 (*.f64 (log.f64 (pow.f64 x 6)) 1/3))
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(fma.f64 1 (fma.f64 x x 1) -1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(fma.f64 (fma.f64 x x 1) 1 -1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(fma.f64 (*.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (fma.f64 x x 1))) (cbrt.f64 (fma.f64 x x 1)) -1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)
(fma.f64 (hypot.f64 1 x) (hypot.f64 1 x) -1)
(+.f64 (fma.f64 x x 1) -1)
(pow.f64 x 2)

eval81.0ms (2.7%)

Compiler: Compiled 1057 to 814 computations (23% saved)

prune87.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	70	3	73

Accuracy

100.0%

Counts

73 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	50.7%	1
✓	52.3%	0

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize143.0ms (4.8%)

Compiler: Compiled 20 to 11 computations (45% saved)
Precisions: Click to see histograms. Total time spent on operations: 90.0ms
Operation ival-add, time spent: 82.0ms, 92.0% of total-time
Operation ival-mult, time spent: 7.0ms, 8.0% of total-time
Operation const, time spent: 1.0ms, 1.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.2%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	50.7%	1
✓	52.3%	0

Compiler

Compiled 37 to 30 computations (18.9% saved)

regimes11.0ms (0.4%)

Counts

5 → 1

Calls

Call 1

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

6.0ms	x
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(/.f64 2 (+.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 18 to 13 computations (27.8% saved)

regimes7.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes23.0ms (0.8%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1

Outputs
1
0

Calls

1 calls:

22.0ms

Results

Accuracy	Segments	Branch
99.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

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
52.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch33.0ms (1.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
33.0ms	7.241559830028355e-6	9257.552687315396

Results

30.0ms	143×	0	valid
0.0ms	1×	0	valid

Compiler

Compiled 121 to 100 computations (17.4% saved)

Precisions

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

Operation ival-exp, time spent: 4.0ms, 49.0% of total-time

Operation ival-add, time spent: 2.0ms, 24.0% of total-time

Operation ival-div, time spent: 1.0ms, 12.0% of total-time

Operation ival-neg, time spent: 1.0ms, 12.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch131.0ms (4.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
131.0ms	7.241559830028355e-6	9257.552687315396

Results

128.0ms	143×	0	valid
0.0ms	1×	0	valid

Compiler

Compiled 67 to 64 computations (4.5% saved)

Precisions

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

Operation ival-exp, time spent: 3.0ms, 40.0% of total-time

Operation ival-add, time spent: 2.0ms, 27.0% of total-time

Operation ival-div, time spent: 1.0ms, 13.0% of total-time

Operation ival-neg, time spent: 1.0ms, 13.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`*-commutative`
3×	`1-exp`
2×	`sub-neg`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	84
1	37	84
2	39	84
3	40	84

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (.f64 -1/2 (.f64 x x))) 0)
(if (<=.f64 x 350) 1 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (.f64 -1/2 (.f64 x x))) 0)
(if (<=.f64 x 350) 1 0)
0

Compiler

Compiled 31 to 25 computations (19.4% saved)

soundness287.0ms (9.7%)

Rules

1350×	`fma-define`
793×	`log1p-expm1-u`
793×	`expm1-log1p-u`
680×	`fma-neg`
448×	`log1p-undefine`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	48	10
2	460	10
3	4331	10
0	12	20
1	144	20
2	2343	20

Stop Event

1×	unsound
1×	node limit

Compiler

Compiled 15 to 12 computations (20% saved)

end0.0ms (0%)

preprocess68.0ms (2.3%)

Compiler: Compiled 152 to 118 computations (22.4% saved)

analyze0.0ms (0%)

sample1.3s (45.2%)

preprocess189.0ms (6.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize39.0ms (1.3%)

series4.0ms (0.1%)

rewrite147.0ms (5%)

simplify76.0ms (2.6%)

eval6.0ms (0.2%)

prune5.0ms (0.2%)

localize49.0ms (1.7%)

series8.0ms (0.3%)

rewrite122.0ms (4.1%)

simplify94.0ms (3.2%)

eval81.0ms (2.7%)

prune87.0ms (2.9%)

localize143.0ms (4.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes11.0ms (0.4%)

regimes7.0ms (0.2%)

regimes23.0ms (0.8%)

regimes3.0ms (0.1%)

bsearch33.0ms (1.1%)

bsearch131.0ms (4.4%)

simplify5.0ms (0.2%)

soundness287.0ms (9.7%)

end0.0ms (0%)

preprocess68.0ms (2.3%)

Profiling