Metrics for Hyperbolic sine

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.7s (60.7%)

Results

811.0ms	2106×	body	1024	valid
476.0ms	4024×	body	256	infinite
211.0ms	1089×	body	512	valid
98.0ms	895×	body	256	valid
51.0ms	142×	body	2048	valid

Bogosity

preprocess141.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-def`
402×	`associate-/l*`
369×	`associate-l`
352×	`associate-/r/`
285×	`difference-of-squares`

Problems

133×	No Errors
123×	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	42	124
2	90	124
3	179	124
4	439	116
5	1418	116
6	5999	116

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) 2)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) 2)
(fma.f64 -1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))
(fma.f64 (exp.f64 x) -1/2 (/.f64 1/2 (exp.f64 x)))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) 2))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))

Symmetry

(negabs x)

Compiler

Compiled 34 to 16 computations (52.9% saved)

eval1.0ms (0%)

Compiler: Compiled 25 to 15 computations (40% saved)

prune3.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize52.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	55.6%	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 25 to 9 computations (64% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite139.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

51×	`add-exp-log`
51×	`add-log-exp`
51×	`log1p-expm1-u`
51×	`expm1-log1p-u`
49×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	118	14
2	1868	14

Stop Event

1×

unsound

Counts

1 → 8

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Outputs
-2
0
1/2
3/2
2
4
6
8

simplify89.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def`
676×	`unswap-sqr`
397×	`associate-*r/`
334×	`associate-r`
262×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	250
1	70	250
2	146	250
3	358	250
4	739	250
5	1698	250
6	2599	250
7	4154	250
8	6906	250

Stop Event

1×	node limit

Counts

16 → 26

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
-2
0
1/2
3/2
2
4
6
8

Outputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 2 x (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 2 x (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/2520 (pow.f64 x 7)))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
-2
0
1/2
3/2
2
4
6
8

eval7.0ms (0.3%)

Compiler: Compiled 298 to 243 computations (18.5% saved)

prune12.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	6	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	7	27

Accuracy

100.0%

Counts

27 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	80.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
	50.9%	(/.f64 (*.f64 2 x) 2)
▶	4.4%	(/.f64 8 2)
▶	4.4%	(/.f64 3/2 2)
▶	4.4%	(/.f64 1/2 2)
▶	3.3%	(/.f64 0 2)
✓	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	80.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
	50.9%	(/.f64 (*.f64 2 x) 2)
▶	4.4%	(/.f64 8 2)
▶	4.4%	(/.f64 3/2 2)
▶	4.4%	(/.f64 1/2 2)
▶	3.3%	(/.f64 0 2)

Compiler

Compiled 154 to 138 computations (10.4% saved)

localize190.0ms (6.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.8%	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 57 to 49 computations (14% saved)

series1.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 1/3 (pow.f64 x 3))
0.0ms	x	@	inf	(*.f64 1/3 (pow.f64 x 3))
0.0ms	x	@	-inf	(*.f64 1/3 (pow.f64 x 3))

rewrite60.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`associate-r`
431×	`associate-l`
240×	`log1p-expm1-u`
240×	`expm1-log1p-u`
233×	`unpow-prod-down`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	74	16
2	735	16

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))

Outputs
(+.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) -1)
(+.f64 0 (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (log.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2)))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)))
(-.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) (+.f64 1 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) 1) (+.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))
(pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)
(pow.f64 (*.f64 x (cbrt.f64 1/3)) 3)
(pow.f64 (*.f64 (pow.f64 x 6) 1/9) 1/2)
(pow.f64 (*.f64 (pow.f64 x 9) 1/27) 1/3)
(pow.f64 (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/3)) 2)
(pow.f64 (E.f64) (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)) 2))) (cbrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))) (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))
(fabs.f64 (*.f64 1/3 (pow.f64 x 3)))
(log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))
(cbrt.f64 (*.f64 (pow.f64 x 9) 1/27))
(expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))
(exp.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(exp.f64 (.f64 (log.f64 (.f64 x (cbrt.f64 1/3))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 9) 1/27)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 3/2) (sqrt.f64 1/3))) 2))
(log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))

simplify54.0ms (2%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-*r/`
499×	`distribute-lft-out`
439×	`fma-neg`
367×	`distribute-rgt-out`
291×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	829
1	224	607
2	627	590
3	3156	590

Stop Event

1×	node limit

Counts

25 → 31

Calls

Call 1

Inputs
(+.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) -1)
(+.f64 0 (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (log.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2)))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)))
(-.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) (+.f64 1 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) 1) (+.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))
(pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)
(pow.f64 (*.f64 x (cbrt.f64 1/3)) 3)
(pow.f64 (*.f64 (pow.f64 x 6) 1/9) 1/2)
(pow.f64 (*.f64 (pow.f64 x 9) 1/27) 1/3)
(pow.f64 (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/3)) 2)
(pow.f64 (E.f64) (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)) 2))) (cbrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))) (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))
(fabs.f64 (*.f64 1/3 (pow.f64 x 3)))
(log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))
(cbrt.f64 (*.f64 (pow.f64 x 9) 1/27))
(expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))
(exp.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(exp.f64 (.f64 (log.f64 (.f64 x (cbrt.f64 1/3))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 9) 1/27)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 3/2) (sqrt.f64 1/3))) 2))
(log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))

Outputs
(+.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) -1)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 0 (*.f64 1/3 (pow.f64 x 3)))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (log.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2)))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 1/6)))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(-.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) 1)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) (+.f64 1 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 3) -1) (fma.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (+.f64 1 (.f64 1/3 (pow.f64 x 3))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) 1) 3)) (fma.f64 (fma.f64 1/3 (pow.f64 x 3) 1) (fma.f64 1/3 (pow.f64 x 3) 1) (+.f64 (*.f64 1/3 (pow.f64 x 3)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) 1) 3)) (+.f64 1 (*.f64 (fma.f64 1/3 (pow.f64 x 3) 1) (fma.f64 1/3 (pow.f64 x 3) 2))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) (+.f64 1 (.f64 1/3 (pow.f64 x 3)))) 1) (+.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(pow.f64 (*.f64 x (cbrt.f64 1/3)) 3)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(pow.f64 (*.f64 (pow.f64 x 6) 1/9) 1/2)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(pow.f64 (*.f64 (pow.f64 x 9) 1/27) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 9) 1/27))
(cbrt.f64 (*.f64 1/27 (pow.f64 x 9)))
(pow.f64 (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/3)) 2)
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(pow.f64 (E.f64) (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)) 2))) (cbrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))) (sqrt.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3))))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(fabs.f64 (*.f64 1/3 (pow.f64 x 3)))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))
(cbrt.f64 (*.f64 (pow.f64 x 9) 1/27))
(cbrt.f64 (*.f64 1/27 (pow.f64 x 9)))
(expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(exp.f64 (fma.f64 3 (log.f64 x) (log.f64 1/3)))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(exp.f64 (.f64 (log.f64 (.f64 x (cbrt.f64 1/3))) 3))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 9) 1/27)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 9) 1/27))
(cbrt.f64 (*.f64 1/27 (pow.f64 x 9)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 3/2) (sqrt.f64 1/3))) 2))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))
(log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))
(+.f64 1 (+.f64 (*.f64 1/3 (pow.f64 x 3)) -1))
(*.f64 1/3 (pow.f64 x 3))

eval12.0ms (0.5%)

Compiler: Compiled 572 to 488 computations (14.7% saved)

prune12.0ms (0.4%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	5	5
Done	0	1	1
Total	31	7	38

Accuracy

100.0%

Counts

38 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	80.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
▶	50.9%	(/.f64 (*.f64 2 x) 2)
✓	4.4%	(/.f64 8 2)
✓	4.4%	(/.f64 3/2 2)
✓	4.4%	(/.f64 1/2 2)
✓	3.3%	(/.f64 0 2)
✓	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	80.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
▶	50.9%	(/.f64 (*.f64 2 x) 2)
✓	4.4%	(/.f64 8 2)
✓	4.4%	(/.f64 3/2 2)
✓	4.4%	(/.f64 1/2 2)
✓	3.3%	(/.f64 0 2)

Compiler

Compiled 86 to 76 computations (11.6% saved)

localize31.0ms (1.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

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

prune4.0ms (0.2%)

Pruning

7 alts after pruning (0 fresh and 7 done)

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

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	80.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
✓	50.9%	(/.f64 (*.f64 2 x) 2)
✓	4.4%	(/.f64 8 2)
✓	4.4%	(/.f64 3/2 2)
✓	4.4%	(/.f64 1/2 2)
✓	3.3%	(/.f64 0 2)

Compiler

Compiled 80 to 70 computations (12.5% saved)

regimes22.0ms (0.8%)

Counts

7 → 2

Calls

Call 1

Inputs
(/.f64 0 2)
(/.f64 1/2 2)
(/.f64 3/2 2)
(/.f64 8 2)
(/.f64 (*.f64 2 x) 2)
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Outputs
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Calls

3 calls:

10.0ms	x
7.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
4.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Results

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

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes6.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

Inputs
(/.f64 0 2)
(/.f64 1/2 2)
(/.f64 3/2 2)
(/.f64 8 2)
(/.f64 (*.f64 2 x) 2)
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)

Outputs
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
80.4%	1	`x`

Compiler

Compiled 31 to 27 computations (12.9% saved)

regimes6.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
(/.f64 0 2)
(/.f64 1/2 2)
(/.f64 3/2 2)
(/.f64 8 2)
(/.f64 (*.f64 2 x) 2)

Outputs
(/.f64 (*.f64 2 x) 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
50.9%	1	`x`

Compiler

Compiled 20 to 18 computations (10% saved)

regimes6.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 0 2)
(/.f64 1/2 2)
(/.f64 3/2 2)
(/.f64 8 2)

Outputs
(/.f64 3/2 2)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
4.4%	1	`x`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 0 2)
(/.f64 1/2 2)

Outputs
(/.f64 1/2 2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
4.4%	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 0 2)

Outputs
(/.f64 0 2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
3.3%	1	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.2506802255239933e-6	0.17278052192233073

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	157
1	42	157
2	47	157
3	50	157
4	51	157

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 4722366482869645/1180591620717411303424) (/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
(/.f64 (*.f64 2 x) 2)
(/.f64 3/2 2)
(/.f64 1/2 2)
(/.f64 0 2)

Outputs
(if (<=.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 4722366482869645/1180591620717411303424) (/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(if (<=.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 4722366482869645/1180591620717411303424) (/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)) 2) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)) 2)
(/.f64 (*.f64 2 x) 2)
(/.f64 (*.f64 x 2) 2)
(/.f64 3/2 2)
3/4
(/.f64 1/2 2)
1/4
(/.f64 0 2)
0

Compiler

Compiled 53 to 40 computations (24.5% saved)

soundness94.0ms (3.4%)

Rules

51×	`add-exp-log`
51×	`add-log-exp`
51×	`log1p-expm1-u`
51×	`expm1-log1p-u`
51×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	118	14
2	1868	14
0	10	14
1	118	14
2	1868	14
0	10	14
1	118	14
2	1868	14

Stop Event

1×	unsound
1×	unsound
1×	unsound

end0.0ms (0%)

preprocess129.0ms (4.7%)

Compiler: Compiled 462 to 312 computations (32.5% saved)

analyze0.0ms (0%)

sample1.7s (60.7%)

preprocess141.0ms (5.1%)

eval1.0ms (0%)

prune3.0ms (0.1%)

localize52.0ms (1.9%)

series1.0ms (0%)

rewrite139.0ms (5%)

simplify89.0ms (3.2%)

eval7.0ms (0.3%)

prune12.0ms (0.4%)

localize190.0ms (6.8%)

series1.0ms (0.1%)

rewrite60.0ms (2.2%)

simplify54.0ms (2%)

eval12.0ms (0.5%)

prune12.0ms (0.4%)

localize31.0ms (1.1%)

eval0.0ms (0%)

prune4.0ms (0.2%)

regimes22.0ms (0.8%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

soundness94.0ms (3.4%)

end0.0ms (0%)

preprocess129.0ms (4.7%)

Profiling