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)

sample1.5s (61.5%)

Results

376.0ms	4065×	256	infinite
768.0ms	2043×	1024	valid
219.0ms	1077×	512	valid
98.0ms	933×	256	valid
52.0ms	138×	2048	valid

Bogosity

preprocess228.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

1024×	`fma-def`
804×	`associate-/l*`
738×	`associate-l`
704×	`associate-/r/`
570×	`difference-of-squares`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
128	0	-	-	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	0	-	-	`x`
0	2	(437.1538754056574)	-	`(exp.f64 (neg.f64 x))`
0	0	-	-	`(neg.f64 x)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`2`
0	0	-	-	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)`

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 59 to 25 computations (57.6% saved)

eval1.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize59.0ms (2.4%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	53.5%	(-.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)))

rewrite148.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

78×	`associate-r`
51×	`add-exp-log`
51×	`add-log-exp`
51×	`log1p-expm1-u`
51×	`expm1-log1p-u`

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

simplify90.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-def`
1352×	`unswap-sqr`
794×	`associate-*r/`
668×	`associate-r`
524×	`*-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)

prune10.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Accuracy

100.0%

Counts

27 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	84.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
▶	52.7%	(/.f64 (*.f64 2 x) 2)
▶	4.2%	(/.f64 8 2)
▶	4.2%	(/.f64 1/2 2)
▶	3.4%	(/.f64 0 2)

Compiler

Compiled 69 to 61 computations (11.6% saved)

localize99.0ms (4%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 62 to 51 computations (17.7% saved)

series2.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite60.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1000×	`associate-r`
862×	`associate-l`
472×	`unpow-prod-down`
306×	`log-prod`
278×	`cbrt-prod`

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 (pow.f64 (cbrt.f64 (cbrt.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 (pow.f64 (cbrt.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 (2.2%)

Algorithm

1×	egg-herbie

Rules

1352×	`associate-*r/`
990×	`distribute-lft-out`
868×	`fma-neg`
718×	`distribute-rgt-out`
582×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	858
1	222	617
2	627	600
3	3120	600

Stop Event

1×	node limit

Counts

25 → 33

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 (pow.f64 (cbrt.f64 (cbrt.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 (pow.f64 (cbrt.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 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))
(*.f64 3 (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 (pow.f64 (cbrt.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))
(+.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))

eval17.0ms (0.7%)

Compiler: Compiled 610 to 521 computations (14.6% saved)

prune7.0ms (0.3%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	33	6	39

Accuracy

100.0%

Counts

39 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.6%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	84.4%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) 2)
✓	52.7%	(/.f64 (*.f64 2 x) 2)
✓	4.2%	(/.f64 8 2)
✓	4.2%	(/.f64 1/2 2)
✓	3.4%	(/.f64 0 2)

Compiler

Compiled 73 to 63 computations (13.7% saved)

regimes20.0ms (0.8%)

Counts

6 → 2

Calls

Call 1

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

9.0ms	x
7.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
3.0ms	(/.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 18 to 13 computations (27.8% saved)

regimes12.0ms (0.5%)

Counts

5 → 1

Calls

Call 1

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

11.0ms

Results

Accuracy	Segments	Branch
84.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
52.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(/.f64 1/2 2)

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
4.2%	1	`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
(/.f64 0 2)

Outputs
(/.f64 0 2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
3.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.0822424527722205e-5	2.74183365920909e+52

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
8×	`*-commutative`
6×	`sub-neg`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	156
1	39	156
2	44	156
3	47	156
4	48	156

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 5902958103587057/147573952589676412928) (/.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 1/2 2)
(/.f64 0 2)

Outputs
(if (<=.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 5902958103587057/147573952589676412928) (/.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))) 5902958103587057/147573952589676412928) (/.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 1/2 2)
1/4
(/.f64 0 2)
0

Compiler

Compiled 51 to 38 computations (25.5% saved)

soundness61.0ms (2.4%)

Rules

78×	`associate-r`
78×	`associate-r`
51×	`add-exp-log`
51×	`add-log-exp`
51×	`log1p-expm1-u`

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

Stop Event

1×	unsound
1×	unsound

end0.0ms (0%)

preprocess62.0ms (2.5%)

Compiler: Compiled 402 to 272 computations (32.3% saved)

analyze0.0ms (0%)

sample1.5s (61.5%)

preprocess228.0ms (9.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize59.0ms (2.4%)

series1.0ms (0%)

rewrite148.0ms (5.9%)

simplify90.0ms (3.6%)

eval7.0ms (0.3%)

prune10.0ms (0.4%)

localize99.0ms (4%)

series2.0ms (0.1%)

rewrite60.0ms (2.4%)

simplify54.0ms (2.2%)

eval17.0ms (0.7%)

prune7.0ms (0.3%)

regimes20.0ms (0.8%)

regimes12.0ms (0.5%)

regimes4.0ms (0.2%)

regimes6.0ms (0.3%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

soundness61.0ms (2.4%)

end0.0ms (0%)

preprocess62.0ms (2.5%)

Profiling