Metrics for expq2 (section 3.11)

analyze69.0ms (3.6%)

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
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
53.1%	53.1%	46.9%	0%	0%	0%	0%	6
54.7%	54.7%	45.3%	0%	0%	0%	0%	7
55.5%	55.4%	44.5%	0%	0%	0%	0%	8
55.9%	55.8%	44.1%	0%	0%	0%	0%	9
56.1%	56%	43.9%	0%	0%	0%	0%	10
56.2%	56.1%	43.8%	0%	0%	0%	0%	11
56.2%	56.2%	43.8%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.2s (64.6%)

Results

537.0ms	2659×	body	1024	valid
306.0ms	3958×	body	256	valid
168.0ms	1334×	body	512	valid
148.0ms	2663×	body	256	unsamplable
68.0ms	304×	body	2048	valid
0.0ms	1×	body	2048	infinite

Bogosity

preprocess44.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1156×	`associate-/r*`
1108×	`distribute-lft-in`
1078×	`fma-def`
1074×	`associate-/l*`
1036×	`distribute-rgt-in`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	23	38
2	31	38
3	42	38
4	77	34
5	221	32
6	1173	32
7	4992	30

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1))

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 (exp.f64 (neg.f64 x)) (expm1.f64 (neg.f64 x)))
(/.f64 1 (fma.f64 (exp.f64 x) -1 1))
(/.f64 1 (-.f64 1 (exp.f64 x)))
(/.f64 1 (neg.f64 (expm1.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	14	15
2	15	15

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accurracy

100.0%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize21.0ms (1.1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 12 to 5 computations (58.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	x	@	0	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite52.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1382×	`pow1`
1268×	`add-exp-log`
1268×	`log1p-expm1-u`
1266×	`expm1-log1p-u`
1238×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	137	15
2	1723	15

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Outputs
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(*.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

simplify51.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1042×	`fma-def`
1032×	`associate-r`
918×	`associate-l`
576×	`distribute-lft-neg-out`
558×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	690
1	223	690
2	664	690
3	4318	690

Stop Event

1×	node limit

Counts

42 → 45

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(*.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
(/.f64 (exp.f64 x) (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval8.0ms (0.4%)

Compiler: Compiled 452 to 207 computations (54.2% saved)

prune9.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Accurracy

100.0%

Counts

46 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	65.0%	(/.f64 1 x)
▶	65.3%	(+.f64 (/.f64 1 x) 1/2)
▶	65.4%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	65.3%	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	65.0%	(/.f64 1 x)
▶	65.3%	(+.f64 (/.f64 1 x) 1/2)
▶	65.4%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	65.3%	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))

Compiler

Compiled 84 to 66 computations (21.4% saved)

localize118.0ms (6.1%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.4%	(*.f64 1/12 x)
✓	99.5%	(*.f64 -1/720 (pow.f64 x 3))
✓	99.4%	(*.f64 1/12 x)

Compiler

Compiled 99 to 74 computations (25.3% saved)

series2.0ms (0.1%)

Counts

3 → 0

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 1/12 x)
0.0ms	x	@	0	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	inf	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	-inf	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	-inf	(*.f64 1/12 x)

rewrite57.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1540×	`pow1`
1442×	`add-exp-log`
1442×	`log1p-expm1-u`
1442×	`expm1-log1p-u`
1412×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	190	27
2	1998	27

Stop Event

1×	node limit

Counts

3 → 33

Calls

Call 1

Inputs
(*.f64 1/12 x)
(*.f64 -1/720 (pow.f64 x 3))
(*.f64 1/12 x)

Outputs
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(pow.f64 (*.f64 1/12 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(exp.f64 (log.f64 (*.f64 1/12 x)))
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(-.f64 (+.f64 1 (*.f64 -1/720 (pow.f64 x 3))) 1)
(pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)
(pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)
(pow.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))
(log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))
(exp.f64 (log.f64 (*.f64 -1/720 (pow.f64 x 3))))
(log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(pow.f64 (*.f64 1/12 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(exp.f64 (log.f64 (*.f64 1/12 x)))
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))

simplify46.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1586×	`log-prod`
1464×	`distribute-rgt-in`
1456×	`distribute-lft-in`
1126×	`associate-r`
972×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	693
1	158	495
2	542	297
3	3351	297

Stop Event

1×	node limit

Counts

33 → 28

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(pow.f64 (*.f64 1/12 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(exp.f64 (log.f64 (*.f64 1/12 x)))
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(-.f64 (+.f64 1 (*.f64 -1/720 (pow.f64 x 3))) 1)
(pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)
(pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)
(pow.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))
(log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))
(exp.f64 (log.f64 (*.f64 -1/720 (pow.f64 x 3))))
(log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(pow.f64 (*.f64 1/12 x) 1)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(exp.f64 (log.f64 (*.f64 1/12 x)))
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))

Outputs
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (*.f64 1/12 x) 1)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(log.f64 (pow.f64 (exp.f64 1/12) x))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(exp.f64 (log.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(-.f64 (+.f64 1 (*.f64 -1/720 (pow.f64 x 3))) 1)
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(pow.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(cbrt.f64 (pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 3))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(exp.f64 (log.f64 (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 3)) 0)
(*.f64 -1/720 (pow.f64 x 3))
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (*.f64 1/12 x) 1)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (pow.f64 (*.f64 1/12 x) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(log.f64 (pow.f64 (exp.f64 1/12) x))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(cbrt.f64 (pow.f64 (*.f64 1/12 x) 3))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(exp.f64 (log.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(+.f64 (+.f64 1 (*.f64 1/12 x)) -1)
(+.f64 (*.f64 1/12 x) 0)
(*.f64 1/12 x)

eval18.0ms (0.9%)

Compiler: Compiled 651 to 536 computations (17.7% saved)

prune7.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	42	5	47

Accurracy

100.0%

Counts

47 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	65.0%	(/.f64 1 x)
✓	65.3%	(+.f64 (/.f64 1 x) 1/2)
✓	65.4%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	65.3%	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))

Compiler

Compiled 87 to 65 computations (25.3% saved)

regimes13.0ms (0.6%)

Counts

6 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Calls

3 calls:

5.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	x
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
100.0%	1	`(exp.f64 x)`

Compiler

Compiled 58 to 40 computations (31% saved)

regimes5.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))

Outputs
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
65.4%	1	`x`

Compiler

Compiled 35 to 27 computations (22.9% saved)

regimes3.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
65.3%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 1 x)

Outputs
(/.f64 1 x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
65.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
2×	`1-exp`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	21	60

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 x 1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(/.f64 1 x)

Compiler

Compiled 26 to 20 computations (23.1% saved)

soundness99.0ms (5.2%)

Rules

1042×	`fma-def`
1032×	`associate-r`
918×	`associate-l`
576×	`distribute-lft-neg-out`
558×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	14	15
2	15	15
0	94	690
1	223	690
2	664	690
3	4318	690

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 24 to 16 computations (33.3% saved)

end0.0ms (0%)

preprocess46.0ms (2.4%)

Compiler: Compiled 78 to 58 computations (25.6% saved)

analyze69.0ms (3.6%)

sample1.2s (64.6%)

preprocess44.0ms (2.3%)

simplify3.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize21.0ms (1.1%)

series1.0ms (0.1%)

rewrite52.0ms (2.7%)

simplify51.0ms (2.7%)

eval8.0ms (0.4%)

prune9.0ms (0.5%)

localize118.0ms (6.1%)

series2.0ms (0.1%)

rewrite57.0ms (3%)

simplify46.0ms (2.4%)

eval18.0ms (0.9%)

prune7.0ms (0.4%)

regimes13.0ms (0.6%)

regimes5.0ms (0.2%)

regimes3.0ms (0.2%)

regimes3.0ms (0.1%)

simplify5.0ms (0.3%)

soundness99.0ms (5.2%)

end0.0ms (0%)

preprocess46.0ms (2.4%)

Profiling