Metrics for expq2 (section 3.11)

analyze102.0ms (4.1%)

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
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)

sample1.8s (70.4%)

Results

826.0ms	2727×	body	1024	valid
542.0ms	3829×	body	256	valid
172.0ms	1394×	body	512	valid
133.0ms	2574×	body	256	unsamplable
75.0ms	304×	body	2048	valid
0.0ms	2×	body	2048	infinite

Bogosity

preprocess47.0ms (1.9%)

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	53
1	23	53
2	31	53
3	42	53
4	77	49
5	221	47
6	1173	47
7	4992	45

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.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 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 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize21.0ms (0.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 12 to 5 computations (58.3% saved)

series2.0ms (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))

rewrite51.0ms (2%)

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))))

simplify57.0ms (2.3%)

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 (0.3%)

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

prune7.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Accuracy

99.0%

Counts

46 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	64.5%	(/.f64 1 x)
▶	64.6%	(+.f64 (/.f64 1 x) 1/2)
▶	64.6%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	64.5%	(/.f64 1 x)
▶	64.6%	(+.f64 (/.f64 1 x) 1/2)
▶	64.6%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize52.0ms (2.1%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	99.5%	(*.f64 1/12 x)

Compiler

Compiled 44 to 32 computations (27.3% saved)

series2.0ms (0.1%)

Counts

2 → 3

Calls

6 calls:

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

rewrite61.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1712×	`pow1`
1596×	`add-exp-log`
1596×	`log1p-expm1-u`
1596×	`expm1-log1p-u`
1564×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	172	22
2	2217	22

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(*.f64 1/12 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 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 (*.f64 1/1728 (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (pow.f64 (*.f64 1/12 x) 2))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (*.f64 1/1728 (pow.f64 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 (fma.f64 1/12 x (/.f64 1 x))) 1)
(-.f64 (/.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(*.f64 1 (fma.f64 1/12 x (/.f64 1 x)))
(*.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(*.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(*.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x)))))
(.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))) (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))
(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (.f64 1/12 x) 2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (-.f64 (.f64 1/12 x) (/.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))) (neg.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (.f64 1/12 x) 2)) (-.f64 (/.f64 1 x) (.f64 1/12 x)))
(pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)
(pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)
(sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))
(log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))
(cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))
(exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))
(log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/12 x) 2)) (cbrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))
(fma.f64 (sqrt.f64 (.f64 1/12 x)) (sqrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))

simplify65.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1708×	`fma-neg`
1078×	`div-sub`
872×	`associate-r`
818×	`associate-l`
730×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1443
1	254	1191
2	875	1027
3	5337	1003

Stop Event

1×	node limit

Counts

49 → 60

Calls

Call 1

Inputs
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(-.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 (*.f64 1/1728 (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(sqrt.f64 (pow.f64 (*.f64 1/12 x) 2))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(cbrt.f64 (*.f64 1/1728 (pow.f64 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 (fma.f64 1/12 x (/.f64 1 x))) 1)
(-.f64 (/.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(*.f64 1 (fma.f64 1/12 x (/.f64 1 x)))
(*.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(*.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(*.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x)))))
(.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))) (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))
(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (.f64 1/12 x) 2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (-.f64 (.f64 1/12 x) (/.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))) (neg.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (.f64 1/12 x) 2)) (-.f64 (/.f64 1 x) (.f64 1/12 x)))
(pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)
(pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)
(sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))
(log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))
(cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))
(expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))
(exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))
(log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/12 x) 2)) (cbrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))
(fma.f64 (sqrt.f64 (.f64 1/12 x)) (sqrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))

Outputs
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(-.f64 (+.f64 1 (*.f64 1/12 x)) 1)
(*.f64 x 1/12)
(pow.f64 (*.f64 1/12 x) 1)
(*.f64 x 1/12)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(*.f64 x 1/12)
(pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)
(cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(*.f64 x 1/12)
(sqrt.f64 (pow.f64 (*.f64 1/12 x) 2))
(*.f64 x 1/12)
(log.f64 (pow.f64 (exp.f64 1/12) x))
(*.f64 x 1/12)
(cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(exp.f64 (log.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(-.f64 (+.f64 1 (fma.f64 1/12 x (/.f64 1 x))) 1)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(-.f64 (/.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(*.f64 1 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x)))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (+.f64 (pow.f64 (.f64 x 1/12) 2) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (.f64 (.f64 x x) 1/144) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))) (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (+.f64 (pow.f64 (.f64 x 1/12) 2) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (.f64 (.f64 x x) 1/144) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (+.f64 (pow.f64 (.f64 x 1/12) 2) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (.f64 (.f64 x x) 1/144) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (.f64 1/12 x) 2) (/.f64 (*.f64 1/12 x) x))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (+.f64 (pow.f64 (.f64 x 1/12) 2) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (.f64 (.f64 x x) 1/144) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2)) (-.f64 (.f64 1/12 x) (/.f64 1 x)))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (pow.f64 (.f64 1/12 x) 2) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (+.f64 (pow.f64 (.f64 x 1/12) 2) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (.f64 (.f64 x x) 1/144) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 1/12 x) 2) (pow.f64 x -2))) (neg.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (.f64 1/12 x) 2)) (-.f64 (/.f64 1 x) (.f64 1/12 x)))
(/.f64 (-.f64 (pow.f64 (.f64 x 1/12) 2) (pow.f64 x -2)) (-.f64 (.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/12 x) 2)) (cbrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 x)))
(fma.f64 (sqrt.f64 (.f64 1/12 x)) (sqrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))
(+.f64 1 (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) 0)
(fma.f64 x 1/12 (/.f64 1 x))

eval19.0ms (0.8%)

Compiler: Compiled 890 to 702 computations (21.1% saved)

prune10.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	60	4	64

Accuracy

99.0%

Counts

64 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	64.5%	(/.f64 1 x)
✓	64.6%	(+.f64 (/.f64 1 x) 1/2)
✓	64.6%	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Compiler

Compiled 56 to 40 computations (28.6% saved)

regimes10.0ms (0.4%)

Counts

5 → 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 (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:

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

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
98.8%	1	`(exp.f64 x)`

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes4.0ms (0.2%)

Counts

3 → 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)))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
64.6%	1	`x`

Compiler

Compiled 20 to 15 computations (25% saved)

regimes5.0ms (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:

4.0ms

Results

Accuracy	Segments	Branch
64.6%	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:

3.0ms

Results

Accuracy	Segments	Branch
64.5%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.2%)

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)

soundness165.0ms (6.6%)

Rules

1156×	`associate-/r*`
1108×	`distribute-lft-in`
1078×	`fma-def`
1074×	`associate-/l*`
1042×	`fma-def`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	23	53
2	31	53
3	42	53
4	77	49
5	221	47
6	1173	47
7	4992	45
0	94	690
1	223	690
2	664	690
3	4318	690

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 24 to 16 computations (33.3% saved)

end0.0ms (0%)

preprocess46.0ms (1.8%)

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

analyze102.0ms (4.1%)

sample1.8s (70.4%)

preprocess47.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

localize21.0ms (0.9%)

series2.0ms (0.1%)

rewrite51.0ms (2%)

simplify57.0ms (2.3%)

eval8.0ms (0.3%)

prune7.0ms (0.3%)

localize52.0ms (2.1%)

series2.0ms (0.1%)

rewrite61.0ms (2.4%)

simplify65.0ms (2.6%)

eval19.0ms (0.8%)

prune10.0ms (0.4%)

regimes10.0ms (0.4%)

regimes4.0ms (0.2%)

regimes5.0ms (0.2%)

regimes3.0ms (0.1%)

simplify5.0ms (0.2%)

soundness165.0ms (6.6%)

end0.0ms (0%)

preprocess46.0ms (1.8%)

Profiling