Metrics for sqrtexp (problem 3.4.4)

analyze121.0ms (3.7%)

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 14 to 12 computations (14.3% saved)

sample2.4s (73.3%)

Results

1.3s	2696×	body	1024	valid
522.0ms	3872×	body	256	valid
260.0ms	1334×	body	512	valid
202.0ms	2588×	body	256	unsamplable
122.0ms	300×	body	2048	valid
6.0ms	54×	body	256	infinite

Bogosity

preprocess42.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1352×	`associate-/l*`
1124×	`associate-r`
1066×	`associate-/r*`
890×	`associate-l`
680×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	48	79
2	78	79
3	157	79
4	375	67
5	1504	49

Stop Event

1×	node limit

Calls

Call 1

Inputs

(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

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

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (neg.f64 x))) 1) (-.f64 (exp.f64 (neg.f64 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 (neg.f64 x))) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x -2)) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 (neg.f64 x))) 1))
(sqrt.f64 (+.f64 1 (exp.f64 (neg.f64 x))))

Compiler

Compiled 13 to 11 computations (15.4% saved)

eval1.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize30.0ms (0.9%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	100.0%	(+.f64 1 (exp.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

series3.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(+.f64 1 (exp.f64 x))
0.0ms	x	@	0	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	0	(+.f64 1 (exp.f64 x))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite59.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1452×	`pow1`
1340×	`add-exp-log`
1340×	`log1p-expm1-u`
1340×	`expm1-log1p-u`
1312×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	157	26
2	1869	26

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

Inputs
(+.f64 1 (exp.f64 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

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

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1132×	`distribute-lft-in`
1108×	`distribute-rgt-in`
1058×	`times-frac`
954×	`fma-def`
478×	`associate-+r+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1842
1	358	1598
2	1195	1260
3	3601	1232

Stop Event

1×	node limit

Counts

66 → 98

Calls

Call 1

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

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

eval29.0ms (0.9%)

Compiler: Compiled 1223 to 875 computations (28.5% saved)

prune16.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	4	99

Accuracy

100.0%

Counts

99 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
▶	65.9%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	72.1%	(sqrt.f64 2)
▶	100.0%	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
▶	65.9%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	72.1%	(sqrt.f64 2)

Compiler

Compiled 46 to 40 computations (13% saved)

localize64.0ms (1.9%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
	100.0%	(+.f64 1 (exp.f64 x))
✓	100.0%	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 38 to 27 computations (28.9% saved)

series48.0ms (1.4%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
21.0ms	x	@	-inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
1.0ms	x	@	inf	(sqrt.f64 (+.f64 2 x))
0.0ms	x	@	0	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
0.0ms	x	@	0	(sqrt.f64 (+.f64 2 x))

rewrite70.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

950×	`log-prod`
624×	`prod-exp`
578×	`pow-prod-down`
524×	`pow-prod-up`
516×	`pow-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	254	28
2	3046	28

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 2 x))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)

Outputs
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(pow.f64 (pow.f64 (+.f64 2 x) 1/6) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 2) 1/4)
(pow.f64 (pow.f64 (+.f64 2 x) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 x)))))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 2 x) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (+.f64 2 x))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 2 x))) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 1)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(*.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(exp.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 3/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) 3/2))
(exp.f64 (.f64 (.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2)) 1/3))
(exp.f64 (.f64 (.f64 2 (log1p.f64 (exp.f64 x))) 3/4))
(exp.f64 (.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) 2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) 2))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) (.f64 1/2 (log1p.f64 (exp.f64 x)))))
(exp.f64 (+.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 3/4 (log1p.f64 (exp.f64 x)))))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

882×	`associate-/l*`
770×	`distribute-lft-in`
730×	`distribute-rgt-in`
720×	`times-frac`
556×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	1623
1	436	1541
2	996	1385
3	3052	1351

Stop Event

1×	node limit

Counts

79 → 96

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(pow.f64 (pow.f64 (+.f64 2 x) 1/6) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 2) 1/4)
(pow.f64 (pow.f64 (+.f64 2 x) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 x)))))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 2 x) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (+.f64 2 x))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 2 x))) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 1)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(*.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(exp.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 3/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) 3/2))
(exp.f64 (.f64 (.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2)) 1/3))
(exp.f64 (.f64 (.f64 2 (log1p.f64 (exp.f64 x))) 3/4))
(exp.f64 (.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) 2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) 2))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) (.f64 1/2 (log1p.f64 (exp.f64 x)))))
(exp.f64 (+.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 3/4 (log1p.f64 (exp.f64 x)))))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(fma.f64 3/4 (*.f64 x (sqrt.f64 8)) (sqrt.f64 8))
(.f64 (+.f64 (.f64 x 3/4) 1) (sqrt.f64 8))
(fma.f64 x (*.f64 (sqrt.f64 8) 3/4) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 (*.f64 x x) (sqrt.f64 8)) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 x (*.f64 x (sqrt.f64 8))) (sqrt.f64 8)))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 x 3/4) (.f64 x (.f64 x 15/32)))))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (.f64 x (+.f64 (*.f64 x 15/32) 3/4))))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (+.f64 (fma.f64 15/32 (.f64 (.f64 x x) (sqrt.f64 8)) (sqrt.f64 8)) (.f64 27/128 (*.f64 (pow.f64 x 3) (sqrt.f64 8)))))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 x (.f64 x (sqrt.f64 8))) (fma.f64 27/128 (.f64 (pow.f64 x 3) (sqrt.f64 8)) (sqrt.f64 8))))
(+.f64 (.f64 (+.f64 (.f64 x 3/4) 1) (sqrt.f64 8)) (.f64 (sqrt.f64 8) (+.f64 (.f64 (pow.f64 x 3) 27/128) (.f64 x (.f64 x 15/32)))))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 (.f64 x x) (+.f64 (.f64 27/128 x) 15/32)) (*.f64 x 3/4))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(sqrt.f64 (+.f64 2 x))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(sqrt.f64 (+.f64 2 x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 1/6) 3)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 2) 1/4)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 3) 1/6)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(sqrt.f64 (+.f64 2 x))
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 x)))))
(sqrt.f64 (+.f64 2 x))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(sqrt.f64 (+.f64 2 x))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1) 1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1/2) 1))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1) 1))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 2 x) 1/6)) 3))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (+.f64 2 x))) 1/3))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 2 x))) 2))
(sqrt.f64 (+.f64 2 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) 1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 1 (exp.f64 x)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 3/2 (log1p.f64 (exp.f64 x))) 1))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))) 1) 1))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 9/2)) 1/3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 2 (log1p.f64 (exp.f64 x))) 3/4))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) 2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) 2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) (.f64 1/2 (log1p.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (+.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 1)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (+.f64 (.f64 3/4 (log1p.f64 (exp.f64 x))) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 3/4 (log1p.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) 3/4) (.f64 (log1p.f64 (exp.f64 x)) 3/4)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)

eval53.0ms (1.6%)

Compiler: Compiled 1923 to 1493 computations (22.4% saved)

prune19.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	149	4	153

Accuracy

100.0%

Counts

153 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
✓	65.9%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	72.1%	(sqrt.f64 2)

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes10.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

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

Calls

3 calls:

4.0ms	x
2.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes4.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes5.0ms (0.2%)

Accuracy

Total -4.4b remaining (-24.7%)

Threshold costs -4.4b (-24.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))

Outputs
(sqrt.f64 2)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
72.1%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	4294967315
1	17	4294967315

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

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

Compiler

Compiled 18 to 16 computations (11.1% saved)

soundness139.0ms (4.2%)

Rules

1452×	`pow1`
1352×	`associate-/l*`
1340×	`add-exp-log`
1340×	`log1p-expm1-u`
1340×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	48	79
2	78	79
3	157	79
4	375	67
5	1504	49
0	8	26
1	157	26
2	1869	26

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 187 to 129 computations (31% saved)

end0.0ms (0%)

preprocess33.0ms (1%)

Compiler: Compiled 58 to 48 computations (17.2% saved)

analyze121.0ms (3.7%)

sample2.4s (73.3%)

preprocess42.0ms (1.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize30.0ms (0.9%)

series3.0ms (0.1%)

rewrite59.0ms (1.8%)

simplify64.0ms (1.9%)

eval29.0ms (0.9%)

prune16.0ms (0.5%)

localize64.0ms (1.9%)

series48.0ms (1.4%)

rewrite70.0ms (2.1%)

simplify63.0ms (1.9%)

eval53.0ms (1.6%)

prune19.0ms (0.6%)

regimes10.0ms (0.3%)

regimes4.0ms (0.1%)

regimes5.0ms (0.2%)

simplify5.0ms (0.1%)

soundness139.0ms (4.2%)

end0.0ms (0%)

preprocess33.0ms (1%)

Profiling