Metrics for sqrtexp (problem 3.4.4)

analyze146.0ms (4.7%)

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)

sample2.3s (75%)

Results

975.0ms	2750×	body	1024	valid
429.0ms	2625×	body	256	unsamplable
417.0ms	3791×	body	256	valid
298.0ms	1374×	body	512	valid
162.0ms	287×	body	2048	valid
6.0ms	54×	body	256	infinite

Bogosity

preprocess174.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

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

Problems

167×	`(-.f64 (exp.f64 (*.f64 2 x)) 1)`
86×	No Errors
3×	`(-.f64 (exp.f64 x) 1)`

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 60 to 45 computations (25% 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)

localize26.0ms (0.8%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 9 computations (40% saved)

series0.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite57.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1302×	`pow1`
1200×	`add-exp-log`
1200×	`log1p-expm1-u`
1200×	`expm1-log1p-u`
1176×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	137	11
2	1649	11

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1118×	`distribute-lft-in`
1082×	`distribute-rgt-in`
996×	`times-frac`
778×	`associate-/l*`
528×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	848
1	199	794
2	593	616
3	2880	592

Stop Event

1×	node limit

Counts

34 → 50

Calls

Call 1

Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2))))
(+.f64 2 (+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 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 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(.f64 (+.f64 1 (exp.f64 (.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 1 (/.f64 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (.f64 x 3)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (exp.f64 (*.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 (exp.f64 (.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 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(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)

Outputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (+.f64 2 x) (.f64 1/2 (.f64 x x)))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(+.f64 2 (+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 2)))))
(+.f64 (+.f64 2 x) (fma.f64 1/6 (pow.f64 x 3) (.f64 1/2 (.f64 x x))))
(+.f64 2 (+.f64 x (fma.f64 1/2 (.f64 x x) (.f64 1/6 (pow.f64 x 3)))))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x)))
(+.f64 (fma.f64 1/6 (pow.f64 x 3) x) (fma.f64 1/2 (*.f64 x x) 2))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.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 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.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)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (-.f64 (exp.f64 x) 1))
(+.f64 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))
(.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (/.f64 1 (+.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 (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 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 1 (/.f64 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (.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 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (+.f64 1 (exp.f64 (.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 (exp.f64 (*.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 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (.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 (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 (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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 1 (exp.f64 x))
(+.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 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 1 (exp.f64 x))
(+.f64 2 (expm1.f64 x))

eval12.0ms (0.4%)

Compiler: Compiled 527 to 344 computations (34.7% saved)

prune8.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	4	51

Accuracy

100.0%

Counts

51 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.0%	(sqrt.f64 (+.f64 (+.f64 2 x) (.f64 1/2 (.f64 x x))))
▶	66.0%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	72.4%	(sqrt.f64 2)
▶	68.0%	(sqrt.f64 (+.f64 (+.f64 2 x) (.f64 1/2 (.f64 x x))))
▶	66.0%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	72.4%	(sqrt.f64 2)

Compiler

Compiled 50 to 40 computations (20% saved)

localize55.0ms (1.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 1/2 (.f64 x x))

Compiler

Compiled 47 to 29 computations (38.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 1/2 (.f64 x x))
0.0ms	x	@	inf	(.f64 1/2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 1/2 (.f64 x x))

rewrite53.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1058×	`pow1`
1024×	`add-sqr-sqrt`
976×	`add-exp-log`
976×	`log1p-expm1-u`
976×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1383	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

simplify58.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2120×	`log-prod`
1106×	`distribute-rgt-in`
1092×	`distribute-lft-in`
768×	`associate-r`
688×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	90	299
2	319	299
3	2131	299
4	7005	299

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

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

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

eval3.0ms (0.1%)

Compiler: Compiled 157 to 112 computations (28.7% saved)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.0%	(sqrt.f64 (+.f64 (+.f64 2 x) (.f64 1/2 (.f64 x x))))
✓	66.0%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	72.4%	(sqrt.f64 2)

Compiler

Compiled 59 to 46 computations (22% saved)

regimes10.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

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 61 to 48 computations (21.3% saved)

regimes5.0ms (0.2%)

Accuracy

Total -4.4b remaining (-24.7%)

Threshold costs -4.4b (-24.7%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
72.4%	1	`x`

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	13	20

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness70.0ms (2.3%)

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

Compiler

Compiled 85 to 56 computations (34.1% saved)

end0.0ms (0%)

preprocess26.0ms (0.8%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

analyze146.0ms (4.7%)

sample2.3s (75%)

preprocess174.0ms (5.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize26.0ms (0.8%)

series0.0ms (0%)

rewrite57.0ms (1.9%)

simplify55.0ms (1.8%)

eval12.0ms (0.4%)

prune8.0ms (0.3%)

localize55.0ms (1.8%)

series1.0ms (0%)

rewrite53.0ms (1.7%)

simplify58.0ms (1.9%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

regimes10.0ms (0.3%)

regimes5.0ms (0.2%)

simplify4.0ms (0.1%)

soundness70.0ms (2.3%)

end0.0ms (0%)

preprocess26.0ms (0.8%)

Profiling