Metrics for Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample795.0ms (42.8%)

Results

688.0ms	7200×	body	256	valid
97.0ms	1056×	body	256	infinite

Bogosity

preprocess214.0ms (11.5%)

Algorithm

1×	egg-herbie

Rules

3066×	`fma-def`
456×	`distribute-rgt-in`
428×	`fma-neg`
346×	`sub-neg`
308×	`cancel-sign-sub-inv`

Problems

256×

No Errors

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	37	308
1	83	272
2	186	268
3	317	254
4	579	235
5	887	222
6	1768	214
7	3245	209
8	3812	204
9	3999	204
10	4078	204
11	4086	204
12	4086	196
13	4405	196
14	4405	196

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 (neg.f64 x) 2) (*.f64 y (neg.f64 x))) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 (neg.f64 y) x)) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) (neg.f64 z))
(+.f64 (+.f64 (/.f64 y 2) (*.f64 x y)) z)
(+.f64 (+.f64 (/.f64 z 2) (*.f64 y z)) x)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 z x)) y)

Outputs
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
(+.f64 (fma.f64 x y (/.f64 x 2)) z)
(+.f64 (/.f64 x 2) (fma.f64 x y z))
(+.f64 (*.f64 x (+.f64 y 1/2)) z)
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x y) z))
(+.f64 (fma.f64 x y (/.f64 x 2)) z)
(+.f64 (/.f64 x 2) (fma.f64 x y z))
(+.f64 (*.f64 x (+.f64 y 1/2)) z)
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (+.f64 (/.f64 (neg.f64 x) 2) (*.f64 y (neg.f64 x))) z)
(+.f64 z (+.f64 (/.f64 (neg.f64 x) 2) (*.f64 x (neg.f64 y))))
(+.f64 z (neg.f64 (fma.f64 x y (/.f64 x 2))))
(-.f64 z (fma.f64 x y (/.f64 x 2)))
(+.f64 z (*.f64 x (-.f64 -1/2 y)))
(fma.f64 x (-.f64 -1/2 y) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 (neg.f64 y) x)) z)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x (neg.f64 y)) z))
(+.f64 z (-.f64 (/.f64 x 2) (*.f64 x y)))
(-.f64 z (fma.f64 x y (*.f64 x -1/2)))
(-.f64 z (*.f64 x (+.f64 y -1/2)))
(+.f64 z (*.f64 x (-.f64 1/2 y)))
(fma.f64 x (-.f64 1/2 y) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) (neg.f64 z))
(-.f64 (+.f64 (/.f64 x 2) (*.f64 x y)) z)
(-.f64 (fma.f64 x y (/.f64 x 2)) z)
(-.f64 (*.f64 x (-.f64 y -1/2)) z)
(-.f64 (*.f64 x (+.f64 y 1/2)) z)
(neg.f64 (fma.f64 x (-.f64 -1/2 y) z))
(+.f64 (+.f64 (/.f64 y 2) (*.f64 x y)) z)
(+.f64 z (+.f64 (*.f64 x y) (/.f64 y 2)))
(+.f64 z (fma.f64 x y (/.f64 y 2)))
(fma.f64 x y (+.f64 z (/.f64 y 2)))
(+.f64 z (fma.f64 x y (*.f64 1/2 y)))
(+.f64 z (*.f64 y (+.f64 x 1/2)))
(fma.f64 y (+.f64 x 1/2) z)
(+.f64 (+.f64 (/.f64 z 2) (*.f64 y z)) x)
(+.f64 x (+.f64 (/.f64 z 2) (*.f64 y z)))
(+.f64 x (fma.f64 y z (/.f64 z 2)))
(+.f64 x (fma.f64 y z (*.f64 1/2 z)))
(+.f64 x (*.f64 z (+.f64 y 1/2)))
(fma.f64 z (+.f64 y 1/2) x)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 z x)) y)
(+.f64 (/.f64 x 2) (+.f64 (*.f64 x z) y))
(+.f64 (/.f64 x 2) (fma.f64 x z y))
(+.f64 (*.f64 x 1/2) (fma.f64 x z y))
(+.f64 y (*.f64 x (+.f64 1/2 z)))
(fma.f64 x (+.f64 z 1/2) y)

Compiler

Compiled 42 to 23 computations (45.2% saved)

eval1.0ms (0.1%)

Compiler: Compiled 41 to 23 computations (43.9% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (*.f64 x (+.f64 y 1/2)) z)
▶	100.0%	(+.f64 (*.f64 x (+.f64 y 1/2)) z)

Compiler

Compiled 20 to 14 computations (30% saved)

localize29.0ms (1.6%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 23 to 14 computations (39.1% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite115.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`unpow-prod-down`
517×	`log1p-expm1-u`
517×	`expm1-log1p-u`
498×	`log-prod`
450×	`prod-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	106	19
2	1414	19

Stop Event

1×	node limit

Counts

1 → 53

Calls

Call 1

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

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

simplify56.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1288×	`associate-/r*`
1128×	`fma-def`
558×	`fma-neg`
446×	`cancel-sign-sub-inv`
418×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1811
1	379	1760
2	1039	1739
3	4189	1735

Stop Event

1×	node limit

Counts

77 → 75

Calls

Call 1

Inputs
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 x (+.f64 1/2 y))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(*.f64 x y)
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(*.f64 x y)
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 1/2 x) (.f64 x y))
(+.f64 (.f64 x y) (.f64 x 1/2))
(+.f64 (.f64 x 1/2) (.f64 x y))
(+.f64 0 (*.f64 x (+.f64 y 1/2)))
(+.f64 (.f64 (.f64 x y) 1) (.f64 (.f64 x 1/2) 1))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 y 1/2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 y 1/2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 y 1/2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 y 1/2)) x))))
(-.f64 (+.f64 1 (*.f64 x (+.f64 y 1/2))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (.f64 (pow.f64 x 3) 1/8)) (+.f64 (pow.f64 (.f64 x y) 2) (-.f64 (pow.f64 (.f64 x 1/2) 2) (.f64 (.f64 x y) (*.f64 x 1/2)))))
(/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (pow.f64 (.f64 x 1/2) 2)) (-.f64 (.f64 x y) (.f64 x 1/2)))
(/.f64 (.f64 x (+.f64 (pow.f64 y 3) 1/8)) (-.f64 (fma.f64 y y 1/4) (.f64 y 1/2)))
(/.f64 (*.f64 x (fma.f64 y y -1/4)) (+.f64 y -1/2))
(/.f64 (.f64 (+.f64 (pow.f64 y 3) 1/8) x) (-.f64 (fma.f64 y y 1/4) (.f64 y 1/2)))
(/.f64 (*.f64 (fma.f64 y y -1/4) x) (+.f64 y -1/2))
(pow.f64 (*.f64 x (+.f64 y 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 y 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 x (+.f64 y 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 y 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (+.f64 y 1/2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (+.f64 y 1/2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (+.f64 y 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (+.f64 y 1/2))))) (sqrt.f64 (log.f64 (.f64 x (+.f64 y 1/2)))))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 y 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 (+.f64 y 1/2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 y 1/2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 y 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (+.f64 y 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (+.f64 y 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 y 1/2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 y 1/2))))
(fma.f64 x y (*.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 x y))
(fma.f64 y x (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 x y))
(fma.f64 1 (.f64 x y) (.f64 x 1/2))
(fma.f64 1 (.f64 x 1/2) (.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) y) (.f64 x 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) x) (.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) y) (.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 x y))
(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) x) (.f64 x 1/2))
(fma.f64 (.f64 x y) 1 (.f64 (*.f64 x 1/2) 1))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 x y))
(fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (*.f64 x 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x y))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 x y))
(fma.f64 (.f64 x (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (.f64 x 1/2))
(fma.f64 (.f64 x (sqrt.f64 y)) (sqrt.f64 y) (.f64 x 1/2))
(fma.f64 (.f64 y (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x 1/2))
(fma.f64 (.f64 y (sqrt.f64 x)) (sqrt.f64 x) (.f64 x 1/2))

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

eval25.0ms (1.4%)

Compiler: Compiled 1025 to 629 computations (38.6% saved)

prune13.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Accuracy

100.0%

Counts

76 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (*.f64 x (+.f64 y 1/2)) z)
▶	75.7%	(+.f64 (*.f64 x y) z)
▶	65.8%	(+.f64 (*.f64 x 1/2) z)
✓	100.0%	(+.f64 (*.f64 x (+.f64 y 1/2)) z)
▶	75.7%	(+.f64 (*.f64 x y) z)
▶	65.8%	(+.f64 (*.f64 x 1/2) z)

Compiler

Compiled 52 to 36 computations (30.8% saved)

localize32.0ms (1.7%)

Compiler: Compiled 26 to 12 computations (53.8% saved)

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (*.f64 x (+.f64 y 1/2)) z)
✓	75.7%	(+.f64 (*.f64 x y) z)
✓	65.8%	(+.f64 (*.f64 x 1/2) z)

Compiler

Compiled 55 to 35 computations (36.4% saved)

regimes62.0ms (3.4%)

Counts

4 → 1

Calls

Call 1

Inputs
(+.f64 (*.f64 x 1/2) z)
(+.f64 (*.f64 x y) z)
(+.f64 (*.f64 x (+.f64 y 1/2)) z)
(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)

Outputs
(+.f64 (*.f64 x (+.f64 y 1/2)) z)

Calls

5 calls:

48.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
3.0ms	y
3.0ms	z
3.0ms	x
3.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)`
100.0%	1	`(+.f64 (/.f64 x 2) (*.f64 y x))`

Compiler

Compiled 63 to 41 computations (34.9% saved)

regimes38.0ms (2%)

Counts

2 → 3

Calls

Call 1

Inputs
(+.f64 (*.f64 x 1/2) z)
(+.f64 (*.f64 x y) z)

Outputs
(+.f64 (*.f64 x y) z)
(+.f64 (*.f64 x 1/2) z)
(+.f64 (*.f64 x y) z)

Calls

3 calls:

14.0ms	z
14.0ms	x
8.0ms	y

Results

Accuracy	Segments	Branch
80.3%	4	`x`
99.6%	3	`y`
81.2%	5	`z`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes40.0ms (2.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

35.0ms	z
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
65.8%	1	`z`
65.8%	1	`x`
65.8%	1	`y`

Compiler

Compiled 20 to 15 computations (25% saved)

bsearch27.0ms (1.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	4.479331575206975e-13	2.86939590396998e-5
10.0ms	-8.20314880224947e+25	-1.6333546562244386e+25

Results

23.0ms	233×	body	256	valid
1.0ms	7×	body	256	infinite

Compiler

Compiled 288 to 208 computations (27.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`*-commutative`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	119
1	38	119

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(+.f64 (*.f64 x (+.f64 y 1/2)) z)

(if (<=.f64 y -16500000000000000528482304) (+.f64 (*.f64 x y) z) (if (<=.f64 y 8264141345021879/295147905179352825856) (+.f64 (*.f64 x 1/2) z) (+.f64 (*.f64 x y) z)))

(+.f64 (*.f64 x 1/2) z)

Outputs
(+.f64 (*.f64 x (+.f64 y 1/2)) z)
(if (<=.f64 y -16500000000000000528482304) (+.f64 (.f64 x y) z) (if (<=.f64 y 8264141345021879/295147905179352825856) (+.f64 (.f64 x 1/2) z) (+.f64 (*.f64 x y) z)))
(if (or (<=.f64 y -16500000000000000528482304) (not (<=.f64 y 8264141345021879/295147905179352825856))) (+.f64 z (.f64 x y)) (+.f64 z (.f64 x 1/2)))
(+.f64 (*.f64 x 1/2) z)
(+.f64 z (*.f64 x 1/2))

Compiler

Compiled 40 to 28 computations (30% saved)

soundness362.0ms (19.5%)

Rules

3066×	`fma-def`
1288×	`associate-/r*`
1128×	`fma-def`
558×	`fma-neg`
456×	`distribute-rgt-in`

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	37	308
1	83	272
2	186	268
3	317	254
4	579	235
5	887	222
6	1768	214
7	3245	209
8	3812	204
9	3999	204
10	4078	204
11	4086	204
12	4086	196
13	4405	196
14	4405	196
0	156	1811
1	379	1760
2	1039	1739
3	4189	1735

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 189 to 118 computations (37.6% saved)

end0.0ms (0%)

preprocess39.0ms (2.1%)

Compiler: Compiled 92 to 60 computations (34.8% saved)

analyze0.0ms (0%)

sample795.0ms (42.8%)

preprocess214.0ms (11.5%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize29.0ms (1.6%)

series2.0ms (0.1%)

rewrite115.0ms (6.2%)

simplify56.0ms (3%)

eval25.0ms (1.4%)

prune13.0ms (0.7%)

localize32.0ms (1.7%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes62.0ms (3.4%)

regimes38.0ms (2%)

regimes40.0ms (2.2%)

bsearch27.0ms (1.4%)

simplify4.0ms (0.2%)

soundness362.0ms (19.5%)

end0.0ms (0%)

preprocess39.0ms (2.1%)

Profiling