Metrics for ENA, Section 1.4, Exercise 4b, n=2

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample3.2s (75.4%)

Results

1.7s	6158×	body	256	valid
1.1s	1078×	body	1024	valid
425.0ms	1000×	body	512	valid
16.0ms	20×	body	2048	valid

Bogosity

preprocess134.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1358×	`fma-def`
852×	`unswap-sqr`
758×	`distribute-lft-out`
646×	`distribute-lft-neg-in`
640×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	141
1	64	125
2	168	125
3	714	95
4	4082	95

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 (neg.f64 x) eps) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (+.f64 x (neg.f64 eps)) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(-.f64 (pow.f64 (+.f64 (neg.f64 x) eps) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (+.f64 eps (neg.f64 x)) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (-.f64 eps x) 2) (*.f64 x x))
(.f64 eps (+.f64 eps (.f64 x -2)))
(-.f64 (pow.f64 (+.f64 x (neg.f64 eps)) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps (neg.f64 x)) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (-.f64 eps x) 2) (*.f64 x x))
(.f64 eps (+.f64 eps (.f64 x -2)))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 eps eps))
(*.f64 x (+.f64 x (+.f64 eps eps)))

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval2.0ms (0%)

Compiler: Compiled 18 to 9 computations (50% saved)

prune4.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 eps (+.f64 x (+.f64 x eps)))
▶	100.0%	(*.f64 eps (+.f64 x (+.f64 x eps)))

Compiler

Compiled 18 to 10 computations (44.4% saved)

localize78.0ms (1.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.9%	(+.f64 x (+.f64 x eps))

Compiler

Compiled 20 to 6 computations (70% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x (+.f64 x eps))
1.0ms	eps	@	0	(+.f64 x (+.f64 x eps))
1.0ms	x	@	0	(+.f64 x (+.f64 x eps))
0.0ms	eps	@	inf	(+.f64 x (+.f64 x eps))
0.0ms	x	@	-inf	(+.f64 x (+.f64 x eps))

rewrite113.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1780×	`pow1`
1660×	`add-exp-log`
1660×	`log1p-expm1-u`
1660×	`expm1-log1p-u`
1630×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	140	13
2	2180	13

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 x (+.f64 x eps))

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

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1352×	`div-sub`
1088×	`associate-r`
1006×	`associate-l`
802×	`fma-def`
570×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1065
1	284	949
2	1011	839
3	6522	839

Stop Event

1×	node limit

Counts

59 → 53

Calls

Call 1

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

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

eval10.0ms (0.2%)

Compiler: Compiled 785 to 305 computations (61.1% saved)

prune10.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Accuracy

100.0%

Counts

54 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 eps (+.f64 (.f64 2 x) eps))
▶	65.8%	(*.f64 eps (+.f64 x x))
▶	74.3%	(*.f64 eps eps)
▶	100.0%	(.f64 eps (+.f64 (.f64 2 x) eps))
▶	65.8%	(*.f64 eps (+.f64 x x))
▶	74.3%	(*.f64 eps eps)

Compiler

Compiled 42 to 26 computations (38.1% saved)

localize45.0ms (1%)

Compiler: Compiled 35 to 16 computations (54.3% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 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	3	3
Done	0	0
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 eps (+.f64 (.f64 2 x) eps))
✓	65.8%	(*.f64 eps (+.f64 x x))
✓	74.3%	(*.f64 eps eps)

Compiler

Compiled 54 to 30 computations (44.4% saved)

regimes14.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(*.f64 eps (+.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(.f64 eps (+.f64 (.f64 2 x) eps))

Calls

3 calls:

5.0ms	eps
5.0ms	x
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`

Compiler

Compiled 50 to 29 computations (42% saved)

regimes8.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(*.f64 eps (+.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))

Outputs
(*.f64 eps (+.f64 x (+.f64 x eps)))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 23 to 12 computations (47.8% saved)

regimes26.0ms (0.6%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 eps eps)
(*.f64 eps (+.f64 x x))

Outputs
(*.f64 eps (+.f64 x x))
(*.f64 eps eps)
(*.f64 eps (+.f64 x x))

Calls

2 calls:

13.0ms	eps
12.0ms	x

Results

Accuracy	Segments	Branch
93.4%	3	`x`
88.3%	3	`eps`

Compiler

Compiled 16 to 9 computations (43.8% saved)

regimes61.0ms (1.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)

Outputs
(*.f64 eps eps)

Calls

2 calls:

55.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
74.3%	1	`eps`
74.3%	1	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch40.0ms (0.9%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
25.0ms	8.97763520023995e-111	9.447402884007247e-104
15.0ms	-5.372481771853609e-128	-2.3282200452817917e-129

Results

26.0ms	177×	body	256	valid
11.0ms	79×	body	512	valid

Compiler

Compiled 240 to 156 computations (35% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	90
1	35	90

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(if (<=.f64 x -8389699228974229/195109284394749514461349826862072894109287383916560696928697309976585733676235351257519131441468248197489183195087913930965498479955517831643136) (.f64 eps (+.f64 x x)) (if (<=.f64 x 1156847945382935/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256) (.f64 eps eps) (*.f64 eps (+.f64 x x))))
(*.f64 eps eps)

Outputs
(.f64 eps (+.f64 (.f64 2 x) eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(*.f64 eps (+.f64 x (+.f64 eps x)))
(if (<=.f64 x -8389699228974229/195109284394749514461349826862072894109287383916560696928697309976585733676235351257519131441468248197489183195087913930965498479955517831643136) (.f64 eps (+.f64 x x)) (if (<=.f64 x 1156847945382935/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256) (.f64 eps eps) (*.f64 eps (+.f64 x x))))
(if (or (<=.f64 x -8389699228974229/195109284394749514461349826862072894109287383916560696928697309976585733676235351257519131441468248197489183195087913930965498479955517831643136) (not (<=.f64 x 1156847945382935/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256))) (.f64 eps (+.f64 x x)) (.f64 eps eps))
(*.f64 eps eps)

Compiler

Compiled 42 to 26 computations (38.1% saved)

soundness274.0ms (6.4%)

Rules

1358×	`fma-def`
1352×	`div-sub`
1088×	`associate-r`
1006×	`associate-l`
852×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	141
1	64	125
2	168	125
3	714	95
4	4082	95
0	102	1065
1	284	949
2	1011	839
3	6522	839

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 112 to 37 computations (67% saved)

end0.0ms (0%)

preprocess158.0ms (3.7%)

Compiler: Compiled 76 to 44 computations (42.1% saved)

analyze0.0ms (0%)

sample3.2s (75.4%)

preprocess134.0ms (3.1%)

eval2.0ms (0%)

prune4.0ms (0.1%)

localize78.0ms (1.8%)

series4.0ms (0.1%)

rewrite113.0ms (2.6%)

simplify67.0ms (1.6%)

eval10.0ms (0.2%)

prune10.0ms (0.2%)

localize45.0ms (1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes14.0ms (0.3%)

regimes8.0ms (0.2%)

regimes26.0ms (0.6%)

regimes61.0ms (1.4%)

bsearch40.0ms (0.9%)

simplify6.0ms (0.1%)

soundness274.0ms (6.4%)

end0.0ms (0%)

preprocess158.0ms (3.7%)

Profiling