Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample879.0ms (60.7%)

Results

640.0ms	6184×	body	256	valid
227.0ms	2072×	body	256	infinite

Bogosity

preprocess28.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

200×	`fma-def`
38×	`associate-r`
34×	`distribute-lft-neg-in`
24×	`associate-l`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	33	30
2	70	30
3	148	30
4	234	30
5	324	30
6	349	30
7	354	30
8	357	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) 2) 1)
(-.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) 2) 1)

Outputs
(-.f64 (.f64 (.f64 x x) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)

Symmetry

(abs x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
6×	`fma-def`
2×	`1-exp`
2×	`fma-neg`
2×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	19	15
2	25	15
3	26	15

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

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

Outputs
(-.f64 (.f64 (.f64 x x) 2) 1)
(fma.f64 (*.f64 x x) 2 -1)
(fma.f64 x (*.f64 x 2) -1)

eval1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	3	4

Accurracy

100.0%

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (*.f64 x 2) -1)
▶	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
▶	100.0%	(fma.f64 x (*.f64 x 2) -1)
▶	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize37.0ms (2.6%)

Local Accuracy

Found 2 expressions with local accuracy:

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

Compiler

Compiled 32 to 19 computations (40.6% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite60.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1492×	`pow1`
1384×	`add-exp-log`
1380×	`log1p-expm1-u`
1380×	`expm1-log1p-u`
1362×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	169	28
2	2013	28

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

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

simplify70.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1006×	`distribute-lft-neg-in`
988×	`log-prod`
850×	`fma-def`
692×	`unswap-sqr`
548×	`div-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	1364
1	224	1304
2	901	1284
3	4604	1254

Stop Event

1×	node limit

Counts

70 → 57

Calls

Call 1

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

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

eval17.0ms (1.2%)

Compiler: Compiled 677 to 518 computations (23.5% saved)

prune11.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	55	4	59

Accurracy

100.0%

Counts

59 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
▶	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
▶	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize19.0ms (1.3%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 12 to 6 computations (50% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1042×	`pow1`
1004×	`add-sqr-sqrt`
956×	`add-exp-log`
956×	`log1p-expm1-u`
956×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	121	13
2	1362	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 2 (.f64 x x))

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

simplify56.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2150×	`log-prod`
1058×	`distribute-lft-in`
1054×	`distribute-rgt-in`
808×	`associate-r`
692×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	299
1	89	299
2	318	299
3	2143	299
4	7034	299

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

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

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

eval3.0ms (0.2%)

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

prune5.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	13	4	17

Accurracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
✓	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
✓	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune5.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
✓	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
✓	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (*.f64 x 2) -1)
✓	100.0%	(-.f64 (.f64 (.f64 x x) 2) 1)
✓	53.7%	(.f64 2 (.f64 x x))
	46.9%	-1

Compiler

Compiled 43 to 30 computations (30.2% saved)

regimes15.0ms (1%)

Counts

4 → 1

Calls

Call 1

Inputs
-1
(.f64 2 (.f64 x x))
(-.f64 (.f64 (.f64 x x) 2) 1)
(fma.f64 x (*.f64 x 2) -1)

Outputs
(fma.f64 x (*.f64 x 2) -1)

Calls

4 calls:

4.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(.f64 (.f64 x x) 2)
2.0ms	(-.f64 (.f64 (.f64 x x) 2) 1)

Results

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

Compiler

Compiled 40 to 26 computations (35% saved)

regimes13.0ms (0.9%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(-.f64 (.f64 (.f64 x x) 2) 1)

Calls

4 calls:

4.0ms	x
3.0ms	(.f64 (.f64 x x) 2)
3.0ms	(*.f64 x x)
2.0ms	(-.f64 (.f64 (.f64 x x) 2) 1)

Results

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

Compiler

Compiled 34 to 22 computations (35.3% saved)

regimes17.0ms (1.2%)

Counts

2 → 2

Calls

Call 1

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

Outputs
-1
(.f64 2 (.f64 x x))

Calls

2 calls:

9.0ms	(*.f64 x x)
7.0ms	x

Results

Accuracy	Segments	Branch
98.9%	2	`x`
98.9%	2	`(*.f64 x x)`

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
-1

Outputs
-1

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
46.9%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch10.0ms (0.7%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.4982283488306095	53.083097748472504

Results

9.0ms

112×

body

256

valid

Compiler

Compiled 68 to 58 computations (14.7% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`sub-neg`
2×	`*-rgt-identity`
2×	`mul-1-neg`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	26	64
2	29	64
3	34	64

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (.f64 (.f64 x x) 2) 1)
(if (<=.f64 (.f64 x x) 1/2) -1 (.f64 2 (*.f64 x x)))
-1

Outputs
(fma.f64 x (*.f64 x 2) -1)
(-.f64 (.f64 (.f64 x x) 2) 1)
(-.f64 (.f64 2 (.f64 x x)) 1)
(+.f64 (.f64 2 (.f64 x x)) -1)
(if (<=.f64 (.f64 x x) 1/2) -1 (.f64 2 (*.f64 x x)))
-1

Compiler

Compiled 30 to 21 computations (30% saved)

soundness98.0ms (6.8%)

Rules

1006×	`distribute-lft-neg-in`
988×	`log-prod`
850×	`fma-def`
692×	`unswap-sqr`
548×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	19	15
2	25	15
3	26	15
0	101	1364
1	224	1304
2	901	1284
3	4604	1254

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 39 to 28 computations (28.2% saved)

end0.0ms (0%)

preprocess38.0ms (2.6%)

Remove: (abs x)
Compiler: Compiled 84 to 56 computations (33.3% saved)

analyze0.0ms (0%)

sample879.0ms (60.7%)

preprocess28.0ms (1.9%)

simplify3.0ms (0.2%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize37.0ms (2.6%)

series2.0ms (0.1%)

rewrite60.0ms (4.1%)

simplify70.0ms (4.9%)

eval17.0ms (1.2%)

prune11.0ms (0.8%)

localize19.0ms (1.3%)

series0.0ms (0%)

rewrite47.0ms (3.3%)

simplify56.0ms (3.9%)

eval3.0ms (0.2%)

prune5.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.2%)

regimes15.0ms (1%)

regimes13.0ms (0.9%)

regimes17.0ms (1.2%)

regimes3.0ms (0.2%)

bsearch10.0ms (0.7%)

simplify6.0ms (0.4%)

soundness98.0ms (6.8%)

end0.0ms (0%)

preprocess38.0ms (2.6%)

Profiling