Metrics for Data.Number.Erf:$dmerfcx from erf-2.0.0.0

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 9 to 6 computations (33.3% saved)

sample888.0ms (68.1%)

Results

449.0ms	4144×	body	256	valid
424.0ms	4112×	body	256	infinite

Bogosity

preprocess65.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-def`
716×	`associate-*r/`
694×	`distribute-lft-in`
660×	`associate-/r*`
648×	`fma-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	38	72
2	83	72
3	201	72
4	567	72
5	2039	72
6	5719	72

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 x (exp.f64 (.f64 y y)))
(.f64 (neg.f64 x) (exp.f64 (.f64 y y)))
(.f64 x (exp.f64 (.f64 (neg.f64 y) (neg.f64 y))))
(.f64 y (exp.f64 (.f64 x x)))

Outputs
(.f64 x (exp.f64 (.f64 y y)))
(*.f64 x (pow.f64 (exp.f64 y) y))
(.f64 (neg.f64 x) (exp.f64 (.f64 y y)))
(*.f64 (pow.f64 (exp.f64 y) y) (neg.f64 x))
(*.f64 x (neg.f64 (pow.f64 (exp.f64 y) y)))
(.f64 x (neg.f64 (exp.f64 (.f64 y y))))
(.f64 x (exp.f64 (.f64 (neg.f64 y) (neg.f64 y))))
(*.f64 x (pow.f64 (exp.f64 y) y))
(.f64 x (exp.f64 (.f64 y y)))
(.f64 y (exp.f64 (.f64 x x)))
(*.f64 y (pow.f64 (exp.f64 x) x))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify79.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

1240×	`sqr-pow`
914×	`associate-r`
890×	`associate-*l/`
736×	`unswap-sqr`
646×	`exp-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	11	17
2	15	17
3	24	17
4	52	17
5	141	17
6	447	17
7	1430	17
8	2551	17
9	3850	17
10	4235	17
11	4810	17
12	6581	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 x (exp.f64 (.f64 y y)))

Outputs
(.f64 x (exp.f64 (.f64 y y)))
(*.f64 x (pow.f64 (exp.f64 y) y))

eval0.0ms (0%)

Compiler: Compiled 14 to 8 computations (42.9% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Accurracy

99.6%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.f64 x (exp.f64 (.f64 y y)))
▶	99.6%	(.f64 x (exp.f64 (.f64 y y)))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize29.0ms (2.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))

Compiler

Compiled 18 to 6 computations (66.7% saved)

series2.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite84.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1370×	`pow1`
1248×	`add-exp-log`
1248×	`log1p-expm1-u`
1248×	`expm1-log1p-u`
1216×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	154	17
2	1783	17

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 x (exp.f64 (.f64 y y)))

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

simplify74.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1110×	`fma-def`
812×	`fma-neg`
704×	`*-commutative`
674×	`distribute-lft-out`
586×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	633
1	137	631
2	410	619
3	2011	615
4	4833	615
5	7573	615

Stop Event

1×	node limit

Counts

35 → 28

Calls

Call 1

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

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

eval7.0ms (0.5%)

Compiler: Compiled 279 to 139 computations (50.2% saved)

prune5.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Accurracy

99.6%

Counts

29 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Accurracy

99.6%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Accurracy

99.6%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Accurracy

99.6%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.f64 x (exp.f64 (.f64 y y)))
	49.7%	x

Compiler

Compiled 20 to 12 computations (40% saved)

regimes14.0ms (1.1%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(.f64 x (exp.f64 (.f64 y y)))

Outputs
(.f64 x (exp.f64 (.f64 y y)))

Calls

5 calls:

4.0ms	(*.f64 y y)
3.0ms	x
3.0ms	y
2.0ms	(.f64 x (exp.f64 (.f64 y y)))
2.0ms	(exp.f64 (*.f64 y y))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`(.f64 x (exp.f64 (.f64 y y)))`
99.6%	1	`(exp.f64 (*.f64 y y))`
99.6%	1	`(*.f64 y y)`

Compiler

Compiled 34 to 21 computations (38.2% saved)

regimes12.0ms (0.9%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

9.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
49.7%	1	`x`
49.7%	1	`y`

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	9	18

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 x (exp.f64 (.f64 y y)))
x

Outputs
(.f64 x (exp.f64 (.f64 y y)))
x

Compiler

Compiled 11 to 7 computations (36.4% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess34.0ms (2.6%)

Compiler: Compiled 50 to 30 computations (40% saved)

analyze0.0ms (0%)

sample888.0ms (68.1%)

preprocess65.0ms (5%)

simplify79.0ms (6.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize29.0ms (2.2%)

series2.0ms (0.2%)

rewrite84.0ms (6.4%)

simplify74.0ms (5.7%)

eval7.0ms (0.5%)

prune5.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes14.0ms (1.1%)

regimes12.0ms (0.9%)

simplify4.0ms (0.3%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess34.0ms (2.6%)

Profiling