Details

analyze35.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (52.4%)

Results

981.0ms	8256×	body	128	valid
53.0ms	426×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify46.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (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

Error

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 55 to 29 computations (47.3% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	14.3b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series55.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
22.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
7.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

6.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
5.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify107.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

147 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2391
1	285	2222
2	879	2113
3	3871	2101
4	4888	2101
5	4981	2101

prune71.0ms (3.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	2	126

Error

Counts

126 → 2

Alt Table

Status	Error	Program
	14.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 2456 to 688 computations (72% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (/.f64 b a) (/.f64 b a) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

series20.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(fma.f64 (/.f64 b a) (/.f64 b a) -1)
9.0ms	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`fabs-mul_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
0.0ms	(fma.f64 (/.f64 b a) (/.f64 b a) -1)

simplify45.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-/r*_binary64`
575×	`associate-/r/_binary64`
575×	`fma-def_binary64`
395×	`associate-/l/_binary64`
213×	`unswap-sqr_binary64`

Counts

55 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	830
1	68	744
2	100	744
3	269	744
4	1431	744
5	5301	744

prune37.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	55	2	57

Error

Counts

57 → 2

Alt Table

Status	Error	Program
▶	14.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 951 to 469 computations (50.7% saved)

localize13.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
✓	0.0b	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
✓	31.2b	(/.f64 (.f64 b b) (.f64 a a))

series72.0ms (3.5%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(/.f64 (.f64 b b) (.f64 a a))
23.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
18.0ms	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
5×	`*-un-lft-identity_binary64`

Counts

3 → 55

Calls

3 calls:

5.0ms	(/.f64 (.f64 b b) (.f64 a a))
3.0ms	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
0.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

simplify101.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

541×	`times-frac_binary64`
347×	`*-commutative_binary64`
346×	`unswap-sqr_binary64`
338×	`associate-/l*_binary64`
220×	`associate-*l/_binary64`

Counts

127 → 92

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	93	1958
1	171	1685
2	516	1660
3	2064	1637
4	3428	1637
5	4757	1393
6	4919	1393

prune115.0ms (5.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	14.8b	(sqrt.f64 (fabs.f64 (expm1.f64 (log1p.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 1680 to 950 computations (43.5% saved)

regimes180.0ms (8.6%)

Accuracy

Total 0.0b remaining (51.1%)

Threshold costs 0.0b (51.1%)

Counts

26 → 1

Compiler

Compiled 2864 to 2014 computations (29.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18
2	20	18
3	22	18
4	23	18
5	22	18

end51.0ms (2.4%)

Compiler: Compiled 53 to 40 computations (24.5% saved)

Details

analyze35.0ms (1.7%)

sample1.1s (52.4%)

simplify46.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.4%)

series55.0ms (2.6%)

rewrite17.0ms (0.8%)

simplify107.0ms (5.1%)

prune71.0ms (3.4%)

localize6.0ms (0.3%)

series20.0ms (0.9%)

rewrite3.0ms (0.1%)

simplify45.0ms (2.1%)

prune37.0ms (1.7%)

localize13.0ms (0.6%)

series72.0ms (3.5%)

rewrite11.0ms (0.5%)

simplify101.0ms (4.8%)

prune115.0ms (5.5%)

regimes180.0ms (8.6%)

simplify2.0ms (0.1%)

end51.0ms (2.4%)

Profiling