Details

analyze36.0ms (0.9%)

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 (29%)

Results

1.0s	8256×	body	128	valid
46.0ms	391×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify51.0ms (1.3%)

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

1 alts after pruning (1 fresh and 0 done)

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

Error

15.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.5b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	15.5b	(/.f64 b (*.f64 a a))

series68.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

36.0ms	(/.f64 b (*.f64 a a))
21.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms	(/.f64 b (*.f64 a a))
3.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-/l*_binary64`
603×	`fma-def_binary64`
491×	`associate-l_binary64`
486×	`associate-/l/_binary64`
431×	`associate-/r*_binary64`

Counts

126 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1587
1	143	1492
2	293	1492
3	866	1490
4	4508	1490
5	5063	1490

prune49.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Error

0.0b

Counts

71 → 3

Alt Table

Status	Error	Program
	15.5b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	1.4b	(sqrt.f64 (fabs.f64 -1))

Compiler

Compiled 1141 to 561 computations (50.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.3b	(/.f64 (/.f64 b a) a)

series59.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f64 (/.f64 b a) a)
21.0ms	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

3 → 103

Calls

3 calls:

4.0ms	(/.f64 (/.f64 b a) a)
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
0.0ms	(fma.f64 b (/.f64 (/.f64 b a) a) -1)

simplify120.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
423×	`unswap-sqr_binary64`
394×	`fma-neg_binary64`
337×	`associate-/l/_binary64`
324×	`times-frac_binary64`

Counts

175 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	184	2634
1	347	2461
2	650	2389
3	1692	2365
4	2633	2345
5	4642	2345
6	4955	2345

prune111.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Alt Table

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

Compiler

Compiled 3031 to 1339 computations (55.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 b (/.f64 (/.f64 b a) a) -1)
✓	0.0b	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
✓	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	0.3b	(/.f64 (/.f64 b a) a)

series34.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
12.0ms	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

1.0ms	(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
0.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

549×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
528×	`fma-def_binary64`
348×	`fma-neg_binary64`
266×	`associate-/l/_binary64`

Counts

80 → 58

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1196
1	71	1110
2	102	1110
3	251	1110
4	1238	1110
5	4871	1110
6	5120	1110

prune182.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	187	4	191

Error

Counts

191 → 4

Alt Table

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

Compiler

Compiled 3711 to 1845 computations (50.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.0b	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.3b	(/.f64 (/.f64 b a) a)

series780.0ms (19.9%)

Counts

2 → 48

Calls

2 calls:

767.0ms

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

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

202×	`sqrt-prod_binary64`
136×	`add-sqr-sqrt_binary64`
48×	`rem-sqrt-square_binary64`
36×	`fabs-mul_binary64`
36×	`sqrt-pow1_binary64`

Counts

2 → 154

Calls

2 calls:

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

2.0ms

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

simplify249.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
365×	`fma-neg_binary64`
315×	`*-commutative_binary64`
236×	`sqr-pow_binary64`
208×	`associate-l_binary64`

Counts

202 → 160

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	116	4930
1	152	4654
2	335	4594
3	742	4433
4	1361	4433
5	2749	4384
6	4414	4378
7	4984	4378
8	4994	4378
9	4890	4378

prune544.0ms (13.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	477	0	477
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	477	4	481

Error

Counts

481 → 4

Alt Table

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

Compiler

Compiled 14687 to 7061 computations (51.9% saved)

regimes151.0ms (3.8%)

Accuracy

Total 0.0b remaining (64.8%)

Threshold costs 0.0b (64.8%)

Counts

21 → 1

Compiler

Compiled 2831 to 1861 computations (34.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	10	16

end78.0ms (2%)

Compiler: Compiled 112 to 70 computations (37.5% saved)

Details

analyze36.0ms (0.9%)

sample1.1s (29%)

simplify51.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series68.0ms (1.7%)

rewrite8.0ms (0.2%)

simplify85.0ms (2.2%)

prune49.0ms (1.3%)

localize7.0ms (0.2%)

series59.0ms (1.5%)

rewrite14.0ms (0.4%)

simplify120.0ms (3.1%)

prune111.0ms (2.8%)

localize11.0ms (0.3%)

series34.0ms (0.9%)

rewrite3.0ms (0.1%)

simplify81.0ms (2.1%)

prune182.0ms (4.6%)

localize8.0ms (0.2%)

series780.0ms (19.9%)

rewrite41.0ms (1%)

simplify249.0ms (6.3%)

prune544.0ms (13.9%)

regimes151.0ms (3.8%)

simplify2.0ms (0%)

end78.0ms (2%)

Profiling