Details

analyze28.0ms (0.6%)

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)

sample891.0ms (18.6%)

Results

787.0ms	8256×	body	128	valid
39.0ms	414×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify46.0ms (1%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

15.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.5b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	15.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 79 to 45 computations (43% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	15.3b	(/.f64 b (*.f64 a a))

series42.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 b (*.f64 a a))
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

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

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

553×	`div-sub_binary64`
385×	`associate-/l*_binary64`
361×	`associate-/l/_binary64`
322×	`*-commutative_binary64`
270×	`fma-def_binary64`

Counts

92 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1190
1	131	1118
2	258	1118
3	623	1118
4	1939	1118
5	2527	1118
6	4267	1118
7	5200	1118

prune40.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Error

0.0b

Counts

55 → 2

Alt Table

Status	Error	Program
	15.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1))))) (cbrt.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)))

Status

Error

Program

15.0b

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

Compiler

Compiled 942 to 461 computations (51.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series43.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (/.f64 b a) a)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 93

Calls

2 calls:

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

simplify144.0ms (3%)

Algorithm

1×	egg-herbie

Rules

360×	`distribute-rgt-in_binary64`
345×	`fma-neg_binary64`
327×	`associate-/l/_binary64`
305×	`distribute-lft-in_binary64`
298×	`fma-def_binary64`

Counts

141 → 146

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	174	2231
1	333	2103
2	605	2031
3	1372	2007
4	1707	2002
5	2563	1952
6	4418	1922
7	4987	1922
8	4849	1922

prune130.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
	15.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1))))) (cbrt.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)))
▶	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 2775 to 1239 computations (55.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

13.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

1.0ms

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

simplify134.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1120×	`fma-def_binary64`
494×	`associate-/r/_binary64`
446×	`unswap-sqr_binary64`
376×	`fma-neg_binary64`
374×	`div-sub_binary64`

Counts

35 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	583
1	31	552
2	47	552
3	76	552
4	155	552
5	407	552
6	1342	552
7	2141	552
8	2450	552
9	2868	552
10	3692	552
11	4203	552
12	4876	552
13	4988	552
14	4790	552

prune140.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	167	3	170

Error

Counts

170 → 3

Alt Table

Status	Error	Program
▶	15.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1))))) (cbrt.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)))
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 3421 to 1718 computations (49.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
✓	0.0b	(cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))))
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
	15.3b	(/.f64 b (*.f64 a a))

series2.2s (45.4%)

Counts

2 → 48

Calls

2 calls:

1.2s

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

1.0s

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

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`cbrt-prod_binary64`
80×	`add-sqr-sqrt_binary64`
67×	`sqrt-prod_binary64`
25×	`unswap-sqr_binary64`
25×	`fabs-mul_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms

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

2.0ms

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

simplify212.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

548×	`log-prod_binary64`
540×	`associate-/l/_binary64`
444×	`associate-/l*_binary64`
287×	`associate-/r/_binary64`
285×	`*-commutative_binary64`

Counts

154 → 129

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	108	5031
1	144	4971
2	323	4517
3	595	4457
4	1046	3995
5	1826	3995
6	4399	3985
7	4932	3985
8	4921	3985

prune359.0ms (7.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	348	0	348
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	348	3	351

Error

Counts

351 → 3

Alt Table

Status	Error	Program
✓	15.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (cbrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1))))) (cbrt.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)))
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 15122 to 7573 computations (49.9% saved)

regimes151.0ms (3.2%)

Accuracy

Total 0.0b remaining (45.6%)

Threshold costs 0.0b (45.6%)

Counts

21 → 1

Compiler

Compiled 3317 to 2175 computations (34.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	9	15

end66.0ms (1.4%)

Compiler: Compiled 87 to 55 computations (36.8% saved)

Details

analyze28.0ms (0.6%)

sample891.0ms (18.6%)

simplify46.0ms (1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series42.0ms (0.9%)

rewrite8.0ms (0.2%)

simplify85.0ms (1.8%)

prune40.0ms (0.8%)

localize7.0ms (0.1%)

series43.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify144.0ms (3%)

prune130.0ms (2.7%)

localize12.0ms (0.2%)

series13.0ms (0.3%)

rewrite2.0ms (0%)

simplify134.0ms (2.8%)

prune140.0ms (2.9%)

localize10.0ms (0.2%)

series2.2s (45.4%)

rewrite28.0ms (0.6%)

simplify212.0ms (4.4%)

prune359.0ms (7.5%)

regimes151.0ms (3.2%)

simplify2.0ms (0%)

end66.0ms (1.4%)

Profiling