Details

analyze188.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample3.2s (25.7%)

Results

2.5s	8256×	body	128	valid
12.0ms	65×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify293.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune6.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize24.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series51.0ms (0.4%)

Counts

2 → 44

Calls

2 calls:

28.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

rewrite64.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
7×	`associate-l_binary64`

Counts

2 → 51

Calls

2 calls:

43.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
12.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify213.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

821×	`times-frac_binary64`
598×	`associate-/l*_binary64`
362×	`fma-neg_binary64`
287×	`distribute-rgt-in_binary64`
274×	`distribute-lft-in_binary64`

Counts

95 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	1437
1	283	1308
2	974	1227
3	4442	1227
4	4991	1227

prune472.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Error

Counts

100 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	17.9b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
▶	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)

Compiler

Compiled 1934 to 1172 computations (39.4% saved)

localize21.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

series64.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

40.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
24.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

rewrite126.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
128×	`add-sqr-sqrt_binary64`
110×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64`

Counts

2 → 148

Calls

2 calls:

61.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
27.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify356.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

692×	`times-frac_binary64`
512×	`associate-/r/_binary64`
400×	`distribute-rgt-in_binary64`
378×	`distribute-lft-in_binary64`
275×	`fma-def_binary64`

Counts

196 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3891
1	556	3655
2	2044	3584
3	4576	3584
4	5018	3584

prune658.0ms (5.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	237	6	243

Error

Counts

243 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	17.9b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
▶	0.2b	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)

Compiler

Compiled 5195 to 2983 computations (42.6% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 v (-.f64 1 m)) m)
✓	0.1b	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)
✓	0.3b	(/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m))

series115.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

60.0ms	(/.f64 (/.f64 v (-.f64 1 m)) m)
31.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)
23.0ms	(/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m))

rewrite418.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

912×	`times-frac_binary64`
568×	`add-sqr-sqrt_binary64`
530×	`*-un-lft-identity_binary64`
367×	`add-cube-cbrt_binary64`
110×	`difference-of-squares_binary64`

Counts

3 → 495

Calls

3 calls:

164.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)
28.0ms	(/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m))
20.0ms	(/.f64 (/.f64 v (-.f64 1 m)) m)

simplify1.1s (8.5%)

Algorithm

1×	egg-herbie

Rules

458×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
357×	`associate-/r/_binary64`
315×	`fma-def_binary64`
271×	`associate-/l/_binary64`

Counts

567 → 688

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	420	14056
1	911	12362
2	2754	12061
3	4786	12013
4	4981	12013

prune2.3s (18.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	688	0	688
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	688	6	694

Error

Counts

694 → 6

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	17.9b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
✓	0.2b	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)

Compiler

Compiled 18066 to 11385 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(/.f64 m (sqrt.f64 v))
✓	0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

series319.0ms (2.5%)

Counts

4 → 64

Calls

4 calls:

109.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
84.0ms	(/.f64 m (sqrt.f64 v))
76.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
49.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite193.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
113×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`

Counts

4 → 221

Calls

4 calls:

52.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
33.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
27.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
11.0ms	(/.f64 m (sqrt.f64 v))

simplify411.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l/_binary64`
442×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
194×	`fma-def_binary64`
178×	`associate-l_binary64`

Counts

285 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	5114
1	598	4634
2	1976	4496
3	4784	4496
4	4984	4496

prune775.0ms (6.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	292	6	298

Error

Counts

298 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	17.9b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
✓	0.2b	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v (-.f64 1 m)) m)) 1) m)

Compiler

Compiled 6778 to 3285 computations (51.5% saved)

regimes824.0ms (6.6%)

Accuracy

Total 0.2b remaining (85.6%)

Threshold costs 0.2b (85.6%)

Counts

85 → 1

Compiler

Compiled 4664 to 3167 computations (32.1% saved)

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	21	16
3	23	16
4	24	16
5	22	16

end272.0ms (2.2%)

Compiler: Compiled 148 to 101 computations (31.8% saved)

Details

analyze188.0ms (1.5%)

sample3.2s (25.7%)

simplify293.0ms (2.3%)

prune6.0ms (0%)

localize24.0ms (0.2%)

series51.0ms (0.4%)

rewrite64.0ms (0.5%)

simplify213.0ms (1.7%)

prune472.0ms (3.8%)

localize21.0ms (0.2%)

series64.0ms (0.5%)

rewrite126.0ms (1%)

simplify356.0ms (2.8%)

prune658.0ms (5.2%)

localize18.0ms (0.1%)

series115.0ms (0.9%)

rewrite418.0ms (3.3%)

simplify1.1s (8.5%)

prune2.3s (18.5%)

localize15.0ms (0.1%)

series319.0ms (2.5%)

rewrite193.0ms (1.5%)

simplify411.0ms (3.3%)

prune775.0ms (6.2%)

regimes824.0ms (6.6%)

simplify35.0ms (0.3%)

end272.0ms (2.2%)

Profiling