Details

analyze68.0ms (1.3%)

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)

sample1.3s (23.6%)

Results

936.0ms	8256×	body	128	valid
7.0ms	52×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify120.0ms (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

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.7%)

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

9.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
8.0ms	(*.f64 m (-.f64 1 m))
8.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify108.0ms (2%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
481×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3059
1	413	2618
2	1688	2595
3	4507	2594
4	4922	2594

prune233.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	240	5	245
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	241	6	247

Error

0.0b

Counts

247 → 6

Alt Table

Status	Error	Program
	13.0b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	37.5b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))
▶	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) m))

Compiler

Compiled 5097 to 3106 computations (39.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series43.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

15.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
9.0ms	(/.f64 v (-.f64 1 m))

rewrite144.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64`
580×	`add-sqr-sqrt_binary64`
546×	`*-un-lft-identity_binary64`
380×	`add-cube-cbrt_binary64`
231×	`prod-diff_binary64`

Counts

4 → 528

Calls

4 calls:

30.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
25.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
8.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify348.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

824×	`times-frac_binary64`
637×	`fma-def_binary64`
234×	`fma-neg_binary64`
220×	`associate-*l/_binary64`
191×	`associate-/r/_binary64`

Counts

612 → 712

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	13214
1	832	12612
2	3028	11485
3	4893	11485
4	5032	11485

prune927.0ms (17.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	709	3	712
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	711	7	718

Error

Counts

718 → 7

Alt Table

Status	Error	Program
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.1b	(.f64 (+.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) (.f64 (-.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) m))
	37.5b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.9b	(/.f64 (fma.f64 (/.f64 (pow.f64 m 3) (*.f64 v (/.f64 v (-.f64 1 m)))) (-.f64 1 m) (neg.f64 m)) (+.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.6b	(.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 19801 to 12832 computations (35.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.2b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

series27.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

3 → 76

Calls

3 calls:

5.0ms	(/.f64 (-.f64 1 m) v)
3.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify101.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
307×	`associate-l_binary64`
305×	`div-sub_binary64`
264×	`exp-prod_binary64`

Counts

140 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2018
1	285	1760
2	745	1726
3	2553	1726
4	4478	1726
5	4976	1726

prune115.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Error

Counts

134 → 7

Alt Table

Status	Error	Program
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.1b	(.f64 (+.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) (.f64 (-.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) m))
	37.5b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.9b	(/.f64 (fma.f64 (/.f64 (pow.f64 m 3) (*.f64 v (/.f64 v (-.f64 1 m)))) (-.f64 1 m) (neg.f64 m)) (+.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.6b	(.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 2227 to 1364 computations (38.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
	0.1b	(/.f64 m (/.f64 v (-.f64 1 m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m))
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m)) (sqrt.f64 m))

series48.0ms (0.9%)

Counts

2 → 32

Calls

2 calls:

25.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m))
22.0ms	(.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
14×	`associate-l_binary64`
12×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`

Counts

2 → 61

Calls

2 calls:

29.0ms	(.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m)) (sqrt.f64 m))
29.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (sqrt.f64 m))

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
538×	`fma-def_binary64`
502×	`times-frac_binary64`
353×	`associate-/r/_binary64`
289×	`associate-/l/_binary64`

Counts

93 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	2022
1	263	1676
2	758	1559
3	2100	1556
4	4673	1556
5	5334	1556

prune587.0ms (11.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	696	1	697
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	698	6	704

Error

Counts

704 → 6

Alt Table

Status	Error	Program
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.1b	(.f64 (+.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) (.f64 (-.f64 (/.f64 (sqrt.f64 m) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) m))
	37.5b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	3.8b	(*.f64 (-.f64 (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 22119 to 13250 computations (40.1% saved)

regimes801.0ms (15.1%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

Counts

232 → 1

Compiler

Compiled 13691 to 9120 computations (33.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	25	16
3	28	16
4	29	16
5	29	16

end93.0ms (1.8%)

Compiler: Compiled 137 to 90 computations (34.3% saved)

Details

analyze68.0ms (1.3%)

sample1.3s (23.6%)

simplify120.0ms (2.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series36.0ms (0.7%)

rewrite40.0ms (0.7%)

simplify108.0ms (2%)

prune233.0ms (4.4%)

localize7.0ms (0.1%)

series43.0ms (0.8%)

rewrite144.0ms (2.7%)

simplify348.0ms (6.6%)

prune927.0ms (17.5%)

localize6.0ms (0.1%)

series27.0ms (0.5%)

rewrite12.0ms (0.2%)

simplify101.0ms (1.9%)

prune115.0ms (2.2%)

localize10.0ms (0.2%)

series48.0ms (0.9%)

rewrite62.0ms (1.2%)

simplify104.0ms (2%)

prune587.0ms (11.1%)

regimes801.0ms (15.1%)

simplify3.0ms (0.1%)

end93.0ms (1.8%)

Profiling