Details

analyze67.0ms (2%)

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)

sample1.2s (36.8%)

Results

941.0ms	8256×	body	128	valid
6.0ms	53×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify121.0ms (3.6%)

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

prune3.0ms (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 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)

localize8.0ms (0.2%)

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 (1.1%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite40.0ms (1.2%)

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)
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify111.0ms (3.3%)

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

prune236.0ms (7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	240	5	245
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	240	7	247

Error

Counts

247 → 7

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	35.2b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	18.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
	38.3b	(.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)))
	9.3b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))

Compiler

Compiled 5118 to 3133 computations (38.8% saved)

localize14.0ms (0.4%)

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)

series54.0ms (1.6%)

Counts

3 → 64

Calls

3 calls:

24.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
18.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
12.0ms	(/.f64 (-.f64 1 m) v)

rewrite19.0ms (0.6%)

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:

9.0ms	(/.f64 (-.f64 1 m) v)
6.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
1.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify98.0ms (2.9%)

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

prune110.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	128	6	134

Error

Counts

134 → 6

Alt Table

Status	Error	Program
	38.3b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	18.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	9.3b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.1b	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))

Compiler

Compiled 2236 to 1369 computations (38.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
✓	0.0b	(-.f64 m (*.f64 m m))
✓	0.2b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))

series35.0ms (1%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
14.0ms	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
2.0ms	(-.f64 m (*.f64 m m))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`
13×	`associate-l_binary64`

Counts

3 → 99

Calls

3 calls:

7.0ms	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
7.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
2.0ms	(-.f64 m (*.f64 m m))

simplify96.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
236×	`fma-neg_binary64`
202×	`div-sub_binary64`
181×	`distribute-lft-neg-out_binary64`

Counts

159 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	2429
1	422	2282
2	1393	2139
3	4407	2136
4	5017	2136

prune139.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	170	6	176

Error

Counts

176 → 6

Alt Table

Status	Error	Program
	38.3b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	18.1b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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 v) (-.f64 m (.f64 m m))) (neg.f64 m))
▶	0.3b	(+.f64 (.f64 (sqrt.f64 (/.f64 m v)) (.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (*.f64 m m)))) (neg.f64 m))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3501 to 856 computations (75.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series90.0ms (2.7%)

Counts

3 → 16

Calls

3 calls:

40.0ms	(.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (.f64 m m)))
32.0ms	(.f64 (sqrt.f64 (/.f64 m v)) (.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (*.f64 m m))))
17.0ms	(sqrt.f64 (/.f64 m v))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
41×	`sqrt-prod_binary64`
34×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
32×	`associate-l_binary64`

Counts

3 → 143

Calls

3 calls:

13.0ms	(.f64 (sqrt.f64 (/.f64 m v)) (.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (*.f64 m m))))
8.0ms	(.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (.f64 m m)))
2.0ms	(sqrt.f64 (/.f64 m v))

simplify113.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

455×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
352×	`fma-def_binary64`
310×	`associate-*l/_binary64`
235×	`associate-*r/_binary64`

Counts

159 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	3139
1	433	2872
2	1340	2762
3	4849	2762
4	5002	2762

prune206.0ms (6.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	281	6	287

Error

Counts

287 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
✓	0.3b	(+.f64 (.f64 (sqrt.f64 (/.f64 m v)) (.f64 (sqrt.f64 (/.f64 m v)) (-.f64 m (*.f64 m m)))) (neg.f64 m))
	38.3b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	8.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	2.9b	(+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 m v)) (.f64 (-.f64 m (*.f64 m m)) (sqrt.f64 m))) (sqrt.f64 v)) (neg.f64 m))

Compiler

Compiled 7366 to 1477 computations (79.9% saved)

regimes380.0ms (11.2%)

Accuracy

Total 0.2b remaining (87.7%)

Threshold costs 0.2b (87.7%)

Counts

132 → 1

Compiler

Compiled 7767 to 4696 computations (39.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	20	16
2	23	16
3	24	16
4	23	16

end80.0ms (2.4%)

Compiler: Compiled 133 to 81 computations (39.1% saved)

Details

analyze67.0ms (2%)

sample1.2s (36.8%)

simplify121.0ms (3.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series36.0ms (1.1%)

rewrite40.0ms (1.2%)

simplify111.0ms (3.3%)

prune236.0ms (7%)

localize14.0ms (0.4%)

series54.0ms (1.6%)

rewrite19.0ms (0.6%)

simplify98.0ms (2.9%)

prune110.0ms (3.2%)

localize7.0ms (0.2%)

series35.0ms (1%)

rewrite24.0ms (0.7%)

simplify96.0ms (2.8%)

prune139.0ms (4.1%)

localize9.0ms (0.3%)

series90.0ms (2.7%)

rewrite36.0ms (1.1%)

simplify113.0ms (3.3%)

prune206.0ms (6.1%)

regimes380.0ms (11.2%)

simplify3.0ms (0.1%)

end80.0ms (2.4%)

Profiling