Details

analyze58.0ms (0.4%)

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)

sample313.0ms (2.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	260×	pre	128	true
0.0ms	4×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify116.0ms (0.8%)

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%)

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

0.2b

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)

localize7.0ms (0%)

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)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series38.0ms (0.3%)

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)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
3.0ms	(*.f64 m (-.f64 1 m))

rewrite39.0ms (0.3%)

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

simplify112.0ms (0.8%)

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

prune247.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	237	8	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	0.9b	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	1.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.4b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
▶	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	11.8b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 5167 to 3154 computations (39% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

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

series48.0ms (0.3%)

Counts

4 → 84

Calls

4 calls:

15.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
13.0ms	(/.f64 v (-.f64 1 m))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
10.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

rewrite145.0ms (1%)

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:

29.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
24.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
9.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify357.0ms (2.5%)

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

prune828.0ms (5.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	711	1	712
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	712	8	720

Error

0.0b

Counts

720 → 8

Alt Table

Status	Error	Program
	11.8b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
▶	0.5b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))) 1) m)
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	1.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.4b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.9b	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 19881 to 12882 computations (35.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series86.0ms (0.6%)

Counts

4 → 64

Calls

4 calls:

41.0ms	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))) 1) m)
25.0ms	(/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m)))
13.0ms	(.f64 (/.f64 (sqrt.f64 v) (.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))
7.0ms	(*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))

rewrite109.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`add-sqr-sqrt_binary64`
142×	`*-un-lft-identity_binary64`
136×	`times-frac_binary64`
116×	`cbrt-prod_binary64`
82×	`add-cube-cbrt_binary64`

Counts

4 → 291

Calls

4 calls:

33.0ms	(.f64 (/.f64 (sqrt.f64 v) (.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))
24.0ms	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))) 1) m)
11.0ms	(*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))
6.0ms	(/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m)))

simplify247.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-def_binary64`
260×	`associate-l_binary64`
245×	`associate-r_binary64`
230×	`associate-*r/_binary64`
213×	`associate-*l/_binary64`

Counts

355 → 429

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	400	9853
1	992	8213
2	3552	7650
3	4874	7650
4	4970	7650

prune529.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	428	1	429
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	429	8	437

Error

0.0b

Counts

437 → 8

Alt Table

Status	Error	Program
	11.8b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.5b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))) 1) m)
	11.1b	(-.f64 (/.f64 m (/.f64 v m)) m)
	1.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.4b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.9b	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 15432 to 10129 computations (34.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series8.4s (57.9%)

Counts

4 → 96

Calls

4 calls:

8.2s	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
83.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
49.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
38.0ms	(cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`cbrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
26×	`cbrt-div_binary64`
23×	`pow1_binary64`

Counts

4 → 130

Calls

4 calls:

21.0ms	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
20.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
6.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
1.0ms	(cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

simplify215.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

438×	`times-frac_binary64`
424×	`fma-def_binary64`
384×	`associate-/l*_binary64`
290×	`associate-/r*_binary64`
203×	`*-commutative_binary64`

Counts

226 → 285

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	14018
1	1903	13236
2	4953	13236

prune481.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	322	9	331

Error

Counts

331 → 9

Alt Table

Status	Error	Program
	11.8b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.5b	(.f64 (-.f64 (/.f64 m (.f64 (/.f64 (sqrt.f64 v) (*.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (/.f64 (sqrt.f64 v) (cbrt.f64 (-.f64 1 m))))) 1) m)
	11.1b	(-.f64 (/.f64 m (/.f64 v m)) m)
	1.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.4b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.9b	(.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 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.9b	(.f64 (.f64 (cbrt.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 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))

Compiler

Compiled 21034 to 14659 computations (30.3% saved)

regimes1.1s (7.3%)

Accuracy

Total 0.2b remaining (91.5%)

Threshold costs 0.2b (91.5%)

Counts

293 → 1

Compiler

Compiled 20711 to 13962 computations (32.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	22	16
3	24	16
4	25	16
5	23	16

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample961.0ms (6.6%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
194.0ms	8060×	pre	128	true
3.0ms	60×	body	128	invalid

Compiler

Compiled 270 to 186 computations (31.1% saved)

Details

analyze58.0ms (0.4%)

sample313.0ms (2.2%)

simplify116.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0%)

series38.0ms (0.3%)

rewrite39.0ms (0.3%)

simplify112.0ms (0.8%)

prune247.0ms (1.7%)

localize7.0ms (0%)

series48.0ms (0.3%)

rewrite145.0ms (1%)

simplify357.0ms (2.5%)

prune828.0ms (5.7%)

localize12.0ms (0.1%)

series86.0ms (0.6%)

rewrite109.0ms (0.8%)

simplify247.0ms (1.7%)

prune529.0ms (3.6%)

localize14.0ms (0.1%)

series8.4s (57.9%)

rewrite64.0ms (0.4%)

simplify215.0ms (1.5%)

prune481.0ms (3.3%)

regimes1.1s (7.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample961.0ms (6.6%)

Profiling