Details

analyze63.0ms (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)

sample1.2s (26%)

Results

902.0ms	8256×	body	128	valid
10.0ms	64×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify115.0ms (2.5%)

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

0.2b

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)

localize6.0ms (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)
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series32.0ms (0.7%)

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite39.0ms (0.8%)

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

simplify106.0ms (2.3%)

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

prune241.0ms (5.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	5.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	19.2b	(/.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))))
	0.3b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	39.0b	(.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)))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))
	9.8b	(.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))
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 5202 to 3191 computations (38.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

11.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
7.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite11.0ms (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)

simplify95.0ms (2%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
308×	`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

prune122.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Error

0.0b

Counts

135 → 8

Alt Table

Status	Error	Program
	19.2b	(/.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))))
	39.0b	(.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 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	5.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.3b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))
	9.8b	(.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))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 2327 to 1428 computations (38.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)
✓	0.0b	(/.f64 v (*.f64 m (-.f64 1 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.3b	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

series54.0ms (1.2%)

Counts

4 → 92

Calls

4 calls:

24.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
12.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
9.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)
9.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite77.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
155×	`add-sqr-sqrt_binary64`
141×	`*-un-lft-identity_binary64`
123×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

4 → 289

Calls

4 calls:

18.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)
17.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
7.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
5.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify179.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-/l*_binary64`
432×	`distribute-rgt-in_binary64`
403×	`distribute-lft-in_binary64`
325×	`associate-/r/_binary64`
323×	`fma-def_binary64`

Counts

381 → 411

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	6616
1	468	5888
2	1524	5517
3	4740	5517
4	5001	5517

prune477.0ms (10.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	411	0	411
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	411	8	419

Error

0.0b

Counts

419 → 8

Alt Table

Status	Error	Program
	19.2b	(/.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))))
	39.0b	(.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 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	5.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.3b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
▶	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))
	9.8b	(.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))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 10813 to 8014 computations (25.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))
✓	0.7b	(cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))

series94.0ms (2%)

Counts

3 → 72

Calls

3 calls:

50.0ms

(*.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))

29.0ms

(cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m))

15.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`associate-*l/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

11.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))

7.0ms

(cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m))

6.0ms

(*.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) m)))

simplify197.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

333×	`associate-r_binary64`
332×	`fma-def_binary64`
322×	`fma-neg_binary64`
299×	`associate-l_binary64`
211×	`times-frac_binary64`

Counts

187 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	501	10757
1	1472	10005
2	4907	9726
3	5144	9726

prune617.0ms (13.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	534	1	535
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	535	8	543

Error

0.0b

Counts

543 → 8

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	5.7b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	19.2b	(/.f64 (.f64 m (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) -1)) (fma.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))
	39.0b	(.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))))
✓	0.3b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)))
	9.8b	(.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 32320 to 22390 computations (30.7% saved)

regimes702.0ms (15.1%)

Accuracy

Total 0.2b remaining (91.7%)

Threshold costs 0.2b (91.7%)

Counts

215 → 1

Compiler

Compiled 14952 to 10311 computations (31% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	16	17
2	19	17
3	21	17
4	22	17
5	21	17

end123.0ms (2.6%)

Compiler: Compiled 213 to 147 computations (31% saved)

Details

analyze63.0ms (1.3%)

sample1.2s (26%)

simplify115.0ms (2.5%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series32.0ms (0.7%)

rewrite39.0ms (0.8%)

simplify106.0ms (2.3%)

prune241.0ms (5.2%)

localize7.0ms (0.1%)

series24.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify95.0ms (2%)

prune122.0ms (2.6%)

localize7.0ms (0.2%)

series54.0ms (1.2%)

rewrite77.0ms (1.7%)

simplify179.0ms (3.8%)

prune477.0ms (10.2%)

localize9.0ms (0.2%)

series94.0ms (2%)

rewrite47.0ms (1%)

simplify197.0ms (4.2%)

prune617.0ms (13.2%)

regimes702.0ms (15.1%)

simplify2.0ms (0%)

end123.0ms (2.6%)

Profiling