Details

analyze65.0ms (2.4%)

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)

sample1.2s (45.8%)

Results

907.0ms	8256×	body	128	valid
7.0ms	70×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify120.0ms (4.5%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.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 (0.2%)

Local error

Found 3 expressions with local error:

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

series22.0ms (0.8%)

Counts

3 → 56

Calls

3 calls:

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

rewrite27.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 102

Calls

3 calls:

10.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify87.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune135.0ms (5.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	1.3b	(.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)))
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	0.6b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (sqrt.f64 m)) (sqrt.f64 m))
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3379 to 1893 computations (44% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
7.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

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

simplify83.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
364×	`fma-neg_binary64`
340×	`div-sub_binary64`
294×	`exp-prod_binary64`
286×	`associate-*l/_binary64`

Counts

80 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1280
1	137	1054
2	385	1024
3	1223	1024
4	3040	1024
5	4753	1024
6	4950	1024

prune54.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Error

Counts

81 → 7

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (cbrt.f64 m)))
	0.6b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (sqrt.f64 m)) (sqrt.f64 m))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 1338 to 786 computations (41.3% saved)

localize6.0ms (0.2%)

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)

series24.0ms (0.9%)

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)
5.0ms	(/.f64 (-.f64 1 m) v)

rewrite11.0ms (0.4%)

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)

simplify96.0ms (3.6%)

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

prune87.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	128	6	134

Error

Counts

134 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (cbrt.f64 m)))
▶	0.1b	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (cbrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))) (cbrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 2184 to 1327 computations (39.2% saved)

localize12.0ms (0.5%)

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)))

series29.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

15.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
12.0ms	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
2.0ms	(-.f64 m (*.f64 m m))

rewrite24.0ms (0.9%)

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:

8.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
7.0ms	(+.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) (neg.f64 m))
2.0ms	(-.f64 m (*.f64 m m))

simplify91.0ms (3.4%)

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

prune112.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Error

Counts

176 → 5

Alt Table

Status	Error	Program
	25.0b	(+.f64 (/.f64 (+.f64 (pow.f64 m 3) (pow.f64 (neg.f64 m) 5)) (*.f64 v (fma.f64 m m m))) (neg.f64 m))
	1.4b	(.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (cbrt.f64 m)))
✓	0.1b	(+.f64 (.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))
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3341 to 749 computations (77.6% saved)

regimes251.0ms (9.4%)

Accuracy

Total 0.1b remaining (80.7%)

Threshold costs 0.1b (80.7%)

Counts

92 → 1

Compiler

Compiled 4634 to 2969 computations (35.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	18
2	21	16
3	23	16
4	24	16
5	23	16

end70.0ms (2.6%)

Compiler: Compiled 106 to 65 computations (38.7% saved)

Details

analyze65.0ms (2.4%)

sample1.2s (45.8%)

simplify120.0ms (4.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series22.0ms (0.8%)

rewrite27.0ms (1%)

simplify87.0ms (3.2%)

prune135.0ms (5.1%)

localize6.0ms (0.2%)

series17.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify83.0ms (3.1%)

prune54.0ms (2%)

localize6.0ms (0.2%)

series24.0ms (0.9%)

rewrite11.0ms (0.4%)

simplify96.0ms (3.6%)

prune87.0ms (3.3%)

localize12.0ms (0.5%)

series29.0ms (1.1%)

rewrite24.0ms (0.9%)

simplify91.0ms (3.4%)

prune112.0ms (4.2%)

regimes251.0ms (9.4%)

simplify2.0ms (0.1%)

end70.0ms (2.6%)

Profiling