Details

analyze59.0ms (1.2%)

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 26 to 19 computations (26.9% saved)

sample142.0ms (2.9%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
5.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify120.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	17

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.7%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(/.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))

rewrite94.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 calls:

60.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify135.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune326.0ms (6.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	29.8b	(.f64 (-.f64 (/.f64 (neg.f64 (.f64 m m)) v) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	19.8b	(.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (-.f64 1 m))

Compiler

Compiled 7229 to 4618 computations (36.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 m (/.f64 m v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
✓	0.2b	(*.f64 (/.f64 m v) m)
✓	7.8b	(/.f64 (pow.f64 m 3) v)

series44.0ms (0.9%)

Counts

4 → 72

Calls

4 calls:

14.0ms	(/.f64 (pow.f64 m 3) v)
12.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
10.0ms	(*.f64 (/.f64 m v) m)
7.0ms	(+.f64 m (/.f64 m v))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 156

Calls

4 calls:

8.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
5.0ms	(+.f64 m (/.f64 m v))
5.0ms	(*.f64 (/.f64 m v) m)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify111.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary64`
441×	`distribute-rgt-in_binary64`
415×	`distribute-lft-in_binary64`
277×	`unswap-sqr_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

228 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3406
1	470	3030
2	1989	2826
3	4999	2742
4	5143	2742

prune217.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

Counts

215 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	19.8b	(+.f64 (cbrt.f64 (pow.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) 3)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (.f64 m (/.f64 (*.f64 m m) v)))

Compiler

Compiled 6214 to 2729 computations (56.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
✓	0.1b	(.f64 m (/.f64 (.f64 m m) v))
	0.2b	(*.f64 (/.f64 m v) m)
✓	14.5b	(/.f64 (*.f64 m m) v)

series24.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.f64 m (/.f64 (.f64 m m) v))
11.0ms	(/.f64 (*.f64 m m) v)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 53

Calls

2 calls:

5.0ms	(.f64 m (/.f64 (.f64 m m) v))
3.0ms	(/.f64 (*.f64 m m) v)

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
521×	`times-frac_binary64`
439×	`associate-/l*_binary64`
398×	`fma-def_binary64`
393×	`unswap-sqr_binary64`

Counts

101 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	966
1	173	861
2	616	861
3	2693	852
4	3350	852
5	4305	852
6	4966	852
7	4903	852

prune190.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	19.8b	(+.f64 (cbrt.f64 (pow.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) 3)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (.f64 m (/.f64 (*.f64 m m) v)))

Compiler

Compiled 5964 to 1934 computations (67.6% saved)

localize6.0ms (0.1%)

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))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
✓	0.1b	(/.f64 m (/.f64 v (-.f64 1 m)))

series138.0ms (2.8%)

Counts

4 → 84

Calls

4 calls:

107.0ms	(/.f64 v (-.f64 1 m))
12.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

rewrite149.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64`
597×	`add-sqr-sqrt_binary64`
563×	`*-un-lft-identity_binary64`
394×	`add-cube-cbrt_binary64`
249×	`prod-diff_binary64`

Counts

4 → 563

Calls

4 calls:

29.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
28.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
9.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify501.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-neg_binary64`
233×	`associate-/l*_binary64`
232×	`*-commutative_binary64`
213×	`associate-l_binary64`
213×	`associate-*l/_binary64`

Counts

647 → 768

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	14395
1	945	13545
2	3863	13035
3	4614	13035
4	4996	13035
5	4935	13035

prune773.0ms (15.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	768	0	768
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	768	4	772

Error

Counts

772 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	19.8b	(+.f64 (cbrt.f64 (pow.f64 (+.f64 m (fma.f64 (/.f64 m v) (-.f64 1 (*.f64 2 m)) -1)) 3)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (.f64 m (/.f64 (*.f64 m m) v)))

Compiler

Compiled 22987 to 15363 computations (33.2% saved)

regimes795.0ms (16.2%)

Accuracy

Total 0.1b remaining (73.1%)

Threshold costs 0.1b (73.1%)

Counts

255 → 1

Compiler

Compiled 16220 to 11636 computations (28.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	12	19
1	19	19
2	22	19
3	24	19
4	25	19
5	22	19

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample866.0ms (17.6%)

Algorithm

1×

intervals

Results

345.0ms	8000×	body	128	valid
182.0ms	8060×	pre	128	true
3.0ms	60×	body	128	invalid

Compiler

Compiled 127 to 86 computations (32.3% saved)

Details

analyze59.0ms (1.2%)

sample142.0ms (2.9%)

simplify120.0ms (2.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series36.0ms (0.7%)

rewrite94.0ms (1.9%)

simplify135.0ms (2.8%)

prune326.0ms (6.6%)

localize10.0ms (0.2%)

series44.0ms (0.9%)

rewrite31.0ms (0.6%)

simplify111.0ms (2.3%)

prune217.0ms (4.4%)

localize11.0ms (0.2%)

series24.0ms (0.5%)

rewrite13.0ms (0.3%)

simplify102.0ms (2.1%)

prune190.0ms (3.9%)

localize6.0ms (0.1%)

series138.0ms (2.8%)

rewrite149.0ms (3%)

simplify501.0ms (10.2%)

prune773.0ms (15.8%)

regimes795.0ms (16.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample866.0ms (17.6%)

Profiling