Details

analyze108.0ms (1.9%)

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)

sample375.0ms (6.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
10.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify138.0ms (2.4%)

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

prune7.0ms (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 (-.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)

localize14.0ms (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)
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series69.0ms (1.2%)

Counts

4 → 80

Calls

4 calls:

25.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
20.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
18.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
5.0ms	(*.f64 m (-.f64 1 m))

rewrite77.0ms (1.3%)

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:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
15.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
14.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
12.0ms	(*.f64 m (-.f64 1 m))

simplify165.0ms (2.9%)

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

prune518.0ms (9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	238	7	245
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Error

Counts

247 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	36.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.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))
	1.6b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	1.4b	(.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)))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	19.7b	(/.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))))
	6.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 5222 to 3193 computations (38.9% saved)

localize12.0ms (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)

series49.0ms (0.9%)

Counts

3 → 64

Calls

3 calls:

22.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
15.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
11.0ms	(/.f64 (-.f64 1 m) v)

rewrite23.0ms (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:

10.0ms	(/.f64 (-.f64 1 m) v)
5.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
1.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify146.0ms (2.5%)

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

prune226.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	127	9	136

Error

Counts

136 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	36.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.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))
	1.6b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
▶	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	19.7b	(/.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))))
	6.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 2345 to 1432 computations (38.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.2b	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.3b	(/.f64 m (sqrt.f64 v))

series245.0ms (4.3%)

Counts

4 → 50

Calls

4 calls:

88.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
72.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
43.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
42.0ms	(/.f64 m (sqrt.f64 v))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
33×	`sqrt-prod_binary64`

Counts

4 → 136

Calls

4 calls:

12.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
5.0ms	(/.f64 m (sqrt.f64 v))
5.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
1.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)

simplify223.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
277×	`fma-neg_binary64`
265×	`associate-/l*_binary64`
247×	`associate-l_binary64`
238×	`times-frac_binary64`

Counts

186 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	3169
1	352	2980
2	941	2765
3	2626	2649
4	4660	2649
5	4990	2649
6	4934	2649

prune415.0ms (7.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	184	9	193

Error

Counts

193 → 9

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	36.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.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))
	1.6b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	19.7b	(/.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))))
	6.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 4044 to 2039 computations (49.6% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 1 m) v)
	0.2b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
✓	0.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

series73.0ms (1.3%)

Counts

2 → 32

Calls

2 calls:

40.0ms	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
32.0ms	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

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

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
339×	`fma-def_binary64`
273×	`exp-prod_binary64`
263×	`*-commutative_binary64`
260×	`unswap-sqr_binary64`

Counts

79 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	1652
1	210	1410
2	598	1289
3	1460	1287
4	3099	1249
5	4381	1249
6	4955	1249

prune248.0ms (4.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	164	9	173

Error

Counts

173 → 9

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	36.4b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.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))
	1.6b	(.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	19.7b	(/.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))))
	6.6b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3383 to 1865 computations (44.9% saved)

regimes950.0ms (16.6%)

Accuracy

Total 0.2b remaining (92.3%)

Threshold costs 0.2b (92.3%)

Counts

147 → 1

Compiler

Compiled 8478 to 5551 computations (34.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	14
1	15	14
2	18	14
3	20	14
4	21	14
5	20	14

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample1.4s (24.7%)

Algorithm

1×

intervals

Results

511.0ms	8000×	body	128	valid
270.0ms	8059×	pre	128	true
4.0ms	59×	body	128	invalid

Compiler

Compiled 237 to 157 computations (33.8% saved)

Details

analyze108.0ms (1.9%)

sample375.0ms (6.5%)

simplify138.0ms (2.4%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

series69.0ms (1.2%)

rewrite77.0ms (1.3%)

simplify165.0ms (2.9%)

prune518.0ms (9%)

localize12.0ms (0.2%)

series49.0ms (0.9%)

rewrite23.0ms (0.4%)

simplify146.0ms (2.5%)

prune226.0ms (3.9%)

localize17.0ms (0.3%)

series245.0ms (4.3%)

rewrite38.0ms (0.7%)

simplify223.0ms (3.9%)

prune415.0ms (7.2%)

localize18.0ms (0.3%)

series73.0ms (1.3%)

rewrite22.0ms (0.4%)

simplify139.0ms (2.4%)

prune248.0ms (4.3%)

regimes950.0ms (16.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.4s (24.7%)

Profiling