Details

analyze355.0ms (11.3%)

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 23 to 16 computations (30.4% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
5.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 38 to 27 computations (28.9% saved)

simplify125.0ms (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

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
▶	0.2b	(.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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (0.9%)

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:

9.0ms	(.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))

series59.0ms (1.9%)

Counts

3 → 56

Calls

3 calls:

29.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
24.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(*.f64 m (-.f64 1 m))

simplify100.0ms (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 → 299

Iterations

Useful iterations: 3 (0.0ms)

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

prune136.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	294	5	299
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	294	7	301

Error

Counts

301 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
▶	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)
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	42.5b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 3))

Compiler

Compiled 3317 to 1855 computations (44.1% saved)

localize7.0ms (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))
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

rewrite13.0ms (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)
4.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

series59.0ms (1.9%)

Counts

3 → 64

Calls

3 calls:

25.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
17.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
16.0ms	(/.f64 (-.f64 1 m) v)

simplify133.0ms (4.2%)

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 → 243

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

prune95.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	243	7	250

Error

Counts

250 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
▶	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	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)
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	42.5b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 3))

Compiler

Compiled 2127 to 1295 computations (39.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.3b	(/.f64 m (sqrt.f64 v))
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite60.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
113×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`

Counts

4 → 221

Calls

4 calls:

23.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
12.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
6.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
3.0ms	(/.f64 m (sqrt.f64 v))

series136.0ms (4.3%)

Counts

4 → 64

Calls

4 calls:

40.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
35.0ms	(/.f64 m (sqrt.f64 v))
31.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
29.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify175.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l/_binary64`
442×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
194×	`fma-def_binary64`
178×	`associate-l_binary64`

Counts

285 → 493

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	5114
1	598	4634
2	1976	4496
3	4784	4496
4	4984	4496

prune214.0ms (6.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	493	0	493
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	493	7	500

Error

Counts

500 → 7

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	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)
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	42.5b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 3))

Compiler

Compiled 6784 to 3294 computations (51.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
✓	0.4b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 55

Calls

2 calls:

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

series60.0ms (1.9%)

Counts

2 → 32

Calls

2 calls:

31.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
29.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

simplify101.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
546×	`associate-/l*_binary64`
487×	`fma-def_binary64`
357×	`times-frac_binary64`
305×	`associate-/r/_binary64`

Counts

87 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1884
1	250	1638
2	727	1451
3	1939	1448
4	4767	1448
5	5248	1448

prune136.0ms (4.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	370	7	377

Error

Counts

377 → 7

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	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)
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	42.5b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 3))

Compiler

Compiled 4873 to 2500 computations (48.7% saved)

regimes188.0ms (6%)

Accuracy

Total 0.2b remaining (84.9%)

Threshold costs 0.2b (84.9%)

Compiler

Compiled 3101 to 2076 computations (33.1% saved)

simplify3.0ms (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	9	14
1	14	14
2	17	14
3	19	14
4	20	14
5	19	14

end0.0ms (0%)

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

sample893.0ms (28.3%)

Algorithm

1×

intervals

Results

348.0ms	8000×	body	128	valid
180.0ms	8044×	pre	128	true
2.0ms	44×	body	128	invalid

Compiler

Compiled 137 to 93 computations (32.1% saved)

Details

analyze355.0ms (11.3%)

sample26.0ms (0.8%)

simplify125.0ms (4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite28.0ms (0.9%)

series59.0ms (1.9%)

simplify100.0ms (3.2%)

prune136.0ms (4.3%)

localize7.0ms (0.2%)

rewrite13.0ms (0.4%)

series59.0ms (1.9%)

simplify133.0ms (4.2%)

prune95.0ms (3%)

localize9.0ms (0.3%)

rewrite60.0ms (1.9%)

series136.0ms (4.3%)

simplify175.0ms (5.5%)

prune214.0ms (6.8%)

localize10.0ms (0.3%)

rewrite26.0ms (0.8%)

series60.0ms (1.9%)

simplify101.0ms (3.2%)

prune136.0ms (4.3%)

regimes188.0ms (6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample893.0ms (28.3%)

Profiling