Details

analyze466.0ms (7.6%)

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)

sample50.0ms (0.8%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
10.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 38 to 27 computations (28.9% saved)

simplify136.0ms (2.2%)

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

prune6.0ms (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 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize13.0ms (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)

rewrite57.0ms (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:

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

series125.0ms (2%)

Counts

3 → 56

Calls

3 calls:

56.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
56.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
13.0ms	(*.f64 m (-.f64 1 m))

simplify192.0ms (3.1%)

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

prune264.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	293	6	299
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	295	6	301

Error

0.0b

Counts

301 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.0b	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)))

Compiler

Compiled 3352 to 1880 computations (43.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite111.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
152×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

3 → 191

Calls

3 calls:

57.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
15.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
8.0ms	(/.f64 v (-.f64 1 m))

series149.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

56.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
52.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
40.0ms	(/.f64 v (-.f64 1 m))

simplify321.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

722×	`times-frac_binary64`
435×	`fma-def_binary64`
416×	`distribute-rgt-in_binary64`
379×	`distribute-lft-in_binary64`
227×	`fma-neg_binary64`

Counts

251 → 453

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	4706
1	638	4431
2	2332	4350
3	4797	4350
4	4981	4350

prune434.0ms (7.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	453	0	453
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	453	6	459

Error

0.0b

Counts

459 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.0b	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)))

Compiler

Compiled 6258 to 3618 computations (42.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 v (*.f64 m (-.f64 1 m)))
✓	0.1b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.3b	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite76.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

36.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
14.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
10.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

series179.0ms (2.9%)

Counts

3 → 68

Calls

3 calls:

70.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
57.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
52.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)

simplify228.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
359×	`distribute-rgt-in_binary64`
334×	`fma-neg_binary64`
327×	`distribute-lft-in_binary64`
273×	`associate-/r/_binary64`

Counts

192 → 350

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3188
1	412	2804
2	1397	2683
3	4268	2683
4	5165	2683

prune444.0ms (7.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	468	1	469
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	468	7	475

Error

0.0b

Counts

475 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	10.1b	(-.f64 (*.f64 (/.f64 m v) m) m)
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.0b	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (sqrt.f64 m)))

Compiler

Compiled 5750 to 3698 computations (35.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite54.0ms (0.9%)

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:

25.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
21.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))

series122.0ms (2%)

Counts

2 → 32

Calls

2 calls:

62.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
59.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

simplify176.0ms (2.9%)

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

prune275.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	487	2	489
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	489	7	496

Error

Counts

496 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	32.9b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (-.f64 1 m) (/.f64 m v) -1))) (sqrt.f64 (*.f64 m (fma.f64 (-.f64 1 m) (/.f64 m v) -1))))
	7.5b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.1b	(-.f64 (*.f64 (/.f64 m v) m) m)
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	25.5b	(.f64 (.f64 (/.f64 (pow.f64 m 3/2) v) (-.f64 1 m)) (sqrt.f64 m))

Compiler

Compiled 4888 to 2511 computations (48.6% saved)

regimes500.0ms (8.2%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Compiler

Compiled 4695 to 3220 computations (31.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	16
2	28	16
3	31	16
4	32	16
5	30	16

end1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample1.7s (27.3%)

Algorithm

1×

intervals

Results

648.0ms	8000×	body	128	valid
307.0ms	8069×	pre	128	true
8.0ms	69×	body	128	invalid

Compiler

Compiled 153 to 104 computations (32% saved)

Details

analyze466.0ms (7.6%)

sample50.0ms (0.8%)

simplify136.0ms (2.2%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite57.0ms (0.9%)

series125.0ms (2%)

simplify192.0ms (3.1%)

prune264.0ms (4.3%)

localize13.0ms (0.2%)

rewrite111.0ms (1.8%)

series149.0ms (2.4%)

simplify321.0ms (5.3%)

prune434.0ms (7.1%)

localize16.0ms (0.3%)

rewrite76.0ms (1.2%)

series179.0ms (2.9%)

simplify228.0ms (3.7%)

prune444.0ms (7.3%)

localize18.0ms (0.3%)

rewrite54.0ms (0.9%)

series122.0ms (2%)

simplify176.0ms (2.9%)

prune275.0ms (4.5%)

regimes500.0ms (8.2%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.7s (27.3%)

Profiling