Details

analyze10.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample2.2s (51.3%)

Results

2.0s	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify209.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(-.f64 1 (*.f64 x x))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

series33.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

13.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
7.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
3.0ms	(-.f64 1 (*.f64 x x))

rewrite76.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`

Counts

4 → 121

Calls

4 calls:

40.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
11.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.0ms	(-.f64 1 (*.f64 x x))

simplify186.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
570×	`associate-/r*_binary64`
471×	`fma-neg_binary64`
315×	`cancel-sign-sub-inv_binary64`
273×	`times-frac_binary64`

Counts

169 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	263	3309
1	610	3141
2	1734	3057
3	4623	3054
4	4878	3054

prune262.0ms (6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	210	2	212

Error

Counts

212 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))) (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))

Status

Error

Program

✓

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

▶

0.0b

(+.f64 (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))) (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))

Compiler

Compiled 4547 to 3155 computations (30.6% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.0b	(-.f64 1 (*.f64 x x))
	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
✓	0.1b	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series12.0ms (0.3%)

Counts

1 → 8

Calls

1 calls:

12.0ms

(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite51.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
21×	`sqrt-prod_binary64`
9×	`hypot-def_binary64`

Counts

1 → 39

Calls

1 calls:

42.0ms

(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify145.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-neg_binary64`
444×	`associate-/r*_binary64`
311×	`associate-l_binary64`
305×	`associate-r_binary64`
243×	`times-frac_binary64`

Counts

47 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1156
1	300	1101
2	863	1073
3	3255	1058
4	4749	1046
5	4995	1046
6	4883	1046

prune825.0ms (19%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	416	2	418

Error

Counts

418 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))) (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))

Status

Error

Program

✓

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

✓

0.0b

(+.f64 (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))) (log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))

Compiler

Compiled 15801 to 10957 computations (30.7% saved)

regimes126.0ms (2.9%)

Accuracy

Total 0.0b remaining (28.7%)

Threshold costs 0.0b (28.7%)

Counts

17 → 1

Compiler

Compiled 989 to 716 computations (27.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	25	44
2	31	44
3	35	44
4	37	44
5	36	44

end129.0ms (3%)

Compiler: Compiled 102 to 69 computations (32.4% saved)

Details

analyze10.0ms (0.2%)

sample2.2s (51.3%)

simplify209.0ms (4.8%)

prune3.0ms (0.1%)

localize18.0ms (0.4%)

series33.0ms (0.8%)

rewrite76.0ms (1.8%)

simplify186.0ms (4.3%)

prune262.0ms (6%)

localize22.0ms (0.5%)

series12.0ms (0.3%)

rewrite51.0ms (1.2%)

simplify145.0ms (3.3%)

prune825.0ms (19%)

regimes126.0ms (2.9%)

simplify6.0ms (0.1%)

end129.0ms (3%)

Profiling