Details

analyze6.0ms (0.3%)

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)

sample232.0ms (11.7%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify202.0ms (10.2%)

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

prune2.0ms (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)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series25.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms	(-.f64 1 (*.f64 x x))

rewrite42.0ms (2.1%)

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:

21.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(-.f64 1 (*.f64 x x))

simplify112.0ms (5.6%)

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

prune136.0ms (6.8%)

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)))
▶	0.2b	(+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)) (log.f64 (/.f64 1 x)))

Compiler

Compiled 4517 to 3137 computations (30.6% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 x))
✓	0.0b	(log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
	0.0b	(-.f64 1 (*.f64 x x))
✓	0.2b	(+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)) (log.f64 (/.f64 1 x)))

series41.0ms (2.1%)

Counts

3 → 32

Calls

3 calls:

23.0ms	(log.f64 (/.f64 1 x))
9.0ms	(+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)) (log.f64 (/.f64 1 x)))
8.0ms	(log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))

rewrite24.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

3 → 92

Calls

3 calls:

11.0ms	(+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)) (log.f64 (/.f64 1 x)))
5.0ms	(log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
2.0ms	(log.f64 (/.f64 1 x))

simplify128.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
405×	`fma-def_binary64`
249×	`times-frac_binary64`
229×	`unsub-neg_binary64`
188×	`associate-l_binary64`

Counts

124 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2297
1	423	1992
2	1211	1932
3	3658	1932
4	4917	1932
5	4995	1932
6	4904	1932

prune151.0ms (7.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	208	2	210

Error

Counts

210 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.2b	(+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)) (log.f64 (/.f64 1 x)))

Compiler

Compiled 4398 to 3200 computations (27.2% saved)

regimes79.0ms (4%)

Accuracy

Total 0.0b remaining (12.2%)

Threshold costs 0.0b (12.2%)

Counts

26 → 1

Compiler

Compiled 1000 to 766 computations (23.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	10	20
1	18	20
2	24	20
3	28	20
4	30	20
5	29	20

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample781.0ms (39.4%)

Algorithm

1×

intervals

Results

541.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 59 to 44 computations (25.4% saved)

Details

analyze6.0ms (0.3%)

sample232.0ms (11.7%)

simplify202.0ms (10.2%)

prune2.0ms (0.1%)

localize10.0ms (0.5%)

series25.0ms (1.3%)

rewrite42.0ms (2.1%)

simplify112.0ms (5.6%)

prune136.0ms (6.8%)

localize10.0ms (0.5%)

series41.0ms (2.1%)

rewrite24.0ms (1.2%)

simplify128.0ms (6.5%)

prune151.0ms (7.6%)

regimes79.0ms (4%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample781.0ms (39.4%)

Profiling