Details

analyze227.0ms (13.3%)

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)

sample25.0ms (1.5%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify215.0ms (12.6%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

rewrite41.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`distribute-lft-out_binary64`

Counts

2 → 68

Calls

2 calls:

20.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
17.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series17.0ms (1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

simplify111.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
302×	`fma-def_binary64`
298×	`associate-/r*_binary64`
284×	`sub-neg_binary64`
231×	`associate-r_binary64`

Counts

92 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1958
1	399	1830
2	1081	1783
3	3637	1748
4	4803	1748
5	4909	1748

prune78.0ms (4.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	2	147

Error

Counts

147 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 2559 to 1742 computations (31.9% saved)

localize9.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`sum-log_binary64`
3×	`associate-+r+_binary64`
3×	`distribute-neg-in_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

series11.0ms (0.7%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

simplify85.0ms (5%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-neg_binary64`
291×	`neg-mul-1_binary64`
290×	`sub-neg_binary64`
288×	`neg-sub0_binary64`
268×	`fma-def_binary64`

Counts

39 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	835
1	295	770
2	808	751
3	2584	743
4	4479	743
5	4993	743

prune38.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	68	2	70

Error

Counts

70 → 2

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1126 to 729 computations (35.3% saved)

regimes46.0ms (2.7%)

Accuracy

Total 0.2b remaining (98.9%)

Threshold costs 0.2b (98.9%)

Compiler

Compiled 478 to 361 computations (24.5% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	22	16
2	29	16
3	34	16
4	36	16
5	35	16

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample786.0ms (46%)

Algorithm

1×

intervals

Results

548.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 53 to 39 computations (26.4% saved)

Details

analyze227.0ms (13.3%)

sample25.0ms (1.5%)

simplify215.0ms (12.6%)

prune2.0ms (0.1%)

localize9.0ms (0.5%)

rewrite41.0ms (2.4%)

series17.0ms (1%)

simplify111.0ms (6.5%)

prune78.0ms (4.6%)

localize9.0ms (0.5%)

rewrite6.0ms (0.3%)

series11.0ms (0.7%)

simplify85.0ms (5%)

prune38.0ms (2.2%)

regimes46.0ms (2.7%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample786.0ms (46%)

Profiling