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)

sample1.2s (57.7%)

Results

962.0ms	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify201.0ms (9.8%)

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

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)

localize9.0ms (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)

series24.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
7.0ms	(/.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))

rewrite78.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
399×	`fma-def_binary64`
203×	`fma-neg_binary64`
189×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

4 → 172

Calls

4 calls:

75.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
75.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
75.0ms	(-.f64 1 (*.f64 x x))
75.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	223	48
2	2931	46
3	5582	46
0	0	0
1	0	0

simplify56.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary64`
659×	`times-frac_binary64`
339×	`associate-/r*_binary64`
322×	`fma-def_binary64`
199×	`associate-r_binary64`

Counts

220 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	909
1	339	876
2	1027	853
3	3544	850
4	5038	850

prune135.0ms (6.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	241	2	243

Error

Counts

243 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 4897 to 3326 computations (32.1% 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	(sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
	0.0b	(-.f64 1 (*.f64 x x))
✓	0.3b	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)

series23.0ms (1.1%)

Counts

2 → 16

Calls

2 calls:

13.0ms	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)
10.0ms	(sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite52.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

880×	`log1p-expm1-u_binary64`
880×	`expm1-log1p-u_binary64`
258×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`

Counts

2 → 56

Calls

2 calls:

51.0ms	(sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
51.0ms	(/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	189	33
2	2237	33
3	5851	33
0	0	0
1	0	0

simplify47.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-neg_binary64`
439×	`associate-/r*_binary64`
357×	`sub-neg_binary64`
346×	`distribute-neg-frac_binary64`
287×	`unswap-sqr_binary64`

Counts

72 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	685
1	290	640
2	940	620
3	3423	594
4	5029	594

prune135.0ms (6.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	191	2	193

Error

Counts

193 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (log.f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 4452 to 3178 computations (28.6% saved)

regimes40.0ms (2%)

Accuracy

Total 0.0b remaining (87.2%)

Threshold costs 0.0b (87.2%)

Counts

12 → 1

Compiler

Compiled 523 to 379 computations (27.5% saved)

simplify2.0ms (0.1%)

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

end47.0ms (2.3%)

Compiler: Compiled 58 to 41 computations (29.3% saved)

Details

analyze6.0ms (0.3%)

sample1.2s (57.7%)

simplify201.0ms (9.8%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

series24.0ms (1.1%)

rewrite78.0ms (3.8%)

simplify56.0ms (2.7%)

prune135.0ms (6.6%)

localize10.0ms (0.5%)

series23.0ms (1.1%)

rewrite52.0ms (2.5%)

simplify47.0ms (2.3%)

prune135.0ms (6.6%)

regimes40.0ms (2%)

simplify2.0ms (0.1%)

end47.0ms (2.3%)

Profiling