Details

analyze105.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
62.4%	34.3%	3.2%	7
62.4%	32.8%	4.8%	8
68.7%	21.1%	10.2%	9
68.7%	19.1%	12.2%	10
71.8%	11.5%	16.7%	11
71.8%	10.2%	18%	12
73.4%	6%	20.6%	13
73.4%	5.3%	21.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample740.0ms (29.5%)

Results

677.0ms	8256×	body	128	valid
36.0ms	415×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`associate-/r*_binary64`
1×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	13	10
3	12	10

prune1.0ms (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

6.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.2b	(-.f64 (/.f64 x (*.f64 y y)) 3)

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.7b	(/.f64 x (*.f64 y y))

series28.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

28.0ms

(/.f64 x (*.f64 y y))

rewrite44.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

529×	`log1p-expm1-u_binary64`
529×	`expm1-log1p-u_binary64`
376×	`unpow-prod-down_binary64`
274×	`log-prod_binary64`
141×	`pow2_binary64`

Counts

1 → 68

Calls

1 calls:

43.0ms

(/.f64 x (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	106	7
2	1367	7
3	5328	7
0	0	0
1	0	0

simplify145.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
434×	`unswap-sqr_binary64`

Counts

92 → 70

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	11	168
2	19	168
3	34	168
4	70	168
5	166	168
6	491	168
7	1148	168
8	1150	168
9	1298	168
10	1468	168
11	1647	168
12	1872	168
13	2157	168
14	2576	168
15	3141	168
16	3827	168
17	4045	168
18	4289	168
19	4371	168
20	4404	168
21	4425	168
22	4993	168

prune52.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Error

0.0b

Counts

71 → 6

Alt Table

Status	Error	Program
	31.9b	(-.f64 (pow.f64 (/.f64 (sqrt.f64 x) y) 2) 3)
	0.6b	(-.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) y)) 3)
▶	0.1b	(-.f64 (*.f64 (/.f64 x y) (/.f64 1 y)) 3)
✓	6.2b	(-.f64 (/.f64 x (*.f64 y y)) 3)
	7.1b	(-.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (pow.f64 y -2))) 3)
	6.8b	(-.f64 (*.f64 x (pow.f64 y -2)) 3)

Compiler

Compiled 1098 to 622 computations (43.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 x y) (/.f64 1 y))

series28.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

28.0ms

(*.f64 (/.f64 x y) (/.f64 1 y))

rewrite47.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

665×	`log1p-expm1-u_binary64`
665×	`expm1-log1p-u_binary64`
362×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

1 → 47

Calls

1 calls:

46.0ms

(*.f64 (/.f64 x y) (/.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	146	7
2	1765	7
3	5453	7
0	0	0
1	0	0

simplify145.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
434×	`unswap-sqr_binary64`

Counts

71 → 48

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	11	168
2	19	168
3	34	168
4	70	168
5	166	168
6	491	168
7	1148	168
8	1150	168
9	1298	168
10	1468	168
11	1647	168
12	1872	168
13	2157	168
14	2576	168
15	3141	168
16	3827	168
17	4045	168
18	4289	168
19	4371	168
20	4404	168
21	4425	168
22	4993	168

prune40.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	46	8	54

Error

0.0b

Counts

54 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) (neg.f64 y)) 3)
	35.6b	(-.f64 (/.f64 (/.f64 (/.f64 x y) (sqrt.f64 y)) (sqrt.f64 y)) 3)
	31.9b	(-.f64 (pow.f64 (/.f64 (sqrt.f64 x) y) 2) 3)
▶	0.1b	(-.f64 (/.f64 1 (*.f64 (/.f64 y x) y)) 3)
✓	0.1b	(-.f64 (*.f64 (/.f64 x y) (/.f64 1 y)) 3)
✓	6.2b	(-.f64 (/.f64 x (*.f64 y y)) 3)
	6.8b	(-.f64 (*.f64 x (pow.f64 y -2)) 3)
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 3) 3)

Compiler

Compiled 668 to 369 computations (44.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 y x) y)
✓	0.4b	(/.f64 1 (*.f64 (/.f64 y x) y))

series45.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(/.f64 1 (*.f64 (/.f64 y x) y))
18.0ms	(*.f64 (/.f64 y x) y)

rewrite47.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`
116×	`log-pow_binary64`

Counts

2 → 57

Calls

2 calls:

46.0ms	(*.f64 (/.f64 y x) y)
46.0ms	(/.f64 1 (*.f64 (/.f64 y x) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	146	14
2	1798	14
3	4950	14
0	0	0
1	0	0

simplify122.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

786×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
428×	`*-commutative_binary64`
423×	`associate-*r/_binary64`
405×	`associate-/r/_binary64`

Counts

105 → 60

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	336
1	12	336
2	21	336
3	39	336
4	85	336
5	220	336
6	732	336
7	1898	336
8	2513	336
9	2660	336
10	2828	336
11	2941	336
12	3117	336
13	3391	336
14	3872	336
15	4431	336
16	4789	336

prune88.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	60	8	68

Error

0.0b

Counts

68 → 8

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) (neg.f64 y)) 3)
	35.6b	(-.f64 (/.f64 (/.f64 (/.f64 x y) (sqrt.f64 y)) (sqrt.f64 y)) 3)
	31.9b	(-.f64 (pow.f64 (/.f64 (sqrt.f64 x) y) 2) 3)
✓	0.1b	(-.f64 (/.f64 1 (*.f64 (/.f64 y x) y)) 3)
✓	0.1b	(-.f64 (*.f64 (/.f64 x y) (/.f64 1 y)) 3)
✓	6.2b	(-.f64 (/.f64 x (*.f64 y y)) 3)
	6.8b	(-.f64 (*.f64 x (pow.f64 y -2)) 3)
	0.5b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 3) 3)

Compiler

Compiled 831 to 473 computations (43.1% saved)

localize14.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) (neg.f64 y))
✓	0.2b	(*.f64 (neg.f64 x) (/.f64 1 y))

series60.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

46.0ms	(/.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) (neg.f64 y))
14.0ms	(*.f64 (neg.f64 x) (/.f64 1 y))

rewrite114.0ms (4.6%)

Algorithm

2×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
162×	`prod-diff_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

2 → 75

Calls

2 calls:

111.0ms	(/.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) (neg.f64 y))
111.0ms	(*.f64 (neg.f64 x) (/.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	191	11
2	1860	11
3	4887	11
4	5117	11
0	0	0
1	0	0

simplify176.0ms (7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
624×	`times-frac_binary64`
489×	`div-sub_binary64`
434×	`unswap-sqr_binary64`
388×	`fma-def_binary64`

Counts

123 → 78

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	312
1	18	312
2	30	312
3	57	312
4	126	312
5	319	312
6	970	312
7	2730	312
8	3302	312
9	3858	312
10	4370	312
11	4704	312
12	4762	312
13	4826	312
14	4615	312

prune113.0ms (4.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	2	4
Picked	1	0	1
Done	0	3	3
Total	79	7	86

Error

Counts

86 → 7

Alt Table

Status	Error	Program
	31.9b	(-.f64 (pow.f64 (/.f64 (sqrt.f64 x) y) 2) 3)
	0.5b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (.f64 (cbrt.f64 (/.f64 x y)) (/.f64 1 y))) 3)
	35.6b	(-.f64 (*.f64 (pow.f64 y -1/2) (/.f64 (/.f64 x y) (sqrt.f64 y))) 3)
✓	0.1b	(-.f64 (/.f64 1 (*.f64 (/.f64 y x) y)) 3)
✓	0.1b	(-.f64 (*.f64 (/.f64 x y) (/.f64 1 y)) 3)
✓	6.2b	(-.f64 (/.f64 x (*.f64 y y)) 3)
	6.8b	(-.f64 (*.f64 x (pow.f64 y -2)) 3)

Compiler

Compiled 996 to 508 computations (49% saved)

regimes167.0ms (6.6%)

Accuracy

Total 0.1b remaining (88.5%)

Threshold costs 0.1b (88.5%)

Counts

17 → 1

Compiler

Compiled 1244 to 825 computations (33.7% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	11	10
3	10	10

end157.0ms (6.2%)

Compiler: Compiled 101 to 71 computations (29.7% saved)

Details

analyze105.0ms (4.2%)

sample740.0ms (29.5%)

simplify9.0ms (0.3%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series28.0ms (1.1%)

rewrite44.0ms (1.7%)

simplify145.0ms (5.8%)

prune52.0ms (2.1%)

localize5.0ms (0.2%)

series28.0ms (1.1%)

rewrite47.0ms (1.9%)

simplify145.0ms (5.8%)

prune40.0ms (1.6%)

localize5.0ms (0.2%)

series45.0ms (1.8%)

rewrite47.0ms (1.9%)

simplify122.0ms (4.9%)

prune88.0ms (3.5%)

localize14.0ms (0.6%)

series60.0ms (2.4%)

rewrite114.0ms (4.6%)

simplify176.0ms (7%)

prune113.0ms (4.5%)

regimes167.0ms (6.6%)

simplify4.0ms (0.2%)

end157.0ms (6.2%)

Profiling