Details

analyze580.0ms (15.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (30%)

Results

871.0ms	8256×	body	128	valid
119.0ms	1064×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

8.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	7.6b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series23.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
7.0ms	(fma.f64 x (-.f64 y z) x)

rewrite50.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

56× egg-rr

Counts

2 → 56

Calls

2 calls:

49.0ms	((/.f64 (fma.f64 x (-.f64 y z) x) z) (fma.f64 x (-.f64 y z) x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	155	19
2	2114	19
3	6096	19
0	0	0
1	0	0

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
383×	`associate-/l*_binary64`
340×	`neg-sub0_binary64`
339×	`neg-mul-1_binary64`
328×	`distribute-rgt-out--_binary64`

Counts

128 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	760
1	75	760
2	166	697
3	366	637
4	1205	637
5	3037	637
6	4643	637
7	5092	637

prune49.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Error

0.5b

Counts

78 → 9

Alt Table

Status	Error	Program
▶	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
✓	8.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	8.3b	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
	20.8b	(-.f64 (/.f64 x z) x)
	9.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) z))
	35.2b	(*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)))
	33.5b	(.f64 (/.f64 1 (cbrt.f64 (.f64 z z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	34.3b	(.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 1 z)))
	9.1b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 2))

Compiler

Compiled 1221 to 410 computations (66.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 y z) x)
✓	7.7b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

series15.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

rewrite85.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

33× egg-rr

Counts

1 → 33

Calls

2 calls:

84.0ms	((*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	191	11
2	2339	11
3	4950	11
4	5221	11
0	0	0
1	0	0

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

731×	`div-sub_binary64`
639×	`fma-neg_binary64`
624×	`fma-def_binary64`
523×	`distribute-rgt-in_binary64`
454×	`distribute-lft-in_binary64`

Counts

69 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	428
1	63	428
2	146	365
3	323	365
4	1160	365
5	3798	365
6	5183	365

prune43.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	77	8	85

Error

0.5b

Counts

85 → 8

Alt Table

Status	Error	Program
▶	8.3b	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
	34.3b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
✓	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	9.2b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 3) (/.f64 1 z))
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	20.8b	(-.f64 (/.f64 x z) x)
	9.2b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) z))
	9.1b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 2))

Compiler

Compiled 1205 to 465 computations (61.4% saved)

localize37.0ms (1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 y z) x)
✓	0.2b	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
✓	7.6b	(/.f64 z (fma.f64 x (-.f64 y z) x))

series641.0ms (17.6%)

Counts

2 → 72

Calls

2 calls:

608.0ms	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
33.0ms	(/.f64 z (fma.f64 x (-.f64 y z) x))

rewrite56.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

81× egg-rr

Counts

2 → 81

Calls

2 calls:

54.0ms	((/.f64 z (fma.f64 x (-.f64 y z) x)) (pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	197	22
2	2501	22
3	5194	22
0	0	0
1	0	0

simplify54.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

762×	`associate-/l*_binary64`
623×	`associate-/r*_binary64`
472×	`fma-def_binary64`
172×	`distribute-rgt-in_binary64`
134×	`distribute-lft-in_binary64`

Counts

153 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1933
1	433	1921
2	1676	1778
3	5530	1778

prune100.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	160	8	168

Error

Counts

168 → 8

Alt Table

Status	Error	Program
✓	8.3b	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
	35.7b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 z (fma.f64 x (-.f64 y z) x))))
	9.1b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) 2))
	8.3b	(pow.f64 (*.f64 z (/.f64 1 (fma.f64 x (-.f64 y z) x))) -1)
✓	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
▶	5.3b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	34.3b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) 1) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))

Compiler

Compiled 3257 to 1252 computations (61.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.0b	(fma.f64 (/.f64 y z) x (/.f64 x z))

series21.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

21.0ms

(fma.f64 (/.f64 y z) x (/.f64 x z))

rewrite43.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

23× egg-rr

Counts

1 → 23

Calls

2 calls:

43.0ms	((fma.f64 (/.f64 y z) x (/.f64 x z)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	148	11
2	1969	11
3	5252	11
0	0	0
1	0	0

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

42×	`fma-def_binary64`
16×	`associate-l_binary64`
15×	`associate-r_binary64`
12×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`

Counts

59 → 30

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	447
1	27	447
2	41	381
3	57	381
4	57	282
5	114	282
6	112	282
7	116	282
8	114	282

prune23.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	31	7	38

Error

Counts

38 → 7

Alt Table

Status	Error	Program
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	5.8b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y z) x (/.f64 x z))) 3) x)
✓	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
✓	5.3b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	34.3b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) 1) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
	16.6b	(-.f64 (*.f64 (/.f64 x z) y) x)
	8.3b	(pow.f64 (*.f64 z (/.f64 1 (fma.f64 x (-.f64 y z) x))) -1)

Compiler

Compiled 531 to 176 computations (66.9% saved)

regimes360.0ms (9.9%)

Accuracy

Total 3.0b remaining (99.7%)

Threshold costs 0b (0%)

Counts

72 → 3

Compiler

Compiled 4568 to 2726 computations (40.3% saved)

bsearch45.0ms (1.2%)

Steps

Iters	Range		Point
10	1.4490963861746216e+235	5.1230545763897275e+245	4.786042295204834e+237
5	5.677812371419575e+89	1.7911229558995487e+96	1.63726535631151e+93

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	47
1	31	47
2	39	47
3	43	47
4	45	47
5	44	47

end89.0ms (2.5%)

Compiler: Compiled 176 to 99 computations (43.8% saved)

Details

analyze580.0ms (15.9%)

sample1.1s (30%)

simplify55.0ms (1.5%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series23.0ms (0.6%)

rewrite50.0ms (1.4%)

simplify78.0ms (2.1%)

prune49.0ms (1.3%)

localize8.0ms (0.2%)

series15.0ms (0.4%)

rewrite85.0ms (2.3%)

simplify56.0ms (1.5%)

prune43.0ms (1.2%)

localize37.0ms (1%)

series641.0ms (17.6%)

rewrite56.0ms (1.5%)

simplify54.0ms (1.5%)

prune100.0ms (2.8%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite43.0ms (1.2%)

simplify18.0ms (0.5%)

prune23.0ms (0.6%)

regimes360.0ms (9.9%)

bsearch45.0ms (1.2%)

simplify3.0ms (0.1%)

end89.0ms (2.5%)

Profiling