Details

analyze419.0ms (11.5%)

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
6.2%	93.6%	0.1%	6
20.3%	79.6%	0.1%	7
28.9%	71%	0.1%	8
39.8%	60.1%	0.1%	9
57.5%	42.3%	0.1%	10
63.9%	36%	0.1%	11
68.6%	31.3%	0.1%	12
79.5%	20.3%	0.1%	13
82.9%	17%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.0s (28.3%)

Results

891.0ms	8254×	body	128	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify212.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

2674×	`fma-neg_binary64`
2270×	`div-sub_binary64`
1877×	`fma-def_binary64`
968×	`associate-/l/_binary64`
705×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	41	13
5	55	13
6	72	13
7	85	13
8	102	13
9	127	13
10	155	13
11	215	13
12	356	13
13	666	13
14	1204	13
15	1746	13
16	1897	13
17	2006	13
18	2246	13
19	2452	13
20	1993	13
21	2354	13
22	2400	13
23	2609	13
24	2737	13
25	2812	13
26	2982	13
27	2984	13
28	3004	13
29	3004	13
30	3850	13
31	5135	13

prune2.0ms (0%)

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

7.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series30.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

30.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite54.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

35× egg-rr

Counts

1 → 35

Calls

2 calls:

53.0ms	((/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	203	13
2	2855	13
3	5099	13
0	0	0
1	0	0

simplify72.0ms (2%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-def_binary64`
330×	`+-commutative_binary64`
304×	`distribute-neg-in_binary64`
284×	`sub-neg_binary64`
246×	`times-frac_binary64`

Counts

71 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	1140
1	265	1140
2	934	1004
3	3610	983
4	4808	980
5	4998	980

prune58.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Error

0.0b

Counts

70 → 7

Alt Table

Status	Error	Program
	8.0b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	37.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	35.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
▶	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	28.9b	(+.f64 y (+.f64 (fma.f64 (/.f64 y z) x x) (*.f64 (/.f64 y z) y)))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	38.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 1570 to 782 computations (50.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	3.3b	(/.f64 x (-.f64 1 (/.f64 y z)))
✓	7.8b	(/.f64 y (-.f64 1 (/.f64 y z)))

series100.0ms (2.8%)

Counts

3 → 75

Calls

3 calls:

54.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
36.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
10.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

rewrite84.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

158× egg-rr

Counts

3 → 158

Calls

2 calls:

80.0ms	((/.f64 y (-.f64 1 (/.f64 y z))) (/.f64 x (-.f64 1 (/.f64 y z))) (+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	230	36
2	3469	36
3	5011	36
0	0	0
1	0	0

simplify72.0ms (2%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
466×	`sub-neg_binary64`
426×	`+-commutative_binary64`
256×	`associate--r+_binary64`
244×	`times-frac_binary64`

Counts

233 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1974
1	337	1974
2	1214	1695
3	4456	1671
4	5038	1671

prune153.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	217	7	224

Error

0.0b

Counts

224 → 7

Alt Table

Status	Error	Program
	35.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
▶	7.8b	(*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x))
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	28.9b	(+.f64 y (+.f64 (fma.f64 (/.f64 y z) x x) (*.f64 (/.f64 y z) y)))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	8.0b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)

Compiler

Compiled 5282 to 2716 computations (48.6% saved)

localize13.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	7.4b	(*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x))

series41.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

30.0ms	(*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x))
10.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

rewrite69.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

100× egg-rr

Counts

2 → 100

Calls

2 calls:

66.0ms	((*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x)) (/.f64 1 (-.f64 1 (/.f64 y z))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	230	23
2	3162	23
3	4956	23
0	0	0
1	0	0

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

455×	`fma-def_binary64`
367×	`+-commutative_binary64`
347×	`sub-neg_binary64`
266×	`times-frac_binary64`
233×	`associate-/l*_binary64`

Counts

160 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1602
1	319	1602
2	1135	1355
3	4313	1343
4	4988	1343

prune103.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	147	7	154

Error

0.0b

Counts

154 → 7

Alt Table

Status	Error	Program
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))
	39.8b	(neg.f64 (/.f64 (*.f64 z (+.f64 x y)) y))
	35.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
✓	7.8b	(*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
▶	8.0b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	28.9b	(*.f64 (+.f64 1 (/.f64 y z)) (+.f64 y x))

Compiler

Compiled 3042 to 1525 computations (49.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
✓	7.8b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series107.0ms (2.9%)

Counts

2 → 72

Calls

2 calls:

84.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
22.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite93.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

169× egg-rr

Counts

2 → 169

Calls

2 calls:

87.0ms	((/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) (pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	247	26
2	3329	26
3	5204	26
0	0	0
1	0	0

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

435×	`associate-+r+_binary64`
354×	`sub-neg_binary64`
308×	`+-commutative_binary64`
297×	`associate-+l+_binary64`
291×	`times-frac_binary64`

Counts

241 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	3973
1	985	3940
2	4355	3931
3	5248	3931

prune206.0ms (5.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	251	7	258

Error

0.0b

Counts

258 → 7

Alt Table

Status	Error	Program
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))
	39.8b	(neg.f64 (/.f64 (*.f64 z (+.f64 x y)) y))
	35.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
✓	7.8b	(*.f64 (/.f64 1 (-.f64 1 (/.f64 y z))) (+.f64 y x))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	8.0b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	28.9b	(*.f64 (+.f64 1 (/.f64 y z)) (+.f64 y x))

Compiler

Compiled 11364 to 4905 computations (56.8% saved)

regimes442.0ms (12.1%)

Accuracy

Total 0.2b remaining (96%)

Threshold costs 0.2b (96%)

Counts

64 → 3

Compiler

Compiled 3654 to 2458 computations (32.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	84
1	34	84
2	41	84
3	46	84
4	49	84
5	50	84
6	49	84

end96.0ms (2.6%)

Compiler: Compiled 219 to 128 computations (41.6% saved)

Details

analyze419.0ms (11.5%)

sample1.0s (28.3%)

simplify212.0ms (5.8%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series30.0ms (0.8%)

rewrite54.0ms (1.5%)

simplify72.0ms (2%)

prune58.0ms (1.6%)

localize8.0ms (0.2%)

series100.0ms (2.8%)

rewrite84.0ms (2.3%)

simplify72.0ms (2%)

prune153.0ms (4.2%)

localize13.0ms (0.4%)

series41.0ms (1.1%)

rewrite69.0ms (1.9%)

simplify64.0ms (1.7%)

prune103.0ms (2.8%)

localize7.0ms (0.2%)

series107.0ms (2.9%)

rewrite93.0ms (2.6%)

simplify96.0ms (2.6%)

prune206.0ms (5.7%)

regimes442.0ms (12.1%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end96.0ms (2.6%)

Profiling