Details

analyze360.0ms (7.8%)

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)

sample1.3s (28.4%)

Results

1.2s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify213.0ms (4.6%)

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

10.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.4b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.4b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series24.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

24.0ms

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

rewrite52.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
190×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Counts

1 → 36

Calls

1 calls:

51.0ms

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

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

simplify67.0ms (1.5%)

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

72 → 70

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

prune60.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Error

0.0b

Counts

71 → 6

Alt Table

Status	Error	Program
	10.5b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	37.0b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 2)
	32.2b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	10.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	33.8b	(+.f64 y (+.f64 (fma.f64 (/.f64 y z) x x) (*.f64 (/.f64 y z) y)))

Compiler

Compiled 1545 to 767 computations (50.4% saved)

localize7.0ms (0.1%)

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)))
✓	10.3b	(/.f64 y (-.f64 1 (/.f64 y z)))

series60.0ms (1.3%)

Counts

3 → 75

Calls

3 calls:

29.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
23.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
8.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

rewrite83.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`fma-def_binary64`
246×	`fma-neg_binary64`
216×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
160×	`egg-rr`

Counts

3 → 160

Calls

3 calls:

79.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
79.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
79.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

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

simplify84.0ms (1.8%)

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

235 → 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

prune165.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	216	7	223

Error

0.0b

Counts

223 → 7

Alt Table

Status	Error	Program
▶	10.5b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	37.0b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 2)
	32.2b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))
	23.2b	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))
✓	10.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))

Compiler

Compiled 5314 to 2736 computations (48.5% saved)

localize8.0ms (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)
✓	10.4b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series69.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

50.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
19.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite94.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
170×	`egg-rr`
125×	`add-sqr-sqrt_binary64`
119×	`log1p-expm1-u_binary64`
119×	`expm1-log1p-u_binary64`

Counts

2 → 170

Calls

2 calls:

85.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
85.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

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

simplify100.0ms (2.2%)

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

242 → 252

Iterations

Useful iterations: 2 (0.0ms)

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

prune218.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	252	7	259

Error

0.0b

Counts

259 → 7

Alt Table

Status	Error	Program
✓	10.5b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	37.0b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 2)
	32.2b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))
▶	23.2b	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))
✓	10.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))

Compiler

Compiled 11486 to 4975 computations (56.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x))
✓	3.3b	(/.f64 (-.f64 1 (/.f64 y z)) x)
✓	4.4b	(fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z)))
✓	22.7b	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))

series156.0ms (3.4%)

Counts

4 → 136

Calls

4 calls:

89.0ms	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))
26.0ms	(fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z)))
24.0ms	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x))
16.0ms	(/.f64 (-.f64 1 (/.f64 y z)) x)

rewrite105.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`prod-diff_binary64`
227×	`log1p-udef_binary64`
193×	`egg-rr`
126×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`

Counts

4 → 193

Calls

4 calls:

99.0ms	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x))
99.0ms	(/.f64 (-.f64 1 (/.f64 y z)) x)
99.0ms	(fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z)))
99.0ms	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	90
1	245	78
2	3597	78
3	5169	78
0	0	0
1	0	0

simplify112.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-def_binary64`
354×	`times-frac_binary64`
316×	`associate-/l*_binary64`
237×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`

Counts

329 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	3699
1	426	3607
2	1456	2995
3	4799	2987
4	4979	2987

prune271.0ms (5.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	350	7	357

Error

0.0b

Counts

357 → 7

Alt Table

Status	Error	Program
✓	10.5b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	37.0b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 2)
	32.2b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))
✓	23.2b	(/.f64 (fma.f64 y (/.f64 (-.f64 1 (/.f64 y z)) x) (-.f64 1 (/.f64 y z))) (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 (-.f64 1 (/.f64 y z)) x)))
✓	10.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))

Compiler

Compiled 14738 to 6764 computations (54.1% saved)

regimes844.0ms (18.4%)

Accuracy

Total 0.1b remaining (91.4%)

Threshold costs 0.1b (91.4%)

Counts

106 → 3

Compiler

Compiled 7208 to 4796 computations (33.5% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-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	25	81
1	31	81
2	38	81
3	43	81
4	46	81
5	47	81
6	46	81

end115.0ms (2.5%)

Compiler: Compiled 237 to 135 computations (43% saved)

Details

analyze360.0ms (7.8%)

sample1.3s (28.4%)

simplify213.0ms (4.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series24.0ms (0.5%)

rewrite52.0ms (1.1%)

simplify67.0ms (1.5%)

prune60.0ms (1.3%)

localize7.0ms (0.1%)

series60.0ms (1.3%)

rewrite83.0ms (1.8%)

simplify84.0ms (1.8%)

prune165.0ms (3.6%)

localize8.0ms (0.2%)

series69.0ms (1.5%)

rewrite94.0ms (2%)

simplify100.0ms (2.2%)

prune218.0ms (4.8%)

localize9.0ms (0.2%)

series156.0ms (3.4%)

rewrite105.0ms (2.3%)

simplify112.0ms (2.4%)

prune271.0ms (5.9%)

regimes844.0ms (18.4%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end115.0ms (2.5%)

Profiling