Details

analyze1.2s (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.6s (28.6%)

Results

1.4s	8256×	body	128	valid
107.0ms	637×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune3.0ms (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

1.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.5b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series84.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

52.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
32.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite199.0ms (3.6%)

Algorithm

2×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
258×	`egg-rr`
204×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`

Counts

2 → 258

Calls

2 calls:

180.0ms	(/.f64 (-.f64 x y) (-.f64 z y))
180.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	23
2	3068	23
3	5326	23
0	0	0
1	0	0

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
665×	`times-frac_binary64`
604×	`fma-neg_binary64`
419×	`cancel-sign-sub-inv_binary64`
327×	`sub-neg_binary64`

Counts

342 → 325

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2783
1	465	2777
2	1760	2157
3	4756	2152
4	5179	2152

prune412.0ms (7.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	320	5	325
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	320	6	326

Error

Counts

326 → 6

Alt Table

Status	Error	Program
	12.8b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 (-.f64 x y) t)))
	10.3b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
✓	1.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) 3))
▶	9.5b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
	12.7b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 14435 to 3701 computations (74.4% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z y))
✓	9.4b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))

series82.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

53.0ms	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
28.0ms	(/.f64 t (-.f64 z y))

rewrite83.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

736×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

2 → 78

Calls

2 calls:

80.0ms	(/.f64 t (-.f64 z y))
80.0ms	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	205	20
2	2958	20
3	5009	20
0	0	0
1	0	0

simplify118.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
573×	`fma-def_binary64`
546×	`associate-/l*_binary64`
477×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`

Counts

150 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	2119
1	348	2083
2	1307	1749
3	4868	1749
4	5237	1749

prune130.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	127	6	133

Error

Counts

133 → 6

Alt Table

Status	Error	Program
	12.8b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 (-.f64 x y) t)))
▶	10.3b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
✓	1.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) 3))
✓	9.5b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
	12.7b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 2632 to 935 computations (64.5% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.3b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))

series65.0ms (1.2%)

Counts

1 → 48

Calls

1 calls:

65.0ms

(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))

rewrite105.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

359×	`fma-def_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
210×	`fma-neg_binary64`
182×	`log-pow_binary64`

Counts

1 → 63

Calls

1 calls:

102.0ms

(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	217	13
2	3444	13
3	5074	13
0	0	0
1	0	0

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

554×	`times-frac_binary64`
472×	`associate-/l*_binary64`
454×	`associate--l+_binary64`
447×	`fma-def_binary64`
246×	`cancel-sign-sub-inv_binary64`

Counts

111 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	1702
1	289	1702
2	1094	1249
3	5067	1249

prune92.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	12.8b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 (-.f64 x y) t)))
✓	10.3b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
✓	1.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) 3))
✓	9.5b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
▶	12.7b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 2223 to 704 computations (68.3% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.1b	(/.f64 (*.f64 t x) (-.f64 z y))
✓	10.3b	(/.f64 (*.f64 y t) (-.f64 z y))

series74.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(/.f64 (*.f64 t x) (-.f64 z y))
30.0ms	(/.f64 (*.f64 y t) (-.f64 z y))

rewrite157.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

413×	`prod-diff_binary64`
338×	`fma-udef_binary64`
236×	`fma-neg_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`

Counts

2 → 90

Calls

2 calls:

154.0ms	(/.f64 (*.f64 t x) (-.f64 z y))
154.0ms	(/.f64 (*.f64 y t) (-.f64 z y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	222	20
2	3251	20
3	4905	20
4	4914	20
5	5007	20
0	0	0
1	0	0

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
539×	`fma-neg_binary64`
454×	`associate-/l*_binary64`
369×	`fma-def_binary64`
310×	`distribute-neg-frac_binary64`

Counts

138 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1392
1	224	1392
2	793	1110
3	3891	1101
4	5013	1101

prune129.0ms (2.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	120	6	126

Error

Counts

126 → 6

Alt Table

Status	Error	Program
	12.8b	(/.f64 1 (/.f64 (-.f64 z y) (*.f64 (-.f64 x y) t)))
✓	10.3b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
✓	1.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	37.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) 3))
✓	9.5b	(*.f64 (/.f64 t (-.f64 z y)) (-.f64 x y))
✓	12.7b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 2735 to 736 computations (73.1% saved)

regimes452.0ms (8.1%)

Accuracy

Total 2.4b remaining (99.5%)

Threshold costs 0b (0%)

Counts

46 → 1

Compiler

Compiled 3968 to 2564 computations (35.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	18	13
3	20	13
4	21	13
5	21	13

end137.0ms (2.5%)

Compiler: Compiled 115 to 71 computations (38.3% saved)

Details

analyze1.2s (20.7%)

sample1.6s (28.6%)

simplify134.0ms (2.4%)

prune3.0ms (0%)

localize10.0ms (0.2%)

series84.0ms (1.5%)

rewrite199.0ms (3.6%)

simplify134.0ms (2.4%)

prune412.0ms (7.4%)

localize11.0ms (0.2%)

series82.0ms (1.5%)

rewrite83.0ms (1.5%)

simplify118.0ms (2.1%)

prune130.0ms (2.3%)

localize12.0ms (0.2%)

series65.0ms (1.2%)

rewrite105.0ms (1.9%)

simplify82.0ms (1.5%)

prune92.0ms (1.7%)

localize15.0ms (0.3%)

series74.0ms (1.3%)

rewrite157.0ms (2.8%)

simplify98.0ms (1.8%)

prune129.0ms (2.3%)

regimes452.0ms (8.1%)

simplify4.0ms (0.1%)

end137.0ms (2.5%)

Profiling