Details

analyze1.1s (21.7%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (22.7%)

Results

975.0ms	8256×	body	128	valid
82.0ms	659×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	13

prune3.0ms (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

9.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.5b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	9.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series36.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
6.0ms	(*.f64 x (-.f64 y z))

rewrite61.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 68

Calls

2 calls:

60.0ms	(*.f64 x (-.f64 y z))
60.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	205	20
2	2981	20
3	5059	20
0	0	0
1	0	0

simplify117.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

531×	`times-frac_binary64`
451×	`fma-def_binary64`
439×	`associate-/l*_binary64`
366×	`associate--l+_binary64`
293×	`cancel-sign-sub-inv_binary64`

Counts

152 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	1753
1	280	1699
2	1049	1531
3	4796	1507
4	4970	1501
5	5019	1501

prune91.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Error

0.0b

Counts

108 → 7

Alt Table

Status	Error	Program
	37.2b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 x (-.f64 y z))) 2) (-.f64 t z))
	10.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 (-.f64 t z))))
	12.4b	(.f64 (-.f64 y z) (.f64 x (/.f64 1 (-.f64 t z))))
✓	9.5b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
▶	3.1b	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))
	5.4b	(*.f64 (/.f64 (-.f64 y z) (pow.f64 (cbrt.f64 (-.f64 t z)) 2)) (/.f64 x (cbrt.f64 (-.f64 t z))))
	12.3b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 2270 to 780 computations (65.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z)))
✓	2.5b	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))

series70.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

34.0ms	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))
19.0ms	(/.f64 (-.f64 t z) (-.f64 y z))
17.0ms	(/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z)))

rewrite134.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

961×	`prod-diff_binary64`
309×	`egg-rr`
129×	`add-sqr-sqrt_binary64`
122×	`log1p-expm1-u_binary64`
122×	`expm1-log1p-u_binary64`

Counts

3 → 309

Calls

3 calls:

120.0ms	(/.f64 (-.f64 t z) (-.f64 y z))
120.0ms	(/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z)))
120.0ms	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	250	33
2	3483	33
3	5368	33
0	0	0
1	0	0

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

967×	`times-frac_binary64`
750×	`cancel-sign-sub-inv_binary64`
511×	`sub-neg_binary64`
288×	`fma-neg_binary64`
220×	`associate--l+_binary64`

Counts

429 → 404

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	3687
1	660	3597
2	2554	3417
3	5385	3417

prune310.0ms (6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	402	2	404
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	403	8	411

Error

Counts

411 → 8

Alt Table

Status	Error	Program
▶	3.0b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 (-.f64 t z))))
	32.7b	(.f64 x (.f64 (/.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z))) (+.f64 t z)))
	5.4b	(*.f64 (/.f64 (-.f64 y z) (pow.f64 (cbrt.f64 (-.f64 t z)) 2)) (/.f64 x (cbrt.f64 (-.f64 t z))))
	12.4b	(.f64 (-.f64 y z) (.f64 x (/.f64 1 (-.f64 t z))))
✓	9.5b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
✓	3.1b	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))
	12.3b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 16831 to 4852 computations (71.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	2.9b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

series32.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

32.0ms

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

rewrite66.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

979×	`prod-diff_binary64`
115×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`
110×	`expm1-log1p-u_binary64`
107×	`add-log-exp_binary64`

Counts

1 → 46

Calls

1 calls:

64.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	214	13
2	3301	13
3	5256	13
0	0	0
1	0	0

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

525×	`times-frac_binary64`
441×	`fma-def_binary64`
428×	`associate-/l*_binary64`
374×	`sub-neg_binary64`
366×	`associate--l+_binary64`

Counts

94 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1513
1	271	1459
2	1031	1291
3	4738	1267
4	5135	1267

prune232.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	342	3	345
Fresh	3	2	5
Picked	0	1	1
Done	1	1	2
Total	346	7	353

Error

Counts

353 → 7

Alt Table

Status	Error	Program
✓	3.0b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	10.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 y z))) 2) (.f64 (cbrt.f64 (.f64 x (-.f64 y z))) (/.f64 1 (-.f64 t z))))
	9.6b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
▶	2.6b	(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x)
	12.4b	(.f64 (-.f64 y z) (.f64 x (/.f64 1 (-.f64 t z))))
✓	9.5b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
	3.1b	(/.f64 x (*.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))

Compiler

Compiled 14905 to 3749 computations (74.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	2.5b	(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x)

series48.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x)
17.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite117.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 260

Calls

2 calls:

104.0ms	(/.f64 (-.f64 y z) (-.f64 t z))
104.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x)

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

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
725×	`fma-neg_binary64`
656×	`times-frac_binary64`
500×	`cancel-sign-sub-inv_binary64`
337×	`sub-neg_binary64`

Counts

344 → 329

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2792
1	468	2525
2	1780	2084
3	4462	2072
4	5008	2072

prune237.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	327	2	329
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	329	7	336

Error

Counts

336 → 7

Alt Table

Status	Error	Program
✓	2.6b	(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) x)
	3.2b	(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))) 3) x)
	9.6b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
✓	3.0b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	12.4b	(/.f64 (-.f64 y z) (/.f64 (-.f64 t z) x))
✓	9.5b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
	3.1b	(/.f64 x (*.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))

Compiler

Compiled 14390 to 3675 computations (74.5% saved)

regimes826.0ms (16.1%)

Accuracy

Total 1.5b remaining (99.3%)

Threshold costs 0b (0%)

Counts

115 → 3

Compiler

Compiled 9032 to 5779 computations (36% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	22	75
2	28	75
3	30	75
4	31	75
5	31	75

end84.0ms (1.6%)

Compiler: Compiled 210 to 97 computations (53.8% saved)

Details

analyze1.1s (21.7%)

sample1.2s (22.7%)

simplify111.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series36.0ms (0.7%)

rewrite61.0ms (1.2%)

simplify117.0ms (2.3%)

prune91.0ms (1.8%)

localize7.0ms (0.1%)

series70.0ms (1.4%)

rewrite134.0ms (2.6%)

simplify90.0ms (1.8%)

prune310.0ms (6%)

localize7.0ms (0.1%)

series32.0ms (0.6%)

rewrite66.0ms (1.3%)

simplify69.0ms (1.3%)

prune232.0ms (4.5%)

localize6.0ms (0.1%)

series48.0ms (0.9%)

rewrite117.0ms (2.3%)

simplify93.0ms (1.8%)

prune237.0ms (4.6%)

regimes826.0ms (16.1%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end84.0ms (1.6%)

Profiling