Details

analyze1.2s (20.6%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (41.6%)

Results

903.0ms	6385×	body	128	valid
600.0ms	932×	body	1024	valid
251.0ms	590×	body	512	valid
202.0ms	1505×	body	128	invalid
120.0ms	197×	body	1024	invalid
107.0ms	235×	body	512	invalid
95.0ms	344×	body	256	valid
42.0ms	159×	body	256	invalid
4.0ms	5×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	56	16
4	119	16
5	280	16
6	672	16
7	2284	16
8	4398	16
9	4953	16

prune3.0ms (0%)

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

4.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.7b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(/.f64 y (+.f64 y z))
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	4.8b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series141.0ms (2.4%)

Counts

4 → 108

Calls

4 calls:

74.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
34.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
25.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
8.0ms	(/.f64 y (+.f64 y z))

rewrite74.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

374×	`fma-def_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
187×	`log-pow_binary64`

Counts

4 → 146

Calls

4 calls:

71.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
71.0ms	(/.f64 y (+.f64 y z))
71.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
71.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	46
2	3119	46
3	5093	46
0	0	0
1	0	0

simplify127.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

347×	`fma-def_binary64`
340×	`associate-+r+_binary64`
336×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
244×	`fma-neg_binary64`

Counts

254 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	5179
1	1183	5024
2	4749	4898
3	4981	4898

prune250.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	264	5	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	5	270

Error

0.0b

Counts

270 → 5

Alt Table

Status	Error	Program
	40.4b	(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) 3)) (/.f64 1 (fma.f64 x x (.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) (-.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)))))
	12.8b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
	14.0b	(fma.f64 (/.f64 1 (cbrt.f64 (*.f64 y y))) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
	8.7b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	3.2b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 8559 to 4015 computations (53.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite47.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
112×	`expm1-udef_binary64`
112×	`log1p-udef_binary64`

Counts

1 → 36

Calls

1 calls:

46.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1568	7
3	5021	7
0	0	0
1	0	0

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

60 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	138
1	9	138
2	8	138

prune30.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (pow.f64 y -1/2) (pow.f64 y -1/2) x)
	40.4b	(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) 3)) (/.f64 1 (fma.f64 x x (.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) (-.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)))))
	12.8b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
	14.0b	(fma.f64 (/.f64 1 (cbrt.f64 (*.f64 y y))) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
▶	8.7b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.2b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 618 to 382 computations (38.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	0.0b	(/.f64 (exp.f64 (neg.f64 z)) y)

series19.0ms (0.3%)

Counts

2 → 44

Calls

2 calls:

12.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
7.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

rewrite53.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

839×	`expm1-log1p-u_binary64`
766×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
84×	`add-log-exp_binary64`

Counts

2 → 70

Calls

2 calls:

52.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
52.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	174	15
2	2128	15
3	5087	15
0	0	0
1	0	0

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-neg_binary64`
661×	`fma-def_binary64`
643×	`cancel-sign-sub-inv_binary64`
361×	`distribute-neg-frac_binary64`
352×	`associate-/l*_binary64`

Counts

114 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	486
1	86	478
2	200	478
3	489	478
4	1399	472
5	3977	472
6	4917	472

prune52.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (pow.f64 y -1/2) (pow.f64 y -1/2) x)
	40.4b	(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) 3)) (/.f64 1 (fma.f64 x x (.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) (-.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)))))
▶	8.7b	(+.f64 x (pow.f64 (*.f64 y (exp.f64 z)) -1))
	14.0b	(fma.f64 (/.f64 1 (cbrt.f64 (*.f64 y y))) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
✓	8.7b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.2b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 1279 to 519 computations (59.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (*.f64 y (exp.f64 z)) -1))
✓	0.0b	(pow.f64 (*.f64 y (exp.f64 z)) -1)
✓	0.0b	(*.f64 y (exp.f64 z))

series41.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

19.0ms	(+.f64 x (pow.f64 (*.f64 y (exp.f64 z)) -1))
15.0ms	(pow.f64 (*.f64 y (exp.f64 z)) -1)
6.0ms	(*.f64 y (exp.f64 z))

rewrite55.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

906×	`expm1-log1p-u_binary64`
633×	`prod-diff_binary64`
96×	`add-sqr-sqrt_binary64`
91×	`log1p-expm1-u_binary64`
89×	`add-log-exp_binary64`

Counts

3 → 79

Calls

3 calls:

54.0ms	(+.f64 x (pow.f64 (*.f64 y (exp.f64 z)) -1))
54.0ms	(pow.f64 (*.f64 y (exp.f64 z)) -1)
54.0ms	(*.f64 y (exp.f64 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	189	27
2	2310	27
3	5094	27
0	0	0
1	0	0

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

705×	`times-frac_binary64`
688×	`fma-neg_binary64`
640×	`cancel-sign-sub-inv_binary64`
553×	`fma-def_binary64`
239×	`associate-l_binary64`

Counts

143 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	714
1	112	704
2	286	653
3	740	645
4	2188	639
5	4303	639
6	5093	639

prune77.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (pow.f64 y -1/2) (pow.f64 y -1/2) x)
	40.4b	(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) 3)) (/.f64 1 (fma.f64 x x (.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) (-.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)))))
✓	8.7b	(+.f64 x (pow.f64 (*.f64 y (exp.f64 z)) -1))
	14.0b	(fma.f64 (/.f64 1 (cbrt.f64 (*.f64 y y))) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
✓	8.7b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.2b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 1483 to 738 computations (50.2% saved)

regimes892.0ms (15.3%)

Accuracy

Total 0.8b remaining (98.2%)

Threshold costs 0.8b (98.2%)

Counts

100 → 2

Compiler

Compiled 10107 to 5662 computations (44% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
10	5.673574932988124e-16	5.798655181805178e-6	5.736736187083638e-6

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	21	25
2	20	25

end92.0ms (1.6%)

Compiler: Compiled 146 to 88 computations (39.7% saved)

Details

analyze1.2s (20.6%)

sample2.4s (41.6%)

simplify52.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series141.0ms (2.4%)

rewrite74.0ms (1.3%)

simplify127.0ms (2.2%)

prune250.0ms (4.3%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite47.0ms (0.8%)

simplify9.0ms (0.1%)

prune30.0ms (0.5%)

localize5.0ms (0.1%)

series19.0ms (0.3%)

rewrite53.0ms (0.9%)

simplify57.0ms (1%)

prune52.0ms (0.9%)

localize6.0ms (0.1%)

series41.0ms (0.7%)

rewrite55.0ms (1%)

simplify64.0ms (1.1%)

prune77.0ms (1.3%)

regimes892.0ms (15.3%)

bsearch39.0ms (0.7%)

simplify2.0ms (0%)

end92.0ms (1.6%)

Profiling