Details

analyze212.0ms (6.2%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample30.0ms (0.9%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune4.0ms (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

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 141 to 90 computations (36.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 a -3 1)
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

series100.0ms (2.9%)

Counts

4 → 84

Calls

4 calls:

46.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
27.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
21.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
5.0ms	(fma.f64 a -3 1)

simplify115.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune112.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	135	4	139

Error

0.0b

Counts

139 → 4

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.6b	(+.f64 (fma.f64 4 (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
	9.8b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 2019 to 1101 computations (45.5% saved)

localize19.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 (fma.f64 a -3 1) (.f64 b b))
	9.4b	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))
	9.4b	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))
✓	9.4b	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(.f64 (fma.f64 a -3 1) (.f64 b b))
1.0ms	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))

series164.0ms (4.8%)

Counts

2 → 48

Calls

2 calls:

137.0ms	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))
27.0ms	(.f64 (fma.f64 a -3 1) (.f64 b b))

simplify107.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

523×	`unswap-sqr_binary64`
443×	`associate-r_binary64`
363×	`fma-def_binary64`
354×	`associate-l_binary64`
233×	`associate-+r+_binary64`

Counts

82 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	4166
1	977	3805
2	3811	3798
3	5212	3798

prune270.0ms (7.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	192	5	197

Error

Counts

197 → 5

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.6b	(+.f64 (fma.f64 4 (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	2.0b	(+.f64 (.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
	9.8b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 11652 to 6777 computations (41.8% saved)

localize30.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(.f64 (fma.f64 a -3 1) (.f64 b b))
	9.4b	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))
	9.4b	(cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))
✓	13.2b	(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`unpow-prod-down_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

2.0ms

(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3)

series139.0ms (4.1%)

Counts

1 → 24

Calls

1 calls:

139.0ms

(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3)

simplify100.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

513×	`unswap-sqr_binary64`
383×	`associate-r_binary64`
358×	`fma-def_binary64`
287×	`associate-l_binary64`
232×	`associate-+r+_binary64`

Counts

44 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	3669
1	936	3445
2	3623	3437
3	4998	3437

prune308.0ms (9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	533	0	533
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	533	5	538

Error

Counts

538 → 5

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.6b	(+.f64 (fma.f64 4 (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	2.0b	(+.f64 (.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	9.8b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 11906 to 6929 computations (41.8% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (fma.f64 a 2 -12))
✓	1.1b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 47

Calls

2 calls:

7.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
3.0ms	(*.f64 a (fma.f64 a 2 -12))

series43.0ms (1.3%)

Counts

2 → 36

Calls

2 calls:

33.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
10.0ms	(*.f64 a (fma.f64 a 2 -12))

simplify90.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

747×	`distribute-rgt-in_binary64`
741×	`distribute-lft-in_binary64`
507×	`fma-def_binary64`
235×	`fma-neg_binary64`
179×	`associate-l_binary64`

Counts

83 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	111	1833
1	290	1283
2	1090	1283
3	4830	1283
4	4994	1283

prune69.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	83	5	88

Error

Counts

88 → 5

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.6b	(+.f64 (fma.f64 4 (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
	2.0b	(+.f64 (.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 1/3) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)))) -1)
	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
	9.8b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 1442 to 896 computations (37.9% saved)

regimes289.0ms (8.4%)

Accuracy

Total 0.1b remaining (73.9%)

Threshold costs 0.1b (73.9%)

Compiler

Compiled 7625 to 4702 computations (38.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	18	25
2	17	25

end1.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

sample1.1s (32%)

Algorithm

1×

intervals

Results

662.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 278 to 166 computations (40.3% saved)

Details

analyze212.0ms (6.2%)

sample30.0ms (0.9%)

simplify65.0ms (1.9%)

prune4.0ms (0.1%)

localize15.0ms (0.4%)

rewrite8.0ms (0.2%)

series100.0ms (2.9%)

simplify115.0ms (3.4%)

prune112.0ms (3.3%)

localize19.0ms (0.6%)

rewrite8.0ms (0.2%)

series164.0ms (4.8%)

simplify107.0ms (3.1%)

prune270.0ms (7.9%)

localize30.0ms (0.9%)

rewrite3.0ms (0.1%)

series139.0ms (4.1%)

simplify100.0ms (2.9%)

prune308.0ms (9%)

localize12.0ms (0.4%)

rewrite12.0ms (0.4%)

series43.0ms (1.3%)

simplify90.0ms (2.6%)

prune69.0ms (2%)

regimes289.0ms (8.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (32%)

Profiling