Details

analyze581.0ms (12.8%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (26.8%)

Results

862.0ms	7590×	body	128	valid
93.0ms	248×	body	1024	valid
70.0ms	644×	body	128	invalid
67.0ms	255×	body	512	valid
33.0ms	163×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify225.0ms (5%)

Algorithm

1×	egg-herbie

Rules

5304×	`fma-neg_binary64`
679×	`unsub-neg_binary64`
400×	`sub-neg_binary64`
376×	`fma-def_binary64`
289×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	59	14
3	157	12
4	438	12
5	1253	12
6	2078	12
7	2563	12
8	2777	12
9	2907	12
10	2949	12
11	2964	12
12	2967	12
13	2967	12
14	2967	12
15	3141	12
16	3015	12
17	3015	12
18	8062	12

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series13.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
2.0ms	(fma.f64 z -6 4)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
0.0ms	(fma.f64 z -6 4)

simplify112.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-def_binary64`
445×	`associate-l_binary64`
416×	`exp-prod_binary64`
398×	`distribute-rgt-in_binary64`
387×	`associate-r_binary64`

Counts

68 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1086
1	149	928
2	343	874
3	949	793
4	4177	793
5	4989	793
6	4976	793

prune51.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	11.4b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	44.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 871 to 523 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(*.f64 y (fma.f64 z -6 4))

series24.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
6.0ms	(*.f64 y (fma.f64 z -6 4))
5.0ms	(fma.f64 6 z -3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 y (fma.f64 z -6 4))
0.0ms	(fma.f64 6 z -3)
0.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

798×	`neg-mul-1_binary64`
520×	`distribute-rgt-neg-out_binary64`
469×	`distribute-lft-neg-out_binary64`
296×	`fma-neg_binary64`
289×	`associate-l_binary64`

Counts

114 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1600
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune100.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	95	5	100

Error

0.0b

Counts

100 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	44.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	11.4b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)

Compiler

Compiled 1698 to 1171 computations (31% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 6 z -3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))
✓	0.2b	(.f64 6 (.f64 y z))

series18.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

13.0ms	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))
5.0ms	(.f64 6 (.f64 y z))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 6 (.f64 y z))
0.0ms	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
587×	`fma-def_binary64`
554×	`distribute-rgt-in_binary64`
542×	`distribute-lft-in_binary64`
387×	`associate-l_binary64`

Counts

66 → 53

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1235
1	205	1034
2	543	873
3	1441	873
4	4413	873
5	5068	873

prune57.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Error

0.0b

Counts

73 → 5

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	44.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))
▶	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	11.4b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)

Compiler

Compiled 1428 to 937 computations (34.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 2 3) z)
✓	0.0b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.3b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series33.0ms (0.7%)

Counts

4 → 108

Calls

4 calls:

16.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
12.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
4.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite80.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`
195×	`prod-diff_binary64`
190×	`add-cube-cbrt_binary64`
146×	`times-frac_binary64`

Counts

4 → 314

Calls

4 calls:

15.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
12.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
6.0ms	(-.f64 (/.f64 2 3) z)
4.0ms	(*.f64 (-.f64 y x) 6)

simplify242.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
372×	`associate-l_binary64`
344×	`associate-r_binary64`
267×	`*-commutative_binary64`
238×	`cancel-sign-sub-inv_binary64`

Counts

422 → 428

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	427	9776
1	723	8689
2	2854	6627
3	4047	6546
4	4842	6546

prune324.0ms (7.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	427	6	433

Error

Counts

433 → 6

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.7b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))
	44.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (-.f64 (.f64 4 y) (.f64 6 (*.f64 y z))))
✓	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	11.4b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)

Compiler

Compiled 13233 to 6904 computations (47.8% saved)

regimes1.2s (25.5%)

Accuracy

Total 0.1b remaining (82.7%)

Threshold costs 0.1b (82.7%)

Counts

207 → 1

Compiler

Compiled 20988 to 15038 computations (28.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	22	21
2	30	21
3	40	21
4	47	21
5	52	21
6	54	21
7	53	21

end111.0ms (2.4%)

Compiler: Compiled 185 to 125 computations (32.4% saved)

Details

analyze581.0ms (12.8%)

sample1.2s (26.8%)

simplify225.0ms (5%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series13.0ms (0.3%)

rewrite1.0ms (0%)

simplify112.0ms (2.5%)

prune51.0ms (1.1%)

localize9.0ms (0.2%)

series24.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.7%)

prune100.0ms (2.2%)

localize12.0ms (0.3%)

series18.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify64.0ms (1.4%)

prune57.0ms (1.3%)

localize8.0ms (0.2%)

series33.0ms (0.7%)

rewrite80.0ms (1.8%)

simplify242.0ms (5.3%)

prune324.0ms (7.1%)

regimes1.2s (25.5%)

simplify3.0ms (0.1%)

end111.0ms (2.4%)

Profiling