Details

analyze611.0ms (17.9%)

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 (36.4%)

Results

902.0ms	7618×	body	128	valid
81.0ms	221×	body	1024	valid
79.0ms	250×	body	512	valid
66.0ms	601×	body	128	invalid
33.0ms	167×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify226.0ms (6.6%)

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
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

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 (0.4%)

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)

rewrite11.0ms (0.3%)

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:

10.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
0.0ms	(fma.f64 z -6 4)

simplify84.0ms (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

prune56.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	12.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 735 to 443 computations (39.7% saved)

localize8.0ms (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))

series23.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

16.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
6.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(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 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
0.0ms	(fma.f64 6 z -3)

simplify82.0ms (2.4%)

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

prune71.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	12.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 1585 to 1108 computations (30.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.3b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series31.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

14.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
8.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
5.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-log-exp_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 93

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
5.0ms	(.f64 6 (.f64 y z))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 z x))

simplify94.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
279×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
271×	`associate-r_binary64`

Counts

111 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2856
1	619	2159
2	2427	1906
3	4509	1906
4	5450	1906

prune131.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	148	4	152

Error

0.0b

Counts

152 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	12.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.1b	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
▶	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))

Compiler

Compiled 4892 to 2991 computations (38.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
✓	0.1b	(fma.f64 x -3 (.f64 z (.f64 y -6)))
✓	0.2b	(.f64 z (.f64 y -6))
	0.3b	(.f64 6 (.f64 z x))

series28.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

15.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
8.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))
5.0ms	(.f64 z (.f64 y -6))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 50

Calls

3 calls:

5.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
4.0ms	(.f64 z (.f64 y -6))
0.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

776×	`associate-l_binary64`
631×	`associate-r_binary64`
434×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
381×	`fma-def_binary64`

Counts

146 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	2252
1	308	1967
2	929	1829
3	4465	1820
4	4960	1820
5	5024	1820

prune85.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Error

0.0b

Counts

121 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	12.3b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	0.1b	(fma.f64 y 4 (fma.f64 -6 (.f64 (-.f64 y x) z) (.f64 x -3)))
✓	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))

Compiler

Compiled 2721 to 1697 computations (37.6% saved)

regimes347.0ms (10.2%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

Counts

79 → 1

Compiler

Compiled 5786 to 4195 computations (27.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	16	18
2	16	18

end74.0ms (2.2%)

Compiler: Compiled 98 to 71 computations (27.6% saved)

Details

analyze611.0ms (17.9%)

sample1.2s (36.4%)

simplify226.0ms (6.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite11.0ms (0.3%)

simplify84.0ms (2.5%)

prune56.0ms (1.6%)

localize8.0ms (0.2%)

series23.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify82.0ms (2.4%)

prune71.0ms (2.1%)

localize11.0ms (0.3%)

series31.0ms (0.9%)

rewrite37.0ms (1.1%)

simplify94.0ms (2.8%)

prune131.0ms (3.8%)

localize12.0ms (0.4%)

series28.0ms (0.8%)

rewrite11.0ms (0.3%)

simplify106.0ms (3.1%)

prune85.0ms (2.5%)

regimes347.0ms (10.2%)

simplify2.0ms (0.1%)

end74.0ms (2.2%)

Profiling