Details

analyze585.0ms (15.8%)

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 (33.1%)

Results

850.0ms	7545×	body	128	valid
116.0ms	288×	body	1024	valid
82.0ms	651×	body	128	invalid
67.0ms	249×	body	512	valid
34.0ms	174×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify228.0ms (6.2%)

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
	0.4b	(+.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)

series12.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
1.0ms	(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)

simplify97.0ms (2.6%)

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

prune52.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Error

0.0b

Counts

51 → 7

Alt Table

Status	Error	Program
	28.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	32.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	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)))
	1.4b	(fma.f64 (-.f64 y x) (.f64 (.f64 (cbrt.f64 (fma.f64 z -6 4)) (cbrt.f64 (fma.f64 z -6 4))) (cbrt.f64 (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)))

Compiler

Compiled 903 to 553 computations (38.8% 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 (0.6%)

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

simplify77.0ms (2.1%)

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

prune84.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	28.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	31.4b	(fma.f64 x (fma.f64 6 z -3) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z -6 4)) 3)))
	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)))
	20.4b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (.f64 z -6)))
	48.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (fma.f64 6 z -3) (.f64 y (fma.f64 z -6 4))) (fma.f64 x (fma.f64 6 z -3) (.f64 y (fma.f64 z -6 4)))) (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)))

Compiler

Compiled 1803 to 1258 computations (30.2% saved)

localize17.0ms (0.5%)

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))

series33.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
7.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite29.0ms (0.8%)

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:

9.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
8.0ms	(.f64 6 (.f64 z x))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
3.0ms	(.f64 6 (.f64 y z))

simplify101.0ms (2.7%)

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

prune156.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	151	5	156

Error

0.0b

Counts

156 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x)))) (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))))) (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x)))) (fma.f64 x -3 (.f64 z (.f64 y -6))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	25.7b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (/.f64 (fma.f64 (.f64 z y) (.f64 (.f64 z y) 36) (.f64 x (.f64 x -9))) (fma.f64 6 (.f64 z y) (.f64 x -3))))
▶	0.1b	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 5012 to 3067 computations (38.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

12.0ms	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
10.0ms	(fma.f64 6 (.f64 z (-.f64 x y)) (.f64 x -3))
9.0ms	(*.f64 z (-.f64 x y))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 75

Calls

3 calls:

5.0ms	(*.f64 z (-.f64 x y))
3.0ms	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
0.0ms	(fma.f64 6 (.f64 z (-.f64 x y)) (.f64 x -3))

simplify120.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
531×	`fma-def_binary64`
419×	`exp-prod_binary64`
409×	`distribute-rgt-in_binary64`
382×	`distribute-lft-in_binary64`

Counts

183 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2787
1	398	2354
2	1228	2292
3	3808	2211
4	4914	2211
5	5046	2211

prune114.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x)))) (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))))) (cbrt.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x)))) (fma.f64 x -3 (.f64 z (.f64 y -6))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	25.7b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (/.f64 (fma.f64 (.f64 z y) (.f64 (.f64 z y) 36) (.f64 x (.f64 x -9))) (fma.f64 6 (.f64 z y) (.f64 x -3))))
✓	0.1b	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 2808 to 1450 computations (48.4% saved)

regimes579.0ms (15.6%)

Accuracy

Total 0.2b remaining (90.9%)

Threshold costs 0.2b (90.9%)

Counts

114 → 1

Compiler

Compiled 10860 to 7670 computations (29.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	23	26
2	23	26

end96.0ms (2.6%)

Compiler: Compiled 169 to 116 computations (31.4% saved)

Details

analyze585.0ms (15.8%)

sample1.2s (33.1%)

simplify228.0ms (6.2%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify97.0ms (2.6%)

prune52.0ms (1.4%)

localize8.0ms (0.2%)

series23.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify77.0ms (2.1%)

prune84.0ms (2.3%)

localize17.0ms (0.5%)

series33.0ms (0.9%)

rewrite29.0ms (0.8%)

simplify101.0ms (2.7%)

prune156.0ms (4.2%)

localize8.0ms (0.2%)

series32.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify120.0ms (3.2%)

prune114.0ms (3.1%)

regimes579.0ms (15.6%)

simplify2.0ms (0.1%)

end96.0ms (2.6%)

Profiling