Details

analyze571.0ms (15.7%)

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 (32.9%)

Results

835.0ms	7526×	body	128	valid
102.0ms	285×	body	1024	valid
75.0ms	275×	body	512	valid
69.0ms	608×	body	128	invalid
39.0ms	170×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify220.0ms (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
	0.7b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.4b	(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)
✓	0.4b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series12.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(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)

simplify104.0ms (2.9%)

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

prune45.0ms (1.2%)

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
	0.7b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.4b	(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)))
	39.8b	(.f64 6 (.f64 z (-.f64 x y)))
	31.3b	(*.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)))
	1.6b	(.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)))

Compiler

Compiled 845 to 509 computations (39.8% saved)

localize14.0ms (0.4%)

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 y z))
✓	0.3b	(.f64 6 (.f64 z x))

series32.0ms (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 z x))
4.0ms	(.f64 6 (.f64 y z))

rewrite27.0ms (0.7%)

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:

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

simplify101.0ms (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

prune144.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	31.3b	(*.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)))
	0.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.2b	(-.f64 (fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y)))) (*.f64 3 x))
	1.6b	(.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)))
	44.6b	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 4 y) (.f64 4 y)) (.f64 (.f64 6 (.f64 z x)) (.f64 6 (.f64 z x)))) (+.f64 (.f64 (.f64 6 (.f64 y z)) (.f64 6 (.f64 y z))) (-.f64 (.f64 (.f64 3 x) (.f64 3 x)) (.f64 (.f64 6 (.f64 y z)) (.f64 3 x))))) (.f64 (-.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (pow.f64 (.f64 6 (.f64 y z)) 3) (pow.f64 (.f64 3 x) 3)))) (.f64 (-.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 (.f64 6 (.f64 y z)) (.f64 6 (.f64 y z))) (-.f64 (.f64 (.f64 3 x) (.f64 3 x)) (.f64 (.f64 6 (.f64 y z)) (.f64 3 x))))))

Compiler

Compiled 5229 to 3202 computations (38.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series47.0ms (1.3%)

Counts

4 → 144

Calls

4 calls:

17.0ms	(-.f64 (fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y)))) (*.f64 3 x))
15.0ms	(fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y))))
8.0ms	(.f64 6 (.f64 z (-.f64 x y)))
6.0ms	(*.f64 z (-.f64 x y))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
57×	`prod-diff_binary64`
55×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`

Counts

4 → 155

Calls

4 calls:

7.0ms	(.f64 6 (.f64 z (-.f64 x y)))
5.0ms	(*.f64 z (-.f64 x y))
2.0ms	(-.f64 (fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y)))) (*.f64 3 x))
0.0ms	(fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y))))

simplify153.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
440×	`distribute-lft-in_binary64`
263×	`fma-neg_binary64`
260×	`associate-r_binary64`

Counts

299 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	4660
1	493	4056
2	1516	3694
3	4591	3694
4	4990	3694
5	4853	3694

prune199.0ms (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Error

Counts

221 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.5b	(-.f64 (fma.f64 y 4 (.f64 (sqrt.f64 6) (.f64 (sqrt.f64 6) (.f64 z (-.f64 x y))))) (.f64 3 x))
✓	0.2b	(-.f64 (fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y)))) (*.f64 3 x))
	0.2b	(+.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 (fma.f64 6 (.f64 z (-.f64 x y)) (.f64 y 4)))
	31.7b	(-.f64 (fma.f64 y 4 (.f64 6 (exp.f64 (log.f64 (.f64 z (-.f64 x y)))))) (*.f64 3 x))

Compiler

Compiled 5514 to 2613 computations (52.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series26.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(fma.f64 x -3 (fma.f64 6 (.f64 z (-.f64 x y)) (.f64 y 4)))
10.0ms	(fma.f64 6 (.f64 z (-.f64 x y)) (.f64 y 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 6 (.f64 z (-.f64 x y)) (.f64 y 4))
0.0ms	(fma.f64 x -3 (fma.f64 6 (.f64 z (-.f64 x y)) (.f64 y 4)))

simplify91.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-neg_binary64`
692×	`fma-def_binary64`
463×	`unsub-neg_binary64`
308×	`sqr-pow_binary64`
288×	`exp-prod_binary64`

Counts

92 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1811
1	156	1401
2	357	1389
3	1082	1315
4	2668	1315
5	4264	1315
6	4987	1315

prune86.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	115	4	119

Error

Counts

119 → 4

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.2b	(-.f64 (fma.f64 y 4 (.f64 6 (.f64 z (-.f64 x y)))) (*.f64 3 x))
	31.6b	(fma.f64 x -3 (fma.f64 6 (exp.f64 (log.f64 (.f64 z (-.f64 x y)))) (.f64 y 4)))
	0.4b	(fma.f64 x -3 (+.f64 (.f64 z (.f64 6 (-.f64 x y))) (*.f64 y 4)))

Compiler

Compiled 2384 to 1168 computations (51% saved)

regimes451.0ms (12.4%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts

88 → 1

Compiler

Compiled 7304 to 5247 computations (28.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18
2	21	18
3	23	18
4	24	18
5	24	18

end68.0ms (1.9%)

Compiler: Compiled 99 to 70 computations (29.3% saved)

Details

analyze571.0ms (15.7%)

sample1.2s (32.9%)

simplify220.0ms (6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify104.0ms (2.9%)

prune45.0ms (1.2%)

localize14.0ms (0.4%)

series32.0ms (0.9%)

rewrite27.0ms (0.7%)

simplify101.0ms (2.8%)

prune144.0ms (3.9%)

localize8.0ms (0.2%)

series47.0ms (1.3%)

rewrite28.0ms (0.8%)

simplify153.0ms (4.2%)

prune199.0ms (5.5%)

localize10.0ms (0.3%)

series26.0ms (0.7%)

rewrite1.0ms (0%)

simplify91.0ms (2.5%)

prune86.0ms (2.4%)

regimes451.0ms (12.4%)

simplify2.0ms (0.1%)

end68.0ms (1.9%)

Profiling