Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.4s (28%)

Results

1.1s	7717×	body	128	valid
107.0ms	219×	body	1024	valid
66.0ms	186×	body	512	valid
35.0ms	134×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify280.0ms (5.4%)

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)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series32.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(fma.f64 z -6 4)
13.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

rewrite3.0ms (0.1%)

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:

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

simplify136.0ms (2.7%)

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

prune88.0ms (1.7%)

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
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.9b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.6b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

Compiler

Compiled 733 to 441 computations (39.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series28.0ms (0.5%)

Counts

2 → 39

Calls

2 calls:

24.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
3.0ms	(-.f64 4 (*.f64 6 z))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(-.f64 4 (*.f64 6 z))
1.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

715×	`unsub-neg_binary64`
492×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
275×	`fma-neg_binary64`
262×	`fma-def_binary64`

Counts

69 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1222
1	219	1026
2	535	900
3	1445	819
4	3706	819
5	4958	819

prune99.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.9b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.6b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	33.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (-.f64 4 (.f64 6 z)) x) (fma.f64 (-.f64 y x) (-.f64 4 (.f64 6 z)) x)) (fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)))

Compiler

Compiled 1169 to 728 computations (37.7% saved)

localize21.0ms (0.4%)

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)
✓	0.2b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series58.0ms (1.1%)

Counts

4 → 108

Calls

4 calls:

24.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
24.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
7.0ms	(*.f64 (-.f64 y x) 6)
2.0ms	(-.f64 (/.f64 2 3) z)

rewrite146.0ms (2.8%)

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:

33.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
14.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
13.0ms	(-.f64 (/.f64 2 3) z)
5.0ms	(*.f64 (-.f64 y x) 6)

simplify375.0ms (7.3%)

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

prune434.0ms (8.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	424	4	428
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	427	6	433

Error

Counts

433 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.6b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	29.4b	(+.f64 x (.f64 (.f64 (*.f64 6 (-.f64 y x)) (+.f64 (sqrt.f64 z) (sqrt.f64 2/3))) (-.f64 (sqrt.f64 (/.f64 2 3)) (sqrt.f64 z))))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
▶	0.1b	(+.f64 x (+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (*.f64 z (-.f64 y x)))))
	0.5b	(+.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)))

Compiler

Compiled 13321 to 6970 computations (47.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series50.0ms (1%)

Counts

4 → 124

Calls

4 calls:

17.0ms	(+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (*.f64 z (-.f64 y x))))
14.0ms	(+.f64 x (+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (*.f64 z (-.f64 y x)))))
12.0ms	(.f64 -6 (.f64 z (-.f64 y x)))
7.0ms	(*.f64 z (-.f64 y x))

rewrite69.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`distribute-lft-in_binary64`
130×	`distribute-rgt-in_binary64`
108×	`prod-diff_binary64`
96×	`*-un-lft-identity_binary64`
96×	`add-sqr-sqrt_binary64`

Counts

4 → 239

Calls

4 calls:

12.0ms	(+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (*.f64 z (-.f64 y x))))
7.0ms	(.f64 -6 (.f64 z (-.f64 y x)))
6.0ms	(+.f64 x (+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (*.f64 z (-.f64 y x)))))
6.0ms	(*.f64 z (-.f64 y x))

simplify217.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-neg_binary64`
533×	`cancel-sign-sub-inv_binary64`
449×	`associate-r_binary64`
408×	`associate-l_binary64`
278×	`exp-prod_binary64`

Counts

363 → 360

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	383	6389
1	737	5091
2	2850	4765
3	4685	4765
4	4921	4765

prune372.0ms (7.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	359	1	360
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	361	5	366

Error

Counts

366 → 5

Alt Table

Status	Error	Program
	0.6b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	29.4b	(+.f64 x (.f64 (.f64 (*.f64 6 (-.f64 y x)) (+.f64 (sqrt.f64 z) (sqrt.f64 2/3))) (-.f64 (sqrt.f64 (/.f64 2 3)) (sqrt.f64 z))))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.5b	(+.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)))
	0.3b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (+.f64 (.f64 4 (-.f64 y x)) (.f64 -6 (.f64 z (-.f64 y x)))))

Compiler

Compiled 10001 to 3922 computations (60.8% saved)

regimes944.0ms (18.4%)

Accuracy

Total 0.2b remaining (94.8%)

Threshold costs 0.2b (94.8%)

Counts

143 → 1

Compiler

Compiled 12476 to 8812 computations (29.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	39	25
3	45	25
4	49	25
5	50	25
6	49	25

end185.0ms (3.6%)

Compiler: Compiled 149 to 103 computations (30.9% saved)

Details

analyze2.0ms (0%)

sample1.4s (28%)

simplify280.0ms (5.4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series32.0ms (0.6%)

rewrite3.0ms (0.1%)

simplify136.0ms (2.7%)

prune88.0ms (1.7%)

localize8.0ms (0.2%)

series28.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify121.0ms (2.4%)

prune99.0ms (1.9%)

localize21.0ms (0.4%)

series58.0ms (1.1%)

rewrite146.0ms (2.8%)

simplify375.0ms (7.3%)

prune434.0ms (8.4%)

localize8.0ms (0.2%)

series50.0ms (1%)

rewrite69.0ms (1.3%)

simplify217.0ms (4.2%)

prune372.0ms (7.2%)

regimes944.0ms (18.4%)

simplify6.0ms (0.1%)

end185.0ms (3.6%)

Profiling