Details

analyze2.0ms (0.1%)

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)

sample899.0ms (28.5%)

Infinites

20.7% of outputs are infinite.

Results

679.0ms	7729×	body	128	valid
54.0ms	203×	body	1024	valid
41.0ms	205×	body	512	valid
18.0ms	119×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify232.0ms (7.4%)

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

prune3.0ms (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)
	0.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.4%)

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)

simplify80.0ms (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

prune42.0ms (1.3%)

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	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	1.6b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

Compiler

Compiled 733 to 441 computations (39.8% saved)

localize9.0ms (0.3%)

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)

series12.0ms (0.4%)

Counts

2 → 39

Calls

2 calls:

10.0ms	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
1.0ms	(-.f64 4 (*.f64 6 z))

rewrite3.0ms (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:

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

simplify64.0ms (2%)

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

prune45.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

Status	Error	Program
	0.3b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	1.6b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
▶	0.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)

Compiler

Compiled 1097 to 684 computations (37.6% saved)

localize9.0ms (0.3%)

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))

series32.0ms (1%)

Counts

4 → 108

Calls

4 calls:

16.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
11.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
3.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite75.0ms (2.4%)

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:

12.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
12.0ms	(-.f64 (/.f64 2 3) z)
9.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
4.0ms	(*.f64 (-.f64 y x) 6)

simplify231.0ms (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

prune368.0ms (11.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	426	2	428
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	427	5	432

Error

Counts

432 → 5

Alt Table

Status	Error	Program
	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)))
	1.6b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
▶	0.1b	(fma.f64 4 y (fma.f64 -6 (.f64 z (-.f64 y x)) (.f64 x -3)))
	0.3b	(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 13269 to 6938 computations (47.7% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series30.0ms (1%)

Counts

3 → 96

Calls

3 calls:

14.0ms	(fma.f64 4 y (fma.f64 -6 (.f64 z (-.f64 y x)) (.f64 x -3)))
10.0ms	(fma.f64 -6 (.f64 z (-.f64 y x)) (.f64 x -3))
6.0ms	(*.f64 z (-.f64 y x))

rewrite10.0ms (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 → 70

Calls

3 calls:

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

simplify98.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-neg_binary64`
475×	`exp-prod_binary64`
447×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
273×	`*-commutative_binary64`

Counts

166 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	2716
1	331	2222
2	1016	2054
3	2501	1926
4	4284	1926
5	4940	1926

prune105.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	118	5	123

Error

Counts

123 → 5

Alt Table

Status	Error	Program
	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)))
	1.6b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.1b	(fma.f64 4 y (fma.f64 -6 (.f64 z (-.f64 y x)) (.f64 x -3)))
	0.3b	(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 2485 to 1229 computations (50.5% saved)

regimes690.0ms (21.9%)

Accuracy

Total 0.2b remaining (94.5%)

Threshold costs 0.2b (94.5%)

Counts

140 → 1

Compiler

Compiled 13628 to 9811 computations (28% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	23	20
2	34	20
3	49	20
4	59	20
5	76	20
6	83	20
7	84	20
8	79	20

end81.0ms (2.6%)

Compiler: Compiled 133 to 91 computations (31.6% saved)

Details

analyze2.0ms (0.1%)

sample899.0ms (28.5%)

simplify232.0ms (7.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.4%)

rewrite1.0ms (0%)

simplify80.0ms (2.5%)

prune42.0ms (1.3%)

localize9.0ms (0.3%)

series12.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify64.0ms (2%)

prune45.0ms (1.4%)

localize9.0ms (0.3%)

series32.0ms (1%)

rewrite75.0ms (2.4%)

simplify231.0ms (7.3%)

prune368.0ms (11.7%)

localize13.0ms (0.4%)

series30.0ms (1%)

rewrite10.0ms (0.3%)

simplify98.0ms (3.1%)

prune105.0ms (3.3%)

regimes690.0ms (21.9%)

simplify3.0ms (0.1%)

end81.0ms (2.6%)

Profiling