Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.3s (33.3%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary64`
523×	`fma-neg_binary64`
142×	`cancel-sign-sub-inv_binary64`
122×	`distribute-rgt-in_binary64`
106×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	11
2	36	11
3	78	11
4	154	11
5	268	11
6	404	11
7	631	11
8	911	11
9	1092	11
10	1291	11
11	1314	11
12	1316	11
13	1316	11
14	1243	11

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	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
▶	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series26.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

19.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
7.0ms	(*.f64 (-.f64 y x) 6)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

9.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

simplify191.0ms (5%)

Algorithm

1×	egg-herbie

Rules

829×	`times-frac_binary64`
732×	`fma-def_binary64`
490×	`unsub-neg_binary64`
306×	`*-commutative_binary64`
289×	`neg-sub0_binary64`

Counts

94 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1108
1	190	899
2	520	893
3	1543	893
4	3149	893
5	4667	893
6	6079	893

prune105.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Error

Counts

72 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
▶	0.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) 6)) z x)
	18.5b	(fma.f64 (/.f64 (.f64 (-.f64 (.f64 y y) (*.f64 x x)) 6) (+.f64 y x)) z x)
	32.9b	(.f64 (sqrt.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x)) (sqrt.f64 (fma.f64 (*.f64 (-.f64 y x) 6) z x)))

Compiler

Compiled 1078 to 527 computations (51.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
9.0ms	(.f64 (.f64 (-.f64 y x) 6) z)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`associate-*l/_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 38

Calls

2 calls:

7.0ms	(.f64 (.f64 (-.f64 y x) 6) z)
3.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))

simplify187.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-neg_binary64`
403×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
369×	`fma-def_binary64`
295×	`distribute-rgt-neg-out_binary64`

Counts

110 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1521
1	282	1208
2	915	1198
3	2962	1196
4	4734	1196
5	4966	1196

prune149.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	115	5	120

Error

Counts

120 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
✓	0.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) 6)) z x)
	0.6b	(+.f64 x (.f64 (.f64 6 (.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 z)))
▶	0.1b	(+.f64 x (.f64 (-.f64 y x) (.f64 6 z)))

Compiler

Compiled 1804 to 880 computations (51.2% saved)

localize27.0ms (0.7%)

Local error

Found 2 expressions with local error:

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

series66.0ms (1.7%)

Counts

2 → 72

Calls

2 calls:

37.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 6 z)))
28.0ms	(.f64 (-.f64 y x) (.f64 6 z))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

26.0ms	(.f64 (-.f64 y x) (.f64 6 z))
10.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 6 z)))

simplify168.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-neg_binary64`
424×	`fma-def_binary64`
371×	`distribute-rgt-in_binary64`
356×	`distribute-lft-in_binary64`
331×	`*-commutative_binary64`

Counts

112 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1552
1	283	1233
2	924	1221
3	3027	1221
4	4742	1221
5	4974	1221

prune74.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	75	5	80

Error

Counts

80 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
✓	0.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) 6)) z x)
	0.6b	(+.f64 x (.f64 (.f64 6 (.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 z)))
✓	0.1b	(+.f64 x (.f64 (-.f64 y x) (.f64 6 z)))

Compiler

Compiled 1250 to 602 computations (51.8% saved)

localize28.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

series62.0ms (1.6%)

Counts

3 → 88

Calls

3 calls:

23.0ms	(.f64 6 (.f64 z (-.f64 y x)))
23.0ms	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
15.0ms	(*.f64 z (-.f64 y x))

rewrite96.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`distribute-lft-in_binary64`
117×	`distribute-rgt-in_binary64`
90×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`

Counts

3 → 190

Calls

3 calls:

23.0ms	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
20.0ms	(.f64 6 (.f64 z (-.f64 y x)))
12.0ms	(*.f64 z (-.f64 y x))

simplify266.0ms (7%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
576×	`fma-neg_binary64`
481×	`distribute-rgt-in_binary64`
446×	`distribute-lft-in_binary64`
282×	`associate-r_binary64`

Counts

278 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3916
1	431	3365
2	1409	2819
3	4520	2819
4	4979	2819
5	4894	2819

prune416.0ms (11%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	273	5	278

Error

Counts

278 → 5

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 6 (.f64 z (-.f64 y x))) x)
✓	0.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
	0.6b	(+.f64 (.f64 6 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (-.f64 y x)))) x)
	0.6b	(+.f64 x (.f64 (.f64 6 (.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 z)))
✓	0.1b	(+.f64 x (.f64 (-.f64 y x) (.f64 6 z)))

Compiler

Compiled 6088 to 2168 computations (64.4% saved)

regimes303.0ms (8%)

Accuracy

Total 0.2b remaining (92.3%)

Threshold costs 0.2b (92.3%)

Counts

44 → 1

Compiler

Compiled 2352 to 1526 computations (35.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	8	11
1	11	11
2	16	11
3	18	11
4	19	11
5	19	11

end153.0ms (4%)

Compiler: Compiled 96 to 60 computations (37.5% saved)

Details

analyze4.0ms (0.1%)

sample1.3s (33.3%)

simplify102.0ms (2.7%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series26.0ms (0.7%)

rewrite13.0ms (0.3%)

simplify191.0ms (5%)

prune105.0ms (2.7%)

localize10.0ms (0.3%)

series24.0ms (0.6%)

rewrite13.0ms (0.3%)

simplify187.0ms (4.9%)

prune149.0ms (3.9%)

localize27.0ms (0.7%)

series66.0ms (1.7%)

rewrite39.0ms (1%)

simplify168.0ms (4.4%)

prune74.0ms (1.9%)

localize28.0ms (0.7%)

series62.0ms (1.6%)

rewrite96.0ms (2.5%)

simplify266.0ms (7%)

prune416.0ms (11%)

regimes303.0ms (8%)

simplify4.0ms (0.1%)

end153.0ms (4%)

Profiling