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 13 to 9 computations (30.8% saved)

sample883.0ms (50.2%)

Infinites

20.6% of outputs are infinite.

Results

714.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify52.0ms (2.9%)

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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize6.0ms (0.3%)

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)

series14.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
5.0ms	(*.f64 (-.f64 y x) 6)

rewrite6.0ms (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:

4.0ms	(*.f64 (-.f64 y x) 6)
0.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

simplify86.0ms (4.9%)

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

prune50.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (.f64 (.f64 (-.f64 y x) (sqrt.f64 6)) (sqrt.f64 6)) z x)
	1.6b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
	22.3b	(.f64 6 (.f64 z (-.f64 y x)))
▶	0.1b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	23.8b	(fma.f64 x (*.f64 z -6) x)
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	32.7b	(.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 1059 to 530 computations (50% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series19.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

13.0ms	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
6.0ms	(*.f64 z (-.f64 y x))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(*.f64 z (-.f64 y x))
0.0ms	(fma.f64 6 (*.f64 z (-.f64 y x)) x)

simplify110.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-neg_binary64`
433×	`exp-prod_binary64`
341×	`fma-def_binary64`
283×	`neg-mul-1_binary64`
228×	`*-commutative_binary64`

Counts

120 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1596
1	271	1231
2	838	1171
3	2033	1117
4	3701	1117
5	4979	1117
6	4994	1117
7	4789	1117

prune59.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
✓	0.1b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
	1.6b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 1544 to 576 computations (62.7% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(fma.f64 (*.f64 6 z) (-.f64 y x) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 6 z) (-.f64 y x) x)

simplify47.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

743×	`distribute-rgt-neg-out_binary64`
441×	`associate-l_binary64`
426×	`distribute-rgt-in_binary64`
414×	`distribute-lft-in_binary64`
395×	`associate-r_binary64`

Counts

46 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	697
1	100	512
2	221	506
3	586	506
4	2785	506
5	5027	506

prune17.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	29	4	33

Error

Counts

33 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
✓	0.1b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
▶	1.6b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 403 to 205 computations (49.1% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 6 (.f64 y z))
✓	0.2b	(.f64 6 (.f64 z x))
✓	1.4b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))

series24.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
9.0ms	(.f64 6 (.f64 z x))
4.0ms	(.f64 6 (.f64 y z))

rewrite21.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 62

Calls

3 calls:

8.0ms	(.f64 6 (.f64 y z))
7.0ms	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
4.0ms	(.f64 6 (.f64 z x))

simplify72.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-neg_binary64`
426×	`fma-def_binary64`
354×	`*-commutative_binary64`
348×	`cancel-sign-sub-inv_binary64`
333×	`distribute-rgt-neg-in_binary64`

Counts

71 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1055
1	308	818
2	996	780
3	2671	777
4	4585	777
5	4883	777

prune69.0ms (3.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
✓	0.1b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
✓	1.6b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 1964 to 1057 computations (46.2% saved)

regimes116.0ms (6.6%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

34 → 1

Compiler

Compiled 1728 to 1162 computations (32.8% saved)

simplify2.0ms (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

end61.0ms (3.5%)

Compiler: Compiled 71 to 46 computations (35.2% saved)

Details

analyze2.0ms (0.1%)

sample883.0ms (50.2%)

simplify52.0ms (2.9%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series14.0ms (0.8%)

rewrite6.0ms (0.3%)

simplify86.0ms (4.9%)

prune50.0ms (2.8%)

localize5.0ms (0.3%)

series19.0ms (1.1%)

rewrite11.0ms (0.6%)

simplify110.0ms (6.3%)

prune59.0ms (3.3%)

localize5.0ms (0.3%)

series12.0ms (0.7%)

rewrite1.0ms (0%)

simplify47.0ms (2.7%)

prune17.0ms (0.9%)

localize7.0ms (0.4%)

series24.0ms (1.4%)

rewrite21.0ms (1.2%)

simplify72.0ms (4.1%)

prune69.0ms (3.9%)

regimes116.0ms (6.6%)

simplify2.0ms (0.1%)

end61.0ms (3.5%)

Profiling