Details

analyze453.0ms (16.3%)

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
40.6%	50.7%	8.7%	10
48.4%	42.1%	9.5%	11
54.2%	35.5%	10.3%	12
59.1%	25.9%	15%	13
63.9%	20.9%	15.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.2s (43.4%)

Results

1.0s	8256×	body	128	valid
60.0ms	607×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify54.0ms (2%)

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
3.0ms	(*.f64 (-.f64 y x) 6)

rewrite6.0ms (0.2%)

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)

simplify83.0ms (3%)

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

prune55.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Error

0.0b

Counts

71 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 6 (.f64 z (-.f64 y x)) x)) (cbrt.f64 (fma.f64 6 (.f64 z (-.f64 y x)) x))) (cbrt.f64 (fma.f64 6 (*.f64 z (-.f64 y x)) x)))
	21.8b	(fma.f64 x (*.f64 z -6) x)
	0.2b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
	38.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x) (fma.f64 (.f64 (-.f64 y x) 6) z x)) (fma.f64 (*.f64 (-.f64 y x) 6) z x)))
	34.8b	(fma.f64 (/.f64 (.f64 (-.f64 (pow.f64 y 3) (pow.f64 x 3)) 6) (+.f64 (.f64 y y) (+.f64 (.f64 x x) (.f64 y x)))) z x)
✓	0.4b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	1.0b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) 6)) (cbrt.f64 (.f64 (-.f64 y x) 6))) (cbrt.f64 (*.f64 (-.f64 y x) 6))) z x)
▶	0.2b	(fma.f64 6 (*.f64 z (-.f64 y x)) x)

Compiler

Compiled 1195 to 598 computations (50% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(fma.f64 6 (*.f64 z (-.f64 y x)) x)
6.0ms	(*.f64 z (-.f64 y x))

rewrite9.0ms (0.3%)

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:

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

simplify111.0ms (4%)

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

prune72.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	91	7	98

Error

Counts

98 → 7

Alt Table

Status	Error	Program
	0.8b	(fma.f64 6 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (cbrt.f64 (-.f64 y x))) x)
▶	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
	0.2b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
	38.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x) (fma.f64 (.f64 (-.f64 y x) 6) z x)) (fma.f64 (*.f64 (-.f64 y x) 6) z x)))
	45.3b	(fma.f64 6 (.f64 (.f64 z (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (-.f64 (sqrt.f64 y) (sqrt.f64 x))) x)
✓	0.4b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	1.0b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) 6)) (cbrt.f64 (.f64 (-.f64 y x) 6))) (cbrt.f64 (*.f64 (-.f64 y x) 6))) z x)

Compiler

Compiled 1727 to 675 computations (60.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(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)

simplify50.0ms (1.8%)

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

prune26.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	29	7	36

Error

Counts

36 → 7

Alt Table

Status	Error	Program
	0.8b	(fma.f64 6 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (cbrt.f64 (-.f64 y x))) x)
✓	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
▶	0.2b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
	38.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 (-.f64 y x) 6) z x) (fma.f64 (.f64 (-.f64 y x) 6) z x)) (fma.f64 (*.f64 (-.f64 y x) 6) z x)))
	45.3b	(fma.f64 6 (.f64 (.f64 z (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (-.f64 (sqrt.f64 y) (sqrt.f64 x))) x)
✓	0.4b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	1.0b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) 6)) (cbrt.f64 (.f64 (-.f64 y x) 6))) (cbrt.f64 (*.f64 (-.f64 y x) 6))) z x)

Compiler

Compiled 586 to 304 computations (48.1% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
✓	0.3b	(.f64 6 (.f64 y z))
✓	0.3b	(.f64 6 (.f64 z x))

series31.0ms (1.1%)

Counts

4 → 18

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
8.0ms	(+.f64 (.f64 6 (.f64 y z)) x)
4.0ms	(.f64 6 (.f64 z x))
4.0ms	(.f64 6 (.f64 y z))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) x)
3.0ms	(.f64 6 (.f64 z x))
3.0ms	(.f64 6 (.f64 y z))

simplify81.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary64`
547×	`fma-neg_binary64`
440×	`distribute-rgt-neg-in_binary64`
419×	`distribute-lft-neg-in_binary64`
386×	`*-commutative_binary64`

Counts

94 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1244
1	355	1039
2	1133	998
3	3152	995
4	4859	995
5	4909	995

prune101.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	0.8b	(fma.f64 6 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (cbrt.f64 (-.f64 y x))) x)
✓	0.1b	(fma.f64 (*.f64 6 z) (-.f64 y x) x)
	1.0b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) 6)) (cbrt.f64 (.f64 (-.f64 y x) 6))) (cbrt.f64 (*.f64 (-.f64 y x) 6))) z x)
	16.0b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 6 (.f64 z y)) 3)) x) (.f64 6 (.f64 z x)))
✓	0.2b	(-.f64 (+.f64 (.f64 6 (.f64 y z)) x) (.f64 6 (.f64 z x)))
	45.3b	(fma.f64 6 (.f64 (.f64 z (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (-.f64 (sqrt.f64 y) (sqrt.f64 x))) x)
✓	0.4b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 2506 to 1336 computations (46.7% saved)

regimes267.0ms (9.6%)

Accuracy

Total 0.2b remaining (92.6%)

Threshold costs 0.2b (92.6%)

Counts

75 → 1

Compiler

Compiled 4456 to 2958 computations (33.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	15	17
2	15	17

end89.0ms (3.2%)

Compiler: Compiled 154 to 96 computations (37.7% saved)

Details

analyze453.0ms (16.3%)

sample1.2s (43.4%)

simplify54.0ms (2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite6.0ms (0.2%)

simplify83.0ms (3%)

prune55.0ms (2%)

localize5.0ms (0.2%)

series17.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify111.0ms (4%)

prune72.0ms (2.6%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify50.0ms (1.8%)

prune26.0ms (0.9%)

localize7.0ms (0.3%)

series31.0ms (1.1%)

rewrite19.0ms (0.7%)

simplify81.0ms (2.9%)

prune101.0ms (3.6%)

regimes267.0ms (9.6%)

simplify2.0ms (0.1%)

end89.0ms (3.2%)

Profiling