Details

analyze590.0ms (17%)

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
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (35.7%)

Results

893.0ms	7602×	body	128	valid
80.0ms	239×	body	1024	valid
78.0ms	641×	body	128	invalid
66.0ms	254×	body	512	valid
36.0ms	161×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify225.0ms (6.5%)

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
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
2.0ms	(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)

simplify86.0ms (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

prune43.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (-.f64 y x) (.f64 (.f64 (cbrt.f64 (fma.f64 z -6 4)) (cbrt.f64 (fma.f64 z -6 4))) (cbrt.f64 (fma.f64 z -6 4))) x)
✓	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	10.9b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (fma.f64 z -6 4)) (sqrt.f64 (fma.f64 z -6 4))) x)
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 807 to 497 computations (38.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
6.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(fma.f64 6 z -3)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 y (fma.f64 z -6 4))
0.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
0.0ms	(fma.f64 6 z -3)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

798×	`neg-mul-1_binary64`
520×	`distribute-rgt-neg-out_binary64`
469×	`distribute-lft-neg-out_binary64`
296×	`fma-neg_binary64`
289×	`associate-l_binary64`

Counts

114 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1600
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune90.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	94	6	100

Error

0.0b

Counts

100 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (-.f64 y x) (.f64 (.f64 (cbrt.f64 (fma.f64 z -6 4)) (cbrt.f64 (fma.f64 z -6 4))) (cbrt.f64 (fma.f64 z -6 4))) x)
✓	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	18.5b	(fma.f64 x (fma.f64 6 z -3) (.f64 -6 (.f64 y z)))
	11.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (exp.f64 (log.f64 (fma.f64 z -6 4)))))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 1666 to 1169 computations (29.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.3b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series33.0ms (1%)

Counts

4 → 18

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
8.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
5.0ms	(.f64 6 (.f64 y z))
5.0ms	(.f64 6 (.f64 z x))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-log-exp_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 93

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 z x))

simplify104.0ms (3%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
279×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
271×	`associate-r_binary64`

Counts

111 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2856
1	619	2159
2	2427	1906
3	4509	1906
4	5450	1906

prune155.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (-.f64 y x) (.f64 (.f64 (cbrt.f64 (fma.f64 z -6 4)) (cbrt.f64 (fma.f64 z -6 4))) (cbrt.f64 (fma.f64 z -6 4))) x)
✓	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	11.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (exp.f64 (log.f64 (fma.f64 z -6 4)))))
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 4965 to 3048 computations (38.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
✓	0.1b	(fma.f64 x -3 (.f64 z (.f64 y -6)))
✓	0.2b	(.f64 z (.f64 y -6))
	0.3b	(.f64 6 (.f64 z x))

series29.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

14.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
10.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))
5.0ms	(.f64 z (.f64 y -6))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

5.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
4.0ms	(.f64 z (.f64 y -6))
0.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))

simplify111.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

776×	`associate-l_binary64`
631×	`associate-r_binary64`
434×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
381×	`fma-def_binary64`

Counts

146 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	2252
1	308	1967
2	929	1829
3	4465	1820
4	4960	1820
5	5024	1820

prune106.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	117	6	123

Error

0.0b

Counts

123 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (-.f64 y x) (.f64 (.f64 (cbrt.f64 (fma.f64 z -6 4)) (cbrt.f64 (fma.f64 z -6 4))) (cbrt.f64 (fma.f64 z -6 4))) x)
✓	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	11.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (exp.f64 (log.f64 (fma.f64 z -6 4)))))
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 2768 to 1733 computations (37.4% saved)

regimes335.0ms (9.7%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

69 → 1

Compiler

Compiled 5351 to 3900 computations (27.1% 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	14	21
1	18	21
2	18	21

end110.0ms (3.2%)

Compiler: Compiled 149 to 109 computations (26.8% saved)

Details

analyze590.0ms (17%)

sample1.2s (35.7%)

simplify225.0ms (6.5%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series15.0ms (0.4%)

rewrite1.0ms (0%)

simplify86.0ms (2.5%)

prune43.0ms (1.2%)

localize9.0ms (0.3%)

series20.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify85.0ms (2.5%)

prune90.0ms (2.6%)

localize11.0ms (0.3%)

series33.0ms (1%)

rewrite26.0ms (0.8%)

simplify104.0ms (3%)

prune155.0ms (4.5%)

localize11.0ms (0.3%)

series29.0ms (0.8%)

rewrite11.0ms (0.3%)

simplify111.0ms (3.2%)

prune106.0ms (3.1%)

regimes335.0ms (9.7%)

simplify2.0ms (0.1%)

end110.0ms (3.2%)

Profiling