Details

analyze518.0ms (16.9%)

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)

sample103.0ms (3.4%)

Algorithm

1×

intervals

Results

10.0ms	230×	body	128	valid
2.0ms	12×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	14×	body	128	invalid
0.0ms	6×	body	256	valid

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify221.0ms (7.2%)

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
▶	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize7.0ms (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)

series13.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(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)

simplify86.0ms (2.8%)

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

prune50.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	1.4b	(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	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 853 to 521 computations (38.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
10.0ms	(*.f64 y (fma.f64 z -6 4))
1.0ms	(fma.f64 6 z -3)

rewrite5.0ms (0.2%)

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)

simplify80.0ms (2.6%)

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 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1678
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune80.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Error

Counts

99 → 7

Alt Table

Status	Error	Program
	1.4b	(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)
	20.8b	(fma.f64 x (fma.f64 6 z -3) (.f64 -6 (.f64 y z)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	12.4b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 6 z -3) (fma.f64 6 z -3)) (fma.f64 6 z -3))) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 1690 to 1186 computations (29.8% saved)

localize11.0ms (0.4%)

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)))
✓	0.2b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series31.0ms (1%)

Counts

4 → 18

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
7.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite27.0ms (0.9%)

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)))
6.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
3.0ms	(.f64 6 (.f64 z x))

simplify95.0ms (3.1%)

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

prune221.0ms (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	1.4b	(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	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	12.4b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 6 z -3) (fma.f64 6 z -3)) (fma.f64 6 z -3))) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 5012 to 3083 computations (38.5% 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 6 (.f64 z x))
✓	0.2b	(.f64 z (.f64 y -6))

series27.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

13.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
7.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))
6.0ms	(.f64 z (.f64 y -6))

rewrite12.0ms (0.4%)

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

simplify103.0ms (3.4%)

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

prune103.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	117	7	124

Error

Counts

124 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	1.4b	(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	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	12.4b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 6 z -3) (fma.f64 6 z -3)) (fma.f64 6 z -3))) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 2793 to 1752 computations (37.3% saved)

regimes359.0ms (11.7%)

Accuracy

Total 0.1b remaining (91.6%)

Threshold costs 0.1b (91.6%)

Counts

75 → 1

Compiler

Compiled 5825 to 4247 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

end1.0ms (0%)

Compiler: Compiled 18 to 13 computations (27.8% saved)

sample856.0ms (28%)

Algorithm

1×

intervals

Results

358.0ms	7318×	body	128	valid
52.0ms	261×	body	1024	valid
33.0ms	247×	body	512	valid
26.0ms	594×	body	128	invalid
14.0ms	174×	body	256	valid

Compiler

Compiled 176 to 131 computations (25.6% saved)

Details

analyze518.0ms (16.9%)

sample103.0ms (3.4%)

simplify221.0ms (7.2%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series13.0ms (0.4%)

rewrite1.0ms (0%)

simplify86.0ms (2.8%)

prune50.0ms (1.6%)

localize8.0ms (0.3%)

series23.0ms (0.8%)

rewrite5.0ms (0.2%)

simplify80.0ms (2.6%)

prune80.0ms (2.6%)

localize11.0ms (0.4%)

series31.0ms (1%)

rewrite27.0ms (0.9%)

simplify95.0ms (3.1%)

prune221.0ms (7.2%)

localize11.0ms (0.3%)

series27.0ms (0.9%)

rewrite12.0ms (0.4%)

simplify103.0ms (3.4%)

prune103.0ms (3.4%)

regimes359.0ms (11.7%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample856.0ms (28%)

Profiling