Details

analyze595.0ms (12.5%)

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 (25.4%)

Results

861.0ms	7559×	body	128	valid
98.0ms	276×	body	1024	valid
68.0ms	260×	body	512	valid
66.0ms	630×	body	128	invalid
28.0ms	161×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify228.0ms (4.8%)

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

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
▶	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.4b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 2 3) z)
✓	0.0b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.3b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series37.0ms (0.8%)

Counts

4 → 108

Calls

4 calls:

20.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
12.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
4.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite73.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`
195×	`prod-diff_binary64`
190×	`add-cube-cbrt_binary64`
146×	`times-frac_binary64`

Counts

4 → 314

Calls

4 calls:

14.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
10.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
6.0ms	(-.f64 (/.f64 2 3) z)
4.0ms	(*.f64 (-.f64 y x) 6)

simplify238.0ms (5%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
372×	`associate-l_binary64`
344×	`associate-r_binary64`
267×	`*-commutative_binary64`
238×	`cancel-sign-sub-inv_binary64`

Counts

422 → 428

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	427	9776
1	723	8689
2	2854	6627
3	4047	6546
4	4842	6546

prune371.0ms (7.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	420	8	428
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	421	9	430

Error

Counts

430 → 9

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	35.5b	(/.f64 (fma.f64 x x (.f64 (.f64 (.f64 (-.f64 2/3 z) (-.f64 2/3 z)) (.f64 (-.f64 y x) (-.f64 y x))) -36)) (+.f64 x (*.f64 (-.f64 y x) (fma.f64 z 6 -4))))
	29.0b	(+.f64 x (/.f64 (.f64 (-.f64 2/3 z) (.f64 6 (-.f64 (.f64 y y) (.f64 x x)))) (+.f64 y x)))
	31.4b	(.f64 (sqrt.f64 (fma.f64 (-.f64 2/3 z) (.f64 6 (-.f64 y x)) x)) (sqrt.f64 (fma.f64 (-.f64 2/3 z) (*.f64 6 (-.f64 y x)) x)))
	0.2b	(fma.f64 4 y (fma.f64 -6 (.f64 z (-.f64 y x)) (.f64 x -3)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.4b	(fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 (*.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.7b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))
	42.1b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 2/3 z) (*.f64 6 (-.f64 y x)) x) 3))

Compiler

Compiled 13490 to 7077 computations (47.5% saved)

localize22.0ms (0.5%)

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 y z))
✓	0.3b	(.f64 6 (.f64 z x))

series34.0ms (0.7%)

Counts

4 → 18

Calls

4 calls:

14.0ms	(-.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))
7.0ms	(.f64 6 (.f64 y z))
5.0ms	(.f64 6 (.f64 z x))

rewrite28.0ms (0.6%)

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

simplify97.0ms (2%)

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

prune161.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	150	7	157

Error

Counts

157 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	35.5b	(/.f64 (fma.f64 x x (.f64 (.f64 (.f64 (-.f64 2/3 z) (-.f64 2/3 z)) (.f64 (-.f64 y x) (-.f64 y x))) -36)) (+.f64 x (*.f64 (-.f64 y x) (fma.f64 z 6 -4))))
	31.5b	(.f64 -1 (.f64 (-.f64 3 (*.f64 6 z)) x))
	31.4b	(.f64 (sqrt.f64 (fma.f64 (-.f64 2/3 z) (.f64 6 (-.f64 y x)) x)) (sqrt.f64 (fma.f64 (-.f64 2/3 z) (*.f64 6 (-.f64 y x)) x)))
▶	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	42.1b	(cbrt.f64 (pow.f64 (fma.f64 y 4 (fma.f64 6 (.f64 z (-.f64 x y)) (.f64 x -3))) 3))
	0.7b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))

Compiler

Compiled 5087 to 3122 computations (38.6% saved)

localize11.0ms (0.2%)

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))

series28.0ms (0.6%)

Counts

3 → 96

Calls

3 calls:

15.0ms	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
8.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))
6.0ms	(.f64 z (.f64 y -6))

rewrite12.0ms (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))))
3.0ms	(.f64 z (.f64 y -6))
0.0ms	(fma.f64 x -3 (.f64 z (.f64 y -6)))

simplify100.0ms (2.1%)

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

prune123.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Error

Counts

124 → 7

Alt Table

Status	Error	Program
	31.5b	(.f64 -1 (.f64 (-.f64 3 (*.f64 6 z)) x))
	31.4b	(.f64 (sqrt.f64 (fma.f64 (-.f64 2/3 z) (.f64 6 (-.f64 y x)) x)) (sqrt.f64 (fma.f64 (-.f64 2/3 z) (*.f64 6 (-.f64 y x)) x)))
✓	0.1b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	42.1b	(cbrt.f64 (pow.f64 (fma.f64 y 4 (fma.f64 6 (.f64 z (-.f64 x y)) (.f64 x -3))) 3))
	0.7b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))
▶	0.3b	(+.f64 (fma.f64 x (fma.f64 z 6 -3) (.f64 y 4)) (.f64 z (*.f64 y -6)))
	0.4b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 2916 to 1837 computations (37% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series26.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

14.0ms	(+.f64 (fma.f64 x (fma.f64 z 6 -3) (.f64 y 4)) (.f64 z (*.f64 y -6)))
9.0ms	(fma.f64 x (fma.f64 z 6 -3) (*.f64 y 4))
2.0ms	(fma.f64 z 6 -3)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-def_binary64`

Counts

3 → 37

Calls

3 calls:

2.0ms	(+.f64 (fma.f64 x (fma.f64 z 6 -3) (.f64 y 4)) (.f64 z (*.f64 y -6)))
0.0ms	(fma.f64 x (fma.f64 z 6 -3) (*.f64 y 4))
0.0ms	(fma.f64 z 6 -3)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

583×	`distribute-rgt-neg-out_binary64`
544×	`associate-l_binary64`
491×	`associate-r_binary64`
418×	`fma-def_binary64`
233×	`distribute-rgt-in_binary64`

Counts

121 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	2013
1	238	1702
2	690	1505
3	3539	1505
4	5223	1505

prune126.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	117	6	123

Error

Counts

123 → 6

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))))
	42.0b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4))) 3))
	0.7b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))
	0.4b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	31.4b	(.f64 (sqrt.f64 (fma.f64 (-.f64 2/3 z) (.f64 6 (-.f64 y x)) x)) (sqrt.f64 (fma.f64 (-.f64 2/3 z) (*.f64 6 (-.f64 y x)) x)))
	22.9b	(+.f64 (fma.f64 x (.f64 6 z) (.f64 y 4)) (.f64 z (.f64 y -6)))

Compiler

Compiled 2454 to 1687 computations (31.3% saved)

regimes1.0s (21.5%)

Accuracy

Total 0.2b remaining (87.3%)

Threshold costs 0.2b (87.3%)

Counts

171 → 1

Compiler

Compiled 17270 to 12556 computations (27.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`neg-sub0_binary64`
7×	`sub-neg_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	24	22
2	32	20
3	40	20
4	53	20
5	62	20
6	78	20
7	83	20
8	84	20
9	79	20

end113.0ms (2.4%)

Compiler: Compiled 164 to 113 computations (31.1% saved)

Details

analyze595.0ms (12.5%)

sample1.2s (25.4%)

simplify228.0ms (4.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series37.0ms (0.8%)

rewrite73.0ms (1.5%)

simplify238.0ms (5%)

prune371.0ms (7.8%)

localize22.0ms (0.5%)

series34.0ms (0.7%)

rewrite28.0ms (0.6%)

simplify97.0ms (2%)

prune161.0ms (3.4%)

localize11.0ms (0.2%)

series28.0ms (0.6%)

rewrite12.0ms (0.3%)

simplify100.0ms (2.1%)

prune123.0ms (2.6%)

localize10.0ms (0.2%)

series26.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify76.0ms (1.6%)

prune126.0ms (2.6%)

regimes1.0s (21.5%)

simplify4.0ms (0.1%)

end113.0ms (2.4%)

Profiling