Details

analyze408.0ms (13.5%)

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
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample956.0ms (31.6%)

Symmetry

(sort x y)

Results

866.0ms	8256×	body	128	valid
57.0ms	514×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
✓	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

series33.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

13.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
12.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
8.0ms	(+.f64 (.f64 x y) (.f64 z z))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 51

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
5.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
3.0ms	(+.f64 (.f64 x y) (.f64 z z))

simplify90.0ms (3%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
652×	`fma-def_binary64`
387×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
267×	`associate-l_binary64`

Counts

159 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1788
1	246	1682
2	775	1595
3	3142	1591
4	4640	1591
5	5115	1591

prune62.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	1.0b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x y) (.f64 z z))) (cbrt.f64 (+.f64 (.f64 x y) (.f64 z z)))) (cbrt.f64 (+.f64 (.f64 x y) (.f64 z z)))) (.f64 z z)) (.f64 z z))
▶	0.1b	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
	18.3b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))

Compiler

Compiled 2151 to 468 computations (78.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series39.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

15.0ms	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
14.0ms	(fma.f64 x y (*.f64 z z))
11.0ms	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

4.0ms	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
2.0ms	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))
0.0ms	(fma.f64 x y (*.f64 z z))

simplify113.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

374×	`fma-def_binary64`
339×	`cancel-sign-sub-inv_binary64`
338×	`fma-neg_binary64`
322×	`associate--r+_binary64`
296×	`distribute-rgt-out_binary64`

Counts

153 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	1729
1	181	1584
2	513	1502
3	2009	1500
4	4453	1500
5	4916	1500
6	4838	1500

prune42.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Error

Counts

90 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	1.0b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
✓	0.1b	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
	18.3b	(fma.f64 (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (*.f64 z z))

Compiler

Compiled 1860 to 410 computations (78% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))

series13.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

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 z (*.f64 z 3) (*.f64 x y))

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
301×	`*-commutative_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	508
1	34	485
2	65	485
3	184	485
4	750	485
5	2905	485
6	3790	485
7	4921	485

prune18.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	23	4	27

Error

Counts

27 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	1.0b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
✓	0.1b	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
	18.3b	(fma.f64 (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (*.f64 z z))

Compiler

Compiled 439 to 191 computations (56.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))
✓	2.0b	(cbrt.f64 (fma.f64 x y (*.f64 z z)))

series149.0ms (4.9%)

Counts

4 → 144

Calls

4 calls:

67.0ms	(.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))
57.0ms	(cbrt.f64 (fma.f64 x y (*.f64 z z)))
15.0ms	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
9.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))

rewrite33.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 111

Calls

4 calls:

11.0ms	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
7.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))
6.0ms	(.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (*.f64 z z))))
1.0ms	(cbrt.f64 (fma.f64 x y (*.f64 z z)))

simplify161.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

392×	`unswap-sqr_binary64`
361×	`associate-r_binary64`
278×	`associate-l_binary64`
254×	`times-frac_binary64`
238×	`associate-/r*_binary64`

Counts

255 → 258

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	6883
1	1139	6363
2	3996	6054
3	5172	6054

prune240.0ms (7.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	392	0	392
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	392	4	396

Error

Counts

396 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	1.0b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z z))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (cbrt.f64 (fma.f64 x y (.f64 z z)))) (.f64 z z)) (*.f64 z z))
✓	0.1b	(+.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z)) (*.f64 z z))
	18.3b	(fma.f64 (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (fma.f64 x y (.f64 z z)) (.f64 z z))) (*.f64 z z))

Compiler

Compiled 18786 to 6131 computations (67.4% saved)

regimes449.0ms (14.8%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

74 → 1

Compiler

Compiled 10959 to 4841 computations (55.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	10	20
2	10	20

end75.0ms (2.5%)

Remove: (sort x y)
Compiler: Compiled 159 to 60 computations (62.3% saved)

Details

analyze408.0ms (13.5%)

sample956.0ms (31.6%)

simplify11.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series33.0ms (1.1%)

rewrite18.0ms (0.6%)

simplify90.0ms (3%)

prune62.0ms (2.1%)

localize10.0ms (0.3%)

series39.0ms (1.3%)

rewrite13.0ms (0.4%)

simplify113.0ms (3.7%)

prune42.0ms (1.4%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite1.0ms (0%)

simplify64.0ms (2.1%)

prune18.0ms (0.6%)

localize12.0ms (0.4%)

series149.0ms (4.9%)

rewrite33.0ms (1.1%)

simplify161.0ms (5.3%)

prune240.0ms (7.9%)

regimes449.0ms (14.8%)

simplify2.0ms (0.1%)

end75.0ms (2.5%)

Profiling