Details

analyze407.0ms (11.8%)

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)

sample917.0ms (26.7%)

Symmetry

(sort x y)

Results

826.0ms	8256×	body	128	valid
51.0ms	465×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify7.0ms (0.2%)

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)

localize36.0ms (1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(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))

simplify58.0ms (1.7%)

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

prune197.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Error

0.0b

Counts

25 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	16.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (sqrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))
	12.4b	(expm1.f64 (log1p.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))

Compiler

Compiled 452 to 242 computations (46.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 z z))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 3 (*.f64 z z))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

(*.f64 3 (*.f64 z z))

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
701×	`associate-/l/_binary64`
384×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
212×	`*-commutative_binary64`

Counts

33 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	306
1	76	270
2	175	261
3	419	261
4	633	261
5	1054	261
6	2130	261
7	4875	261
8	4875	261

prune32.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	23	6	29

Error

0.0b

Counts

29 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	0.2b	(fma.f64 y x (.f64 (.f64 (sqrt.f64 3) z) (*.f64 (sqrt.f64 3) z)))
	0.5b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 z z))) (cbrt.f64 (.f64 3 (.f64 z z)))) (cbrt.f64 (.f64 3 (.f64 z z)))))
	12.4b	(expm1.f64 (log1p.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))

Compiler

Compiled 473 to 283 computations (40.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
✓	0.3b	(.f64 (cbrt.f64 3) (.f64 z z))

series19.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
5.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
28×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

2 → 55

Calls

2 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
5.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

717×	`associate-l_binary64`
475×	`*-commutative_binary64`
434×	`unswap-sqr_binary64`
392×	`associate-/l*_binary64`
339×	`associate-/r/_binary64`

Counts

79 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	895
1	140	727
2	431	697
3	1108	697
4	1725	697
5	3106	697
6	5136	697

prune86.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	76	6	82

Error

Counts

82 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z))))
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	0.2b	(fma.f64 y x (.f64 (.f64 (sqrt.f64 3) z) (*.f64 (sqrt.f64 3) z)))
	12.4b	(expm1.f64 (log1p.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))

Compiler

Compiled 1638 to 1129 computations (31.1% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 3)) z)
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z))

series864.0ms (25.1%)

Counts

3 → 36

Calls

3 calls:

316.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z)))

315.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z))

232.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) z)

rewrite45.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`pow1_binary64`
80×	`pow-prod-down_binary64`
58×	`add-exp-log_binary64`
40×	`cbrt-unprod_binary64`
40×	`prod-exp_binary64`

Counts

3 → 124

Calls

3 calls:

18.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z)))

12.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z))

4.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) z)

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

986×	`fma-def_binary64`
521×	`*-commutative_binary64`
403×	`sqr-pow_binary64`
345×	`associate-+l+_binary64`
277×	`exp-prod_binary64`

Counts

160 → 130

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	3390
1	240	1990
2	983	1869
3	2083	1767
4	3473	1740
5	5040	1740

prune182.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	0	2
Picked	1	0	1
Done	0	3	3
Total	173	5	178

Error

Counts

178 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	0.3b	(fma.f64 y x (pow.f64 (.f64 (cbrt.f64 3) (.f64 (cbrt.f64 (sqrt.f64 3)) z)) 2))
	1.8b	(fma.f64 y x (expm1.f64 (log1p.f64 (.f64 (pow.f64 3 2/3) (pow.f64 (.f64 z (cbrt.f64 (sqrt.f64 3))) 2)))))

Compiler

Compiled 4426 to 3576 computations (19.2% saved)

regimes194.0ms (5.7%)

Accuracy

Total 0.1b remaining (88.8%)

Threshold costs 0.1b (88.8%)

Counts

30 → 1

Compiler

Compiled 3373 to 2440 computations (27.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end89.0ms (2.6%)

Remove: (sort x y)
Compiler: Compiled 119 to 85 computations (28.6% saved)

Details

analyze407.0ms (11.8%)

sample917.0ms (26.7%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize36.0ms (1%)

series9.0ms (0.3%)

rewrite1.0ms (0%)

simplify58.0ms (1.7%)

prune197.0ms (5.7%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify60.0ms (1.7%)

prune32.0ms (0.9%)

localize8.0ms (0.2%)

series19.0ms (0.6%)

rewrite20.0ms (0.6%)

simplify66.0ms (1.9%)

prune86.0ms (2.5%)

localize11.0ms (0.3%)

series864.0ms (25.1%)

rewrite45.0ms (1.3%)

simplify108.0ms (3.2%)

prune182.0ms (5.3%)

regimes194.0ms (5.7%)

simplify4.0ms (0.1%)

end89.0ms (2.6%)

Profiling