Details

analyze1.4s (20.1%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	98.7%	1.3%	9
0%	97.9%	2.1%	10
0%	95.6%	4.4%	11
0%	94.4%	5.6%	12
0%	93.4%	6.6%	13
0%	92.7%	7.3%	14

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample2.4s (33.5%)

Symmetry

(sort d2 d3)

Results

1.3s	8218×	body	128	valid
989.0ms	1139×	body	8192	exit
46.0ms	351×	body	128	invalid
5.0ms	18×	body	512	valid
3.0ms	10×	body	1024	valid
2.0ms	10×	body	256	valid

Compiler

Compiled 33 to 23 computations (30.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
61×	`associate-+l+_binary64`
40×	`associate-+r+_binary64`
34×	`distribute-lft-out_binary64`
33×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	21	14
2	50	10
3	125	10
4	216	10
5	237	10
6	249	10
7	235	10

prune3.0ms (0%)

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
▶	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

Compiler

Compiled 75 to 51 computations (32% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

series12.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

6.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

961×	`distribute-rgt-in_binary64`
953×	`distribute-lft-in_binary64`
416×	`associate-l_binary64`
318×	`associate-r_binary64`
261×	`fma-def_binary64`

Counts

62 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	687
1	163	645
2	700	643
3	4006	643
4	4316	643
5	5142	643

prune39.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Status	Error	Program
	26.7b	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (*.f64 (+.f64 d3 37) (+.f64 d3 37)))) (-.f64 d2 (+.f64 d3 37)))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 776 to 465 computations (40.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d3 5) d1)
✓	0.0b	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
✓	0.0b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

series38.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

24.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
9.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
4.0ms	(*.f64 (+.f64 d3 5) d1)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 55

Calls

3 calls:

5.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
4.0ms	(*.f64 (+.f64 d3 5) d1)
3.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
695×	`fma-neg_binary64`
486×	`cancel-sign-sub-inv_binary64`
332×	`*-commutative_binary64`
298×	`associate-+l+_binary64`

Counts

151 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1635
1	348	1544
2	1326	1485
3	3601	1483
4	4941	1483
5	4843	1483

prune77.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
	26.7b	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (*.f64 (+.f64 d3 37) (+.f64 d3 37)))) (-.f64 d2 (+.f64 d3 37)))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 2062 to 1231 computations (40.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))
✓	0.6b	(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

series826.0ms (11.5%)

Counts

3 → 108

Calls

3 calls:

483.0ms

(*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

321.0ms

(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

21.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

7.0ms

(*.f64 (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

5.0ms

(cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37))))

simplify228.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
328×	`times-frac_binary64`
262×	`associate-/r*_binary64`
250×	`associate-/l*_binary64`
238×	`*-commutative_binary64`

Counts

223 → 283

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	690	10556
1	1989	9753
2	4935	9490
3	4962	9490

prune575.0ms (8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	584	1	585
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	585	4	589

Error

Counts

589 → 4

Alt Table

Status	Error	Program
▶	26.7b	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))) (-.f64 d2 (+.f64 37 d3)))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 29882 to 19730 computations (34% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 37 d3) 2)
✓	2.4b	(-.f64 (*.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))
✓	6.9b	(.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2)))
✓	18.2b	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))) (-.f64 d2 (+.f64 37 d3)))

series112.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

67.0ms	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))) (-.f64 d2 (+.f64 37 d3)))
34.0ms	(.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2)))
9.0ms	(-.f64 (*.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))
2.0ms	(pow.f64 (+.f64 37 d3) 2)

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`unpow-prod-down_binary64`
27×	`cancel-sign-sub-inv_binary64`
27×	`prod-diff_binary64`

Counts

4 → 154

Calls

4 calls:

16.0ms	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))) (-.f64 d2 (+.f64 37 d3)))
10.0ms	(.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2)))
7.0ms	(-.f64 (*.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))
6.0ms	(pow.f64 (+.f64 37 d3) 2)

simplify177.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

315×	`times-frac_binary64`
299×	`associate-/l*_binary64`
265×	`associate-r_binary64`
257×	`fma-neg_binary64`
255×	`associate-l_binary64`

Counts

262 → 281

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	382	6488
1	982	5449
2	4521	5449
3	4996	5449
4	4955	5449

prune219.0ms (3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	281	4	285

Error

Counts

285 → 4

Alt Table

Status	Error	Program
✓	26.7b	(/.f64 (.f64 d1 (-.f64 (.f64 d2 d2) (pow.f64 (+.f64 37 d3) 2))) (-.f64 d2 (+.f64 37 d3)))
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37)))) (cbrt.f64 (.f64 d1 (+.f64 d2 (+.f64 d3 37))))) (cbrt.f64 (*.f64 d1 (+.f64 d2 (+.f64 d3 37)))))

Compiler

Compiled 8456 to 5537 computations (34.5% saved)

regimes469.0ms (6.5%)

Accuracy

Total 0.0b remaining (82.7%)

Threshold costs 0.0b (82.7%)

Counts

84 → 1

Compiler

Compiled 8030 to 5698 computations (29% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	13	13

end232.0ms (3.2%)

Compiler: Compiled 123 to 84 computations (31.7% saved)

Details

analyze1.4s (20.1%)

sample2.4s (33.5%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series12.0ms (0.2%)

rewrite7.0ms (0.1%)

simplify69.0ms (1%)

prune39.0ms (0.5%)

localize11.0ms (0.2%)

series38.0ms (0.5%)

rewrite15.0ms (0.2%)

simplify106.0ms (1.5%)

prune77.0ms (1.1%)

localize11.0ms (0.2%)

series826.0ms (11.5%)

rewrite37.0ms (0.5%)

simplify228.0ms (3.2%)

prune575.0ms (8%)

localize10.0ms (0.1%)

series112.0ms (1.6%)

rewrite48.0ms (0.7%)

simplify177.0ms (2.5%)

prune219.0ms (3%)

regimes469.0ms (6.5%)

simplify3.0ms (0%)

end232.0ms (3.2%)

Profiling