Details

analyze85.0ms (1.7%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample689.0ms (13.7%)

Results

644.0ms	8256×	body	128	valid
17.0ms	197×	body	128	invalid

Compiler

Compiled 23 to 14 computations (39.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	9	7
2	10	7
3	10	7

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x y) y)

Compiler

Compiled 26 to 13 computations (50% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x y) y)

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 (*.f64 x y) y)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x y) y)

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-def_binary64`
373×	`associate-l_binary64`
319×	`unswap-sqr_binary64`
312×	`associate-*r/_binary64`
263×	`associate-*l/_binary64`

Counts

44 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	389
1	95	344
2	300	344
3	591	342
4	859	342
5	1608	342
6	4153	342
7	4970	342

prune18.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
	40.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y)))
✓	0.2b	(.f64 (.f64 x y) y)
	31.4b	(.f64 (.f64 x (pow.f64 y 3/2)) (sqrt.f64 y))
▶	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	10.3b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 422 to 145 computations (65.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x y) y)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (*.f64 x y) y)))
✓	19.8b	(cbrt.f64 (.f64 (.f64 x y) y))

series1.7s (33.6%)

Counts

3 → 72

Calls

3 calls:

960.0ms

(cbrt.f64 (*.f64 (*.f64 x y) y))

698.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x y) y)) (cbrt.f64 (*.f64 (*.f64 x y) y)))

25.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x y) y)) (cbrt.f64 (*.f64 (*.f64 x y) y))) (cbrt.f64 (*.f64 (*.f64 x y) y)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

10.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x y) y)) (cbrt.f64 (*.f64 (*.f64 x y) y))) (cbrt.f64 (*.f64 (*.f64 x y) y)))

4.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x y) y)) (cbrt.f64 (*.f64 (*.f64 x y) y)))

2.0ms

(cbrt.f64 (*.f64 (*.f64 x y) y))

simplify118.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

651×	`unswap-sqr_binary64`
407×	`fma-neg_binary64`
356×	`fma-def_binary64`
202×	`exp-prod_binary64`
202×	`log-prod_binary64`

Counts

151 → 129

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2312
1	275	1992
2	681	1634
3	1466	1454
4	4527	1450
5	4958	1450
6	4975	1450

prune199.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	272	4	276
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	272	9	281

Error

0.0b

Counts

281 → 9

Alt Table

Status	Error	Program
	40.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y)))
✓	0.2b	(.f64 (.f64 x y) y)
	1.0b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 x y)) (cbrt.f64 (.f64 x y))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (.f64 x y) y)))
	31.4b	(.f64 (.f64 x (pow.f64 y 3/2)) (sqrt.f64 y))
▶	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (.f64 x y)) (cbrt.f64 y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))))
✓	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	10.3b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 6858 to 1396 computations (79.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (*.f64 x y)) (cbrt.f64 y)))
✓	0.6b	(cbrt.f64 y)
✓	10.0b	(cbrt.f64 (*.f64 x y))
	19.8b	(cbrt.f64 (.f64 (.f64 x y) y))

series1.0s (20%)

Counts

3 → 60

Calls

3 calls:

594.0ms	(.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (*.f64 x y)) (cbrt.f64 y)))
377.0ms	(cbrt.f64 (*.f64 x y))
32.0ms	(cbrt.f64 y)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1/3_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-prod_binary64`

Counts

3 → 49

Calls

3 calls:

5.0ms	(.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (*.f64 x y)) (cbrt.f64 y)))
2.0ms	(cbrt.f64 (*.f64 x y))
1.0ms	(cbrt.f64 y)

simplify105.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
324×	`fma-def_binary64`
284×	`exp-prod_binary64`
268×	`*-commutative_binary64`

Counts

109 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1646
1	279	1546
2	728	1368
3	1637	1208
4	4338	1082
5	4927	1082
6	4928	1082

prune119.0ms (2.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	136	9	145

Error

0.0b

Counts

145 → 9

Alt Table

Status	Error	Program
	40.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y)))
✓	0.2b	(.f64 (.f64 x y) y)
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (.f64 x y) y)))
	31.4b	(.f64 (.f64 x (pow.f64 y 3/2)) (sqrt.f64 y))
✓	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (.f64 x y)) (cbrt.f64 y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))))
✓	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	10.3b	(*.f64 (pow.f64 y 2) x)
▶	1.1b	(.f64 (.f64 (.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 (.f64 x y)) 2)) (cbrt.f64 y)) (cbrt.f64 (.f64 (.f64 x y) y)))

Compiler

Compiled 3771 to 992 computations (73.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
	0.6b	(cbrt.f64 y)
	10.0b	(cbrt.f64 (*.f64 x y))
	19.8b	(cbrt.f64 (.f64 (.f64 x y) y))

series418.0ms (8.3%)

Counts

1 → 24

Calls

1 calls:

418.0ms

(pow.f64 (cbrt.f64 (*.f64 x y)) 2)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`unpow-prod-down_binary64`
3×	`pow-unpow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (*.f64 x y)) 2)

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-l_binary64`
709×	`fma-def_binary64`
538×	`associate-r_binary64`
529×	`unswap-sqr_binary64`
365×	`exp-prod_binary64`

Counts

46 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	753
1	163	707
2	290	630
3	842	457
4	3238	457
5	4997	457
6	4872	457

prune106.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	119	9	128

Error

0.0b

Counts

128 → 9

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))))) (cbrt.f64 (.f64 (.f64 x y) y)))
	1.5b	(.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x y))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x y))) 2))) (cbrt.f64 y)) (cbrt.f64 (.f64 (.f64 x y) y)))
✓	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (.f64 (cbrt.f64 (.f64 x y)) (cbrt.f64 y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	19.1b	(.f64 (.f64 (.f64 (cbrt.f64 y) (pow.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (.f64 x y)))) 2)) (cbrt.f64 y)) (cbrt.f64 (.f64 (.f64 x y) y)))
	31.4b	(.f64 (.f64 x (pow.f64 y 3/2)) (sqrt.f64 y))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 x y) y)))))
✓	0.2b	(.f64 (.f64 x y) y)
✓	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
	10.3b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 3022 to 1115 computations (63.1% saved)

regimes126.0ms (2.5%)

Accuracy

Total 0.1b remaining (77.8%)

Threshold costs 0.1b (77.8%)

Counts

37 → 1

Compiler

Compiled 2420 to 1243 computations (48.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	7	7

end113.0ms (2.3%)

Compiler: Compiled 228 to 91 computations (60.1% saved)

Details

analyze85.0ms (1.7%)

sample689.0ms (13.7%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series9.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify58.0ms (1.2%)

prune18.0ms (0.4%)

localize7.0ms (0.1%)

series1.7s (33.6%)

rewrite21.0ms (0.4%)

simplify118.0ms (2.4%)

prune199.0ms (4%)

localize13.0ms (0.3%)

series1.0s (20%)

rewrite9.0ms (0.2%)

simplify105.0ms (2.1%)

prune119.0ms (2.4%)

localize11.0ms (0.2%)

series418.0ms (8.3%)

rewrite3.0ms (0.1%)

simplify80.0ms (1.6%)

prune106.0ms (2.1%)

regimes126.0ms (2.5%)

simplify3.0ms (0.1%)

end113.0ms (2.3%)

Profiling