Details

analyze83.0ms (1.2%)

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)

sample700.0ms (10.3%)

Results

645.0ms	8256×	body	128	valid
25.0ms	222×	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%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite77.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

816×	`log1p-udef_binary64`
431×	`log1p-expm1-u_binary64`
431×	`expm1-log1p-u_binary64`
366×	`unpow-prod-down_binary64`
273×	`log-prod_binary64`

Counts

1 → 17

Calls

1 calls:

76.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	99	7
2	1159	7
3	4806	7
4	6204	7
0	0	0
1	0	0

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

41 → 19

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	12	168
2	22	168
3	41	168
4	88	168
5	221	168
6	693	168
7	1098	168
8	1100	168
9	1248	168
10	1418	168
11	1600	168
12	1825	168
13	2110	168
14	2529	168
15	3094	168
16	3780	168
17	3998	168
18	4242	168
19	4324	168
20	4357	168
21	4378	168
22	4947	168

prune12.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	15	4	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	5	20

Error

0.1b

Counts

20 → 5

Alt Table

Status	Error	Program
	39.9b	(sqrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 4))
	29.5b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
▶	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
	11.4b	(*.f64 (pow.f64 y 2) x)
✓	0.2b	(.f64 (.f64 x y) y)

Compiler

Compiled 236 to 115 computations (51.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (.f64 x y))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
✓	18.6b	(cbrt.f64 (.f64 y (.f64 x y)))

series1.5s (22.3%)

Counts

3 → 72

Calls

3 calls:

937.0ms	(cbrt.f64 (.f64 y (.f64 x y)))
567.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
8.0ms	(.f64 y (.f64 x y))

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
343×	`log-prod_binary64`
121×	`pow1/3_binary64`
121×	`expm1-udef_binary64`

Counts

3 → 83

Calls

3 calls:

79.0ms	(.f64 y (.f64 x y))
79.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
79.0ms	(cbrt.f64 (.f64 y (.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	147	23
2	1609	23
3	4960	23
4	4899	23
0	0	0
1	0	0

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

698×	`unswap-sqr_binary64`
316×	`unsub-neg_binary64`
281×	`fma-neg_binary64`
273×	`exp-sum_binary64`
247×	`fma-def_binary64`

Counts

155 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	1348
1	129	1220
2	237	948
3	708	604
4	2555	604
5	5004	604

prune57.0ms (0.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	79	11	90

Error

0.0b

Counts

90 → 11

Alt Table

Status	Error	Program
	11.7b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
	11.4b	(*.f64 (pow.f64 y 2) x)
	25.2b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
✓	0.2b	(.f64 (.f64 x y) y)
	39.9b	(sqrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 4))
	29.5b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
✓	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
	29.7b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 y x)))
▶	0.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	11.8b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 y x)))
	1.2b	(pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 y x))) 3)

Compiler

Compiled 1250 to 590 computations (52.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (.f64 y x)) y)
✓	0.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
✓	8.7b	(cbrt.f64 (*.f64 y x))

series1.5s (22.7%)

Counts

4 → 96

Calls

4 calls:

657.0ms	(.f64 (cbrt.f64 (.f64 y x)) y)
453.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
394.0ms	(cbrt.f64 (*.f64 y x))
35.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))

rewrite59.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
88×	`associate-r_binary64`

Counts

4 → 77

Calls

4 calls:

58.0ms	(.f64 (cbrt.f64 (.f64 y x)) y)
58.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
58.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
58.0ms	(cbrt.f64 (*.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	180	29
2	1932	29
3	4909	29
0	0	0
1	0	0

simplify126.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-neg_binary64`
439×	`associate-l_binary64`
411×	`exp-sum_binary64`
385×	`associate-r_binary64`
309×	`exp-prod_binary64`

Counts

173 → 102

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	1472
1	172	1440
2	308	1228
3	968	920
4	3447	908
5	4789	908
6	4655	908
7	4959	908
8	4835	908

prune92.0ms (1.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	132	13	145

Error

0.0b

Counts

145 → 13

Alt Table

Status	Error	Program
	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (pow.f64 (cbrt.f64 (.f64 y (cbrt.f64 (.f64 y x)))) 3))
	39.9b	(sqrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 4))
	11.7b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
	11.4b	(*.f64 (pow.f64 y 2) x)
	25.2b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
✓	0.2b	(.f64 (.f64 x y) y)
	22.7b	(pow.f64 (sqrt.f64 (.f64 y (.f64 y x))) 2)
✓	0.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	26.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (exp.f64 (log.f64 (cbrt.f64 (.f64 y x)))) y))
▶	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) 3) y))
✓	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
	11.8b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 y x)))
	1.2b	(pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 y x))) 3)

Compiler

Compiled 2430 to 1079 computations (55.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
✓	0.6b	(cbrt.f64 (cbrt.f64 (*.f64 y x)))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y x))) 3)
	8.7b	(cbrt.f64 (*.f64 y x))

series1.7s (25%)

Counts

2 → 48

Calls

2 calls:

876.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y x))) 3)
819.0ms	(cbrt.f64 (cbrt.f64 (*.f64 y x)))

rewrite52.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

571×	`unpow-prod-down_binary64`
564×	`log1p-expm1-u_binary64`
564×	`expm1-log1p-u_binary64`
306×	`log-prod_binary64`
162×	`pow2_binary64`

Counts

2 → 107

Calls

2 calls:

50.0ms	(cbrt.f64 (cbrt.f64 (*.f64 y x)))
50.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	143	13
2	1512	13
3	5597	13
0	0	0
1	0	0

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
640×	`unswap-sqr_binary64`
268×	`distribute-neg-out_binary64`
238×	`associate-l_binary64`
228×	`unsub-neg_binary64`

Counts

155 → 121

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	44	840
1	117	840
2	209	744
3	555	552
4	1809	480
5	4933	456
6	4927	456
7	4928	456

prune161.0ms (2.4%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	8	9
Picked	0	1	1
Done	0	3	3
Total	213	13	226

Error

0.0b

Counts

226 → 13

Alt Table

Status	Error	Program
	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (pow.f64 (cbrt.f64 (.f64 y (cbrt.f64 (.f64 y x)))) 3))
	39.9b	(sqrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 4))
	11.7b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
	11.4b	(*.f64 (pow.f64 y 2) x)
	25.2b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
✓	0.2b	(.f64 (.f64 x y) y)
	22.7b	(pow.f64 (sqrt.f64 (.f64 y (.f64 y x))) 2)
✓	0.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	26.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (exp.f64 (log.f64 (cbrt.f64 (.f64 y x)))) y))
✓	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) 3) y))
✓	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
	0.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) y))
	1.2b	(pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 y x))) 3)

Compiler

Compiled 4716 to 2392 computations (49.3% saved)

regimes54.0ms (0.8%)

Accuracy

Total 0.2b remaining (84.3%)

Threshold costs 0.2b (84.3%)

Counts

21 → 1

Compiler

Compiled 791 to 511 computations (35.4% saved)

simplify2.0ms (0%)

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

end123.0ms (1.8%)

Compiler: Compiled 178 to 111 computations (37.6% saved)

Details

analyze83.0ms (1.2%)

sample700.0ms (10.3%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0%)

series8.0ms (0.1%)

rewrite77.0ms (1.1%)

simplify157.0ms (2.3%)

prune12.0ms (0.2%)

localize6.0ms (0.1%)

series1.5s (22.3%)

rewrite81.0ms (1.2%)

simplify61.0ms (0.9%)

prune57.0ms (0.8%)

localize8.0ms (0.1%)

series1.5s (22.7%)

rewrite59.0ms (0.9%)

simplify126.0ms (1.9%)

prune92.0ms (1.4%)

localize9.0ms (0.1%)

series1.7s (25%)

rewrite52.0ms (0.8%)

simplify85.0ms (1.3%)

prune161.0ms (2.4%)

regimes54.0ms (0.8%)

simplify2.0ms (0%)

end123.0ms (1.8%)

Profiling