Details

analyze79.0ms (1.4%)

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)

sample1.2s (21.6%)

Results

1.1s	8256×	body	128	valid
13.0ms	186×	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)

series11.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite77.0ms (1.4%)

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 → 18

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

simplify155.0ms (2.8%)

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

42 → 20

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	16	4	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Error

0.1b

Counts

21 → 5

Alt Table

Status	Error	Program
	48.2b	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 6))
	30.3b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
▶	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
	13.6b	(*.f64 (pow.f64 y 2) x)
✓	0.2b	(.f64 (.f64 x y) y)

Compiler

Compiled 241 to 115 computations (52.3% 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)
✓	17.2b	(cbrt.f64 (.f64 y (.f64 x y)))

series948.0ms (17.3%)

Counts

3 → 72

Calls

3 calls:

484.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
455.0ms	(cbrt.f64 (.f64 y (.f64 x y)))
9.0ms	(.f64 y (.f64 x y))

rewrite77.0ms (1.4%)

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 → 85

Calls

3 calls:

75.0ms	(.f64 y (.f64 x y))
75.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 x y))) 3)
75.0ms	(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 (1.1%)

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

157 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	1348
1	129	1220
2	237	1140
3	708	604
4	2555	604
5	5004	604

prune73.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	79	12	91

Error

0.0b

Counts

91 → 12

Alt Table

Status	Error	Program
	14.0b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
✓	0.2b	(.f64 (.f64 x y) y)
	1.3b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) (pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 2)))
▶	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	14.0b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 y x)))
	1.0b	(.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (.f64 y x)) (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 2)))
	48.2b	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 6))
	30.3b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
	13.6b	(*.f64 (pow.f64 y 2) x)
	31.2b	(cbrt.f64 (pow.f64 (.f64 y (.f64 y x)) 3))
	29.4b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
	31.5b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 y x)))

Compiler

Compiled 1353 to 622 computations (54% saved)

localize7.0ms (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)
✓	9.4b	(cbrt.f64 (*.f64 y x))

series1.1s (19.8%)

Counts

4 → 96

Calls

4 calls:

415.0ms	(.f64 (cbrt.f64 (.f64 y x)) y)
329.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
305.0ms	(cbrt.f64 (*.f64 y x))
33.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))

rewrite47.0ms (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 → 81

Calls

4 calls:

46.0ms	(.f64 (cbrt.f64 (.f64 y x)) y)
46.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
46.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
46.0ms	(cbrt.f64 (*.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify138.0ms (2.5%)

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

177 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	1472
1	172	1440
2	308	1308
3	968	968
4	3447	956
5	4789	956
6	4655	956
7	4959	956
8	4835	956

prune122.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	139	12	151

Error

0.0b

Counts

151 → 12

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) (pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 2)))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 x)) (.f64 (cbrt.f64 (.f64 y x)) y))
	30.3b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
	14.0b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
✓	0.2b	(.f64 (.f64 x y) y)
	4.2b	(.f64 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) 2))) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	29.4b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 y (cbrt.f64 (.f64 y x))))
	1.0b	(.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (.f64 y x)) (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 2)))
	48.2b	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 6))
	13.6b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 2575 to 1107 computations (57% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 y (*.f64 y x))) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
	9.4b	(cbrt.f64 (*.f64 y x))
✓	17.2b	(cbrt.f64 (.f64 y (.f64 y x)))

series877.0ms (16%)

Counts

3 → 60

Calls

3 calls:

466.0ms	(.f64 (cbrt.f64 (.f64 y (*.f64 y x))) (cbrt.f64 x))
382.0ms	(cbrt.f64 (.f64 y (.f64 y x)))
29.0ms	(cbrt.f64 x)

rewrite50.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

645×	`log1p-expm1-u_binary64`
645×	`expm1-log1p-u_binary64`
412×	`log-prod_binary64`
130×	`expm1-udef_binary64`
130×	`log1p-udef_binary64`

Counts

3 → 71

Calls

3 calls:

49.0ms	(.f64 (cbrt.f64 (.f64 y (*.f64 y x))) (cbrt.f64 x))
49.0ms	(cbrt.f64 x)
49.0ms	(cbrt.f64 (.f64 y (.f64 y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	155	21
2	1746	21
3	5194	21
0	0	0
1	0	0

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Rules

581×	`div-exp_binary64`
520×	`exp-sum_binary64`
486×	`fma-neg_binary64`
415×	`exp-diff_binary64`
403×	`exp-prod_binary64`

Counts

131 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	71	940
1	164	868
2	307	768
3	922	644
4	2931	556
5	4751	556
6	4202	556
7	4403	556
8	5462	556

prune88.0ms (1.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	121	13	134

Error

Counts

134 → 13

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	30.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) 2) (cbrt.f64 x)) (.f64 (cbrt.f64 (*.f64 y x)) y))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y x)))) (pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 2)))
✓	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 x)) (.f64 (cbrt.f64 (.f64 y x)) y))
	30.3b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
	14.0b	(.f64 (.f64 (.f64 y x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
✓	0.2b	(.f64 (.f64 x y) y)
	4.2b	(.f64 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) 2))) 2) (.f64 (cbrt.f64 (.f64 y x)) y))
	29.4b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) y))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 y (cbrt.f64 (.f64 y x))))
	1.0b	(.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (.f64 y x)) (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 2)))
	48.2b	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 6))
	13.6b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 2617 to 856 computations (67.3% saved)

regimes117.0ms (2.1%)

Accuracy

Total 0.2b remaining (86.7%)

Threshold costs 0.2b (86.7%)

Counts

43 → 1

Compiler

Compiled 2027 to 1237 computations (39% 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

end131.0ms (2.4%)

Compiler: Compiled 213 to 126 computations (40.8% saved)

Details

analyze79.0ms (1.4%)

sample1.2s (21.6%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series11.0ms (0.2%)

rewrite77.0ms (1.4%)

simplify155.0ms (2.8%)

prune12.0ms (0.2%)

localize6.0ms (0.1%)

series948.0ms (17.3%)

rewrite77.0ms (1.4%)

simplify61.0ms (1.1%)

prune73.0ms (1.3%)

localize7.0ms (0.1%)

series1.1s (19.8%)

rewrite47.0ms (0.9%)

simplify138.0ms (2.5%)

prune122.0ms (2.2%)

localize13.0ms (0.2%)

series877.0ms (16%)

rewrite50.0ms (0.9%)

simplify107.0ms (2%)

prune88.0ms (1.6%)

regimes117.0ms (2.1%)

simplify2.0ms (0%)

end131.0ms (2.4%)

Profiling