Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.0s (22.7%)

Results

862.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify143.0ms (3.2%)

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

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

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

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

35.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	33.6b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series5.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
2.0ms	(*.f64 2 (pow.f64 x 2))

rewrite85.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`log1p-udef_binary64`
450×	`log1p-expm1-u_binary64`
450×	`expm1-log1p-u_binary64`
402×	`unpow-prod-down_binary64`
251×	`log-prod_binary64`

Counts

2 → 73

Calls

2 calls:

84.0ms	(*.f64 2 (pow.f64 x 2))
84.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1214	13
3	4880	13
4	6252	13

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

85 → 75

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune123.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Error

0.2b

Counts

76 → 8

Alt Table

Status	Error	Program
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
▶	16.3b	(.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	33.2b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	35.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 905 to 704 computations (22.2% saved)

localize97.0ms (2.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	0.7b	(pow.f64 (cbrt.f64 x) 4)
✓	15.0b	(pow.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2)

series1.2s (25.3%)

Counts

4 → 48

Calls

4 calls:

1.0s	(pow.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2)
51.0ms	(pow.f64 (cbrt.f64 x) 4)
39.0ms	(pow.f64 (cbrt.f64 x) 2)
28.0ms	(cbrt.f64 x)

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
362×	`log-prod_binary64`
142×	`expm1-udef_binary64`
142×	`log1p-udef_binary64`

Counts

4 → 101

Calls

4 calls:

51.0ms	(pow.f64 (cbrt.f64 x) 2)
51.0ms	(cbrt.f64 x)
51.0ms	(pow.f64 (cbrt.f64 x) 4)
51.0ms	(pow.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	207	26
2	1853	26
3	5259	26

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-def_binary64`
712×	`unswap-sqr_binary64`
504×	`associate-l_binary64`
409×	`associate-r_binary64`
337×	`unsub-neg_binary64`

Counts

149 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	436
1	57	436
2	130	436
3	370	432
4	1293	432
5	2621	432
6	2813	432
7	3513	432
8	4511	432
9	4830	432

prune101.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	6	143
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	139	12	151

Error

0.1b

Counts

151 → 12

Alt Table

Status	Error	Program
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	16.4b	(.f64 (pow.f64 (.f64 2 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	16.1b	(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x (cbrt.f64 x)))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 x (cbrt.f64 x)))))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	17.4b	(.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (*.f64 x (cbrt.f64 x)))))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.2b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
▶	1.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	1.4b	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	16.9b	(.f64 (pow.f64 (.f64 2 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	35.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 2953 to 2031 computations (31.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
✓	0.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))
	0.5b	(pow.f64 (cbrt.f64 x) 2)
	0.6b	(cbrt.f64 x)

series177.0ms (3.9%)

Counts

2 → 24

Calls

2 calls:

118.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))

59.0ms

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

rewrite119.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
152×	`log1p-udef_binary64`
96×	`associate-r_binary64`
90×	`add-sqr-sqrt_binary64`

Counts

2 → 32

Calls

2 calls:

118.0ms

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

118.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	203	17
2	2091	17
3	4976	17

simplify144.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

874×	`fabs-mul_binary64`
827×	`cube-prod_binary64`
756×	`sqr-pow_binary64`
706×	`pow-sqr_binary64`
458×	`cube-mult_binary64`

Counts

56 → 36

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	236
1	32	236
2	64	236
3	157	236
4	502	236
5	654	236
6	980	236
7	990	236
8	1100	236
9	1240	236
10	1427	236
11	1609	236
12	1859	236
13	2202	236
14	2775	236
15	3509	236
16	3852	236
17	4234	236
18	4556	236
19	4718	236
20	4792	236
21	5115	236

prune153.0ms (3.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	153	13	166

Error

0.1b

Counts

166 → 13

Alt Table

Status	Error	Program
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	1.7b	(.f64 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2))) 3) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	16.4b	(.f64 (pow.f64 (.f64 2 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	1.8b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)))
✓	1.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	17.4b	(.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (*.f64 x (cbrt.f64 x)))))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.2b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.4b	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	16.9b	(.f64 (pow.f64 (.f64 2 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	35.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 3526 to 2460 computations (30.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
✓	0.5b	(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2))
	0.5b	(pow.f64 (cbrt.f64 x) 2)
	0.6b	(cbrt.f64 x)

series63.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

46.0ms	(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2))
16.0ms	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))

rewrite73.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
357×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

2 → 38

Calls

2 calls:

73.0ms	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
73.0ms	(*.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	161	17
2	1670	17
3	4963	17
4	4932	17

simplify141.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

874×	`fabs-mul_binary64`
827×	`cube-prod_binary64`
756×	`sqr-pow_binary64`
706×	`pow-sqr_binary64`
458×	`cube-mult_binary64`

Counts

62 → 43

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	236
1	32	236
2	64	236
3	157	236
4	502	236
5	654	236
6	980	236
7	990	236
8	1100	236
9	1240	236
10	1427	236
11	1609	236
12	1859	236
13	2202	236
14	2775	236
15	3509	236
16	3852	236
17	4234	236
18	4556	236
19	4718	236
20	4792	236
21	5115	236

prune95.0ms (2.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	161	15	176

Error

0.1b

Counts

176 → 15

Alt Table

Status	Error	Program
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	1.7b	(.f64 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2))) 3) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	16.4b	(.f64 (pow.f64 (.f64 2 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (cbrt.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))) 4)) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.2b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	1.8b	(.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)))
	1.8b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2)))
✓	1.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	1.8b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x))) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	15.9b	(.f64 (.f64 (sqrt.f64 (*.f64 x (cbrt.f64 x))) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
✓	35.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	17.4b	(.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (*.f64 x (cbrt.f64 x)))))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	2.2b	(.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 2) (sqrt.f64 2)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 2867 to 2020 computations (29.5% saved)

regimes442.0ms (9.7%)

Accuracy

Total 1.3b remaining (94%)

Threshold costs 0b (0%)

Counts

97 → 1

Compiler

Compiled 5846 to 4598 computations (21.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	13	22
2	13	22

end233.0ms (5.1%)

Compiler: Compiled 259 to 203 computations (21.6% saved)

Details

analyze6.0ms (0.1%)

sample1.0s (22.7%)

simplify143.0ms (3.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite85.0ms (1.9%)

simplify12.0ms (0.3%)

prune123.0ms (2.7%)

localize97.0ms (2.1%)

series1.2s (25.3%)

rewrite52.0ms (1.2%)

simplify79.0ms (1.7%)

prune101.0ms (2.2%)

localize9.0ms (0.2%)

series177.0ms (3.9%)

rewrite119.0ms (2.6%)

simplify144.0ms (3.2%)

prune153.0ms (3.4%)

localize7.0ms (0.2%)

series63.0ms (1.4%)

rewrite73.0ms (1.6%)

simplify141.0ms (3.1%)

prune95.0ms (2.1%)

regimes442.0ms (9.7%)

simplify2.0ms (0%)

end233.0ms (5.1%)

Profiling