Details

analyze6.0ms (0.3%)

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)

sample994.0ms (54.5%)

Results

917.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify52.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
454×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	105	9
5	327	9
6	1242	9
7	2119	9
8	2283	9
9	2467	9
10	2675	9
11	2968	9
12	3359	9
13	3837	9
14	4400	9

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0.1%)

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

31.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	30.4b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series5.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

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

rewrite34.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`log1p-expm1-u_binary64`
450×	`expm1-log1p-u_binary64`
393×	`unpow-prod-down_binary64`
251×	`log-prod_binary64`
134×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	123	13
2	1337	13

Stop Event

1×	node limit

Counts

2 → 72

Calls

2 calls:

33.0ms	(*.f64 2 (pow.f64 x 2))
33.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify11.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

84 → 74

prune38.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Error

0.1b

Counts

75 → 7

Alt Table

Status	Error	Program
✓	31.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	32.0b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	32.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (.f64 (cbrt.f64 (*.f64 x x)) 2) 1/2))
	35.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
▶	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 875 to 674 computations (23% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite32.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
303×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`
124×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1479	6

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

31.0ms

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

simplify11.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

35 → 25

prune14.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	25	7	32

Error

0.1b

Counts

32 → 7

Alt Table

Status	Error	Program
✓	31.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	32.0b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	32.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (.f64 (cbrt.f64 (*.f64 x x)) 2) 1/2))
	35.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 310 to 258 computations (16.8% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
✓	31.4b	(cbrt.f64 (.f64 2 (.f64 x x)))

series23.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

12.0ms	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
8.0ms	(cbrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite40.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
321×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	166	22
2	1810	22

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

39.0ms	(.f64 2 (.f64 x x))
39.0ms	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
39.0ms	(cbrt.f64 (.f64 2 (.f64 x x)))

simplify61.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
271×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	84
1	11	84
2	22	84
3	44	84
4	105	84
5	316	84
6	1215	84
7	2089	84
8	2253	84
9	2437	84
10	2645	84
11	2937	84
12	3328	84
13	3806	84
14	4369	84

Stop Event

1×	node limit

Counts

82 → 72

prune40.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	69	10	79

Error

0.1b

Counts

79 → 10

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
✓	31.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	1.5b	(pow.f64 (*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) 3/2)
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	35.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	1.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
▶	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
	32.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (.f64 (cbrt.f64 (*.f64 x x)) 2) 1/2))
	35.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 967 to 758 computations (21.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))
✓	0.4b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
✓	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 2 x))

series74.0ms (4%)

Counts

4 → 0

Calls

4 calls:

30.0ms	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
21.0ms	(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))
13.0ms	(cbrt.f64 (*.f64 2 x))
9.0ms	(cbrt.f64 x)

rewrite46.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
83×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	187	27
2	2085	27

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

45.0ms	(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))
45.0ms	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
45.0ms	(cbrt.f64 x)
45.0ms	(cbrt.f64 (*.f64 2 x))

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

79 → 79

prune39.0ms (2.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	76	13	89

Error

0.0b

Counts

89 → 13

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 2) 3/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2))
✓	31.7b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	1.9b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 x))) 3) (cbrt.f64 x)) 3/2)
✓	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	1.5b	(pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 2)) (cbrt.f64 x)) 3/2)
	35.1b	(*.f64 (sqrt.f64 2) x)
	35.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	1.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
	36.0b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
	32.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (.f64 (cbrt.f64 (*.f64 x x)) 2) 1/2))
	2.0b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)) 3/2)
	1.9b	(pow.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 2 x))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 x))) 2)) (cbrt.f64 x)) 3/2)

Compiler

Compiled 1085 to 777 computations (28.4% saved)

regimes118.0ms (6.5%)

Accuracy

Total 1.2b remaining (93.4%)

Threshold costs 0b (0%)

Counts

35 → 1

Compiler

Compiled 1498 to 1242 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end152.0ms (8.4%)

Compiler: Compiled 162 to 134 computations (17.3% saved)

Details

analyze6.0ms (0.3%)

sample994.0ms (54.5%)

simplify52.0ms (2.8%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite34.0ms (1.9%)

simplify11.0ms (0.6%)

prune38.0ms (2.1%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite32.0ms (1.7%)

simplify11.0ms (0.6%)

prune14.0ms (0.7%)

localize7.0ms (0.4%)

series23.0ms (1.2%)

rewrite40.0ms (2.2%)

simplify61.0ms (3.3%)

prune40.0ms (2.2%)

localize8.0ms (0.4%)

series74.0ms (4%)

rewrite46.0ms (2.5%)

simplify6.0ms (0.3%)

prune39.0ms (2.1%)

regimes118.0ms (6.5%)

simplify2.0ms (0.1%)

end152.0ms (8.4%)

Profiling