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)

sample1.0s (45.8%)

Results

929.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify53.0ms (2.4%)

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

29.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.2b	(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))
✓	28.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

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

rewrite55.0ms (2.5%)

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 (0.5%)

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

prune52.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	9	75

Error

0.2b

Counts

75 → 9

Alt Table

Status	Error	Program
	29.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (.f64 (cbrt.f64 (*.f64 x x)) 2) 1/2))
	31.7b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
▶	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	29.6b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
	31.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	31.8b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
✓	29.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	41.1b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 3) 1/2) (sqrt.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2)))))

Compiler

Compiled 931 to 724 computations (22.2% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (sqrt.f64 2))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite38.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
335×	`pow1_binary64`
247×	`unpow-prod-down_binary64`
204×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1080	6

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

37.0ms

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

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

45 → 34

prune23.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	34	9	43

Error

0.1b

Counts

43 → 9

Alt Table

Status	Error	Program
	31.8b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
	43.6b	(fabs.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3)))
✓	29.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
▶	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
	31.7b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	29.6b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
	41.1b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 3) 1/2) (sqrt.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2)))))

Compiler

Compiled 496 to 418 computations (15.7% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

series361.0ms (16.5%)

Counts

2 → 24

Calls

2 calls:

193.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
168.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite44.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
492×	`unpow-prod-down_binary64`
278×	`log-prod_binary64`
155×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	161	14
2	1561	14

Stop Event

1×	node limit

Counts

2 → 110

Calls

2 calls:

42.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
42.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

simplify29.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-def_binary64`
406×	`unswap-sqr_binary64`
271×	`associate-+l+_binary64`
225×	`associate-+r+_binary64`
155×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	448
1	74	448
2	163	424
3	443	220
4	1554	220

Stop Event

1×	node limit

Counts

134 → 119

prune89.0ms (4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	5	1	6
Picked	1	0	1
Done	0	2	2
Total	154	8	162

Error

0.0b

Counts

162 → 8

Alt Table

Status	Error	Program
	29.6b	(fabs.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x))))))
	31.7b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
✓	29.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	1.4b	(fabs.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
▶	0.5b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	1.5b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
	32.1b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 3/2) (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3/2)))

Compiler

Compiled 2280 to 1878 computations (17.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

series32.0ms (1.5%)

Counts

2 → 12

Calls

2 calls:

29.0ms	(*.f64 (pow.f64 2 1/4) x)
3.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite35.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
311×	`log-prod_binary64`
168×	`pow2_binary64`
119×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1623	13

Stop Event

1×	node limit

Counts

2 → 42

Calls

2 calls:

35.0ms	(*.f64 (pow.f64 2 1/4) x)
35.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

54 → 43

prune25.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Error

0.0b

Counts

51 → 8

Alt Table

Status	Error	Program
	29.6b	(fabs.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x))))))
	31.7b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
✓	29.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	1.4b	(fabs.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
✓	0.5b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	1.5b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
	32.1b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 3/2) (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3/2)))

Compiler

Compiled 610 to 539 computations (11.6% saved)

regimes115.0ms (5.3%)

Accuracy

Total 0.4b remaining (94.5%)

Threshold costs 0.4b (94.5%)

Counts

32 → 1

Compiler

Compiled 1450 to 1226 computations (15.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fabs-mul_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	11	8

Stop Event

1×

saturated

end172.0ms (7.9%)

Compiler: Compiled 103 to 87 computations (15.5% saved)

Details

analyze6.0ms (0.3%)

sample1.0s (45.8%)

simplify53.0ms (2.4%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite55.0ms (2.5%)

simplify11.0ms (0.5%)

prune52.0ms (2.4%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite38.0ms (1.7%)

simplify7.0ms (0.3%)

prune23.0ms (1%)

localize6.0ms (0.3%)

series361.0ms (16.5%)

rewrite44.0ms (2%)

simplify29.0ms (1.3%)

prune89.0ms (4.1%)

localize5.0ms (0.2%)

series32.0ms (1.5%)

rewrite35.0ms (1.6%)

simplify8.0ms (0.4%)

prune25.0ms (1.1%)

regimes115.0ms (5.3%)

simplify2.0ms (0.1%)

end172.0ms (7.9%)

Profiling