Details

analyze5.0ms (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 6 computations (25% saved)

sample694.0ms (34.9%)

Alt Table

Status	Error	Program
▶	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

665.0ms

8256×

body

128

valid

Compiler

Compiled 37 to 27 computations (27% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(sqrt.f64 (.f64 (.f64 2 x) x))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite96.0ms (4.8%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`log1p-expm1-u_binary64`
488×	`expm1-log1p-u_binary64`
483×	`unpow-prod-down_binary64`
289×	`log-prod_binary64`
142×	`pow2_binary64`

Counts

1 → 55

Calls

1 calls:

95.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1317	6
3	4961	6
0	0	0
1	0	0

prune37.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	7	68

Error

0.1b

Counts

68 → 7

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	40.0b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	12.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 833 to 552 computations (33.7% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite80.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

711×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
336×	`pow1_binary64`
245×	`unpow-prod-down_binary64`

Counts

1 → 37

Calls

1 calls:

79.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	0	0
1	0	0

prune29.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	48	8	56

Error

0.1b

Counts

56 → 8

Alt Table

Status	Error	Program
▶	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	40.0b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x x))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x x)) x) 1/2))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	12.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 585 to 465 computations (20.5% 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)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

series543.0ms (27.4%)

Counts

3 → 36

Calls

3 calls:

321.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
219.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
3.0ms	(*.f64 x (sqrt.f64 2))

rewrite53.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 134

Calls

3 calls:

50.0ms	(*.f64 x (sqrt.f64 2))
50.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
50.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	147	20
2	1449	20
3	5269	20
0	0	0
1	0	0

prune94.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	169	9	178

Error

0.0b

Counts

178 → 9

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	1.4b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	0.4b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
	1.3b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2))))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	12.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 2466 to 2108 computations (14.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

series32.0ms (1.6%)

Counts

2 → 12

Calls

2 calls:

27.0ms	(*.f64 (pow.f64 2 1/4) x)
5.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite60.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
392×	`unpow-prod-down_binary64`
310×	`log-prod_binary64`
168×	`pow2_binary64`

Counts

2 → 34

Calls

2 calls:

59.0ms	(*.f64 (pow.f64 2 1/4) x)
59.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1523	13
3	5396	13
0	0	0
1	0	0

prune27.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	46	9	55

Error

0.0b

Counts

55 → 9

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	1.4b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	0.4b	(fabs.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
	1.3b	(fabs.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2))))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	12.5b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	12.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))

Compiler

Compiled 547 to 466 computations (14.8% saved)

regimes101.0ms (5.1%)

Accuracy

Total 0.4b remaining (94.9%)

Threshold costs 0.4b (94.9%)

Counts

35 → 1

Compiler

Compiled 1206 to 983 computations (18.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	13	15
2	17	15
3	17	15

end107.0ms (5.4%)

Compiler: Compiled 119 to 93 computations (21.8% saved)

Details

analyze5.0ms (0.3%)

sample694.0ms (34.9%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite96.0ms (4.8%)

prune37.0ms (1.8%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite80.0ms (4%)

prune29.0ms (1.5%)

localize6.0ms (0.3%)

series543.0ms (27.4%)

rewrite53.0ms (2.7%)

prune94.0ms (4.8%)

localize5.0ms (0.3%)

series32.0ms (1.6%)

rewrite60.0ms (3%)

prune27.0ms (1.3%)

regimes101.0ms (5.1%)

simplify2.0ms (0.1%)

end107.0ms (5.4%)

Profiling