Details

analyze4.0ms (0.2%)

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)

sample872.0ms (42.7%)

Alt Table

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

Results

843.0ms

8256×

body

128

valid

Compiler

Compiled 37 to 27 computations (27% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite87.0ms (4.3%)

Algorithm

2×	batch-egg-rewrite

Rules

884×	`log1p-udef_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
449×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`

Counts

1 → 53

Calls

1 calls:

86.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1257	6
3	4991	6
4	6461	6
0	0	0
1	0	0

prune33.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Error

0.1b

Counts

66 → 6

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
▶	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	39.9b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	40.1b	(.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 749 to 588 computations (21.5% 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 (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite74.0ms (3.6%)

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:

73.0ms

(*.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

prune27.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	48	7	55

Error

0.1b

Counts

55 → 7

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
▶	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	39.9b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	40.1b	(.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 551 to 459 computations (16.7% 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)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

series493.0ms (24.2%)

Counts

3 → 36

Calls

3 calls:

264.0ms	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
226.0ms	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
3.0ms	(*.f64 x (sqrt.f64 2))

rewrite53.0ms (2.6%)

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

prune88.0ms (4.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	168	9	177

Error

0.0b

Counts

177 → 9

Alt Table

Status	Error	Program
	1.4b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
✓	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
▶	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))))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	39.9b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))

Compiler

Compiled 2437 to 2096 computations (14% 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))

series39.0ms (1.9%)

Counts

2 → 12

Calls

2 calls:

36.0ms	(*.f64 (pow.f64 2 1/4) x)
4.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite47.0ms (2.3%)

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:

46.0ms	(*.f64 (pow.f64 2 1/4) x)
46.0ms	(.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

prune28.0ms (1.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	46	9	55

Error

0.0b

Counts

55 → 9

Alt Table

Status	Error	Program
	1.4b	(fabs.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 3/2) (pow.f64 (cbrt.f64 2) 3/2)))
✓	1.4b	(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.9b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
✓	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))))
✓	0.5b	(fabs.f64 (*.f64 x (sqrt.f64 2)))
	39.9b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))

Compiler

Compiled 537 to 464 computations (13.6% saved)

regimes63.0ms (3.1%)

Accuracy

Total 0.4b remaining (95%)

Threshold costs 0.4b (95%)

Counts

17 → 1

Compiler

Compiled 738 to 612 computations (17.1% 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 (5.2%)

Compiler: Compiled 109 to 91 computations (16.5% saved)

Details

analyze4.0ms (0.2%)

sample872.0ms (42.7%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite87.0ms (4.3%)

prune33.0ms (1.6%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite74.0ms (3.6%)

prune27.0ms (1.3%)

localize6.0ms (0.3%)

series493.0ms (24.2%)

rewrite53.0ms (2.6%)

prune88.0ms (4.3%)

localize5.0ms (0.3%)

series39.0ms (1.9%)

rewrite47.0ms (2.3%)

prune28.0ms (1.4%)

regimes63.0ms (3.1%)

simplify2.0ms (0.1%)

end107.0ms (5.2%)

Profiling