Details

analyze4.0ms (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
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.4%	13
66.6%	0%	33.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample707.0ms (47.2%)

Results

689.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess47.0ms (3.1%)

Algorithm

2×	egg-herbie

Rules

783×	`fma-neg_binary64`
701×	`fma-def_binary64`
349×	`associate-l_binary64`
313×	`distribute-rgt-neg-in_binary64`
258×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	45	11
3	118	11
4	232	11
5	311	11
6	465	11
7	796	11
8	1677	11
9	2538	11
10	3445	11
11	4626	11
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 7 computations (30% saved)

simplify36.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
701×	`fma-def_binary64`
349×	`associate-l_binary64`
313×	`distribute-rgt-neg-in_binary64`
258×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	45	11
3	118	11
4	232	11
5	311	11
6	465	11
7	796	11
8	1677	11
9	2538	11
10	3445	11
11	4626	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	0.2b	(.f64 (.f64 x x) (-.f64 3 (*.f64 x 2)))

Compiler

Compiled 56 to 38 computations (32.1% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x -2 3))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))

series5.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))	x	-inf
1.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))	x	inf
1.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))	x	0
1.0ms	(*.f64 x (fma.f64 x -2 3))	x	-inf
1.0ms	(*.f64 x (fma.f64 x -2 3))	x	inf

rewrite35.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
124×	`pow1/3_binary64`
123×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	143	19
2	1623	19

Stop Event

1×	node limit

Counts

2 → 48

simplify38.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
495×	`distribute-rgt-neg-in_binary64`
487×	`fma-neg_binary64`
428×	`distribute-lft-neg-in_binary64`
340×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	300
1	42	264
2	102	246
3	318	210
4	1031	210
5	2232	210
6	3763	210

Stop Event

1×	node limit

Counts

72 → 59

prune48.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	6	59
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	6	61

Error

0.0b

Counts

61 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	16.2b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
	9.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
	0.2b	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))

Compiler

Compiled 826 to 579 computations (29.9% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series6.0ms (0.4%)

Counts

2 → 3

Calls

6 calls:

1.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))	x	-inf
1.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))	x	inf
1.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))	x	0
1.0ms	(*.f64 3 (pow.f64 x 2))	x	0
1.0ms	(*.f64 3 (pow.f64 x 2))	x	-inf

rewrite50.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`
90×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	214	21
2	2532	21

Stop Event

1×	node limit

Counts

2 → 63

simplify66.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

674×	`sqr-pow_binary64`
536×	`unswap-sqr_binary64`
419×	`associate-l_binary64`
387×	`*-commutative_binary64`
279×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	23	21
2	52	21
3	114	21
4	311	21
5	1272	21
6	2442	21
7	2608	21
8	2858	21
9	3145	21
10	3524	21
11	4023	21
12	4628	21

Stop Event

1×	node limit

Counts

66 → 66

prune60.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Error

0.0b

Counts

72 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))
▶	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	26.1b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 6) 27)) (.f64 2 (pow.f64 x 3)))
	9.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
	0.2b	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))

Compiler

Compiled 1481 to 1093 computations (26.2% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))	x	-inf
1.0ms	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))	x	0
1.0ms	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))	x	inf

rewrite36.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`log1p-expm1-u_binary64`
629×	`expm1-log1p-u_binary64`
316×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	165	14
2	1793	14

Stop Event

1×	node limit

Counts

1 → 29

simplify33.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
501×	`distribute-rgt-neg-in_binary64`
431×	`distribute-lft-neg-in_binary64`
385×	`fma-neg_binary64`
336×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	165
1	31	147
2	83	138
3	283	120
4	876	120
5	1948	120
6	3341	120

Stop Event

1×	node limit

Counts

41 → 35

prune31.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	35	6	41

Error

0.0b

Counts

41 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	26.1b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 6) 27)) (.f64 2 (pow.f64 x 3)))
	9.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
▶	0.2b	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))

Compiler

Compiled 665 to 466 computations (29.9% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (.f64 x -2) (.f64 x 3))
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))

series6.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))	x	-inf
1.0ms	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))	x	0
1.0ms	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))	x	inf
1.0ms	(fma.f64 x (.f64 x -2) (.f64 x 3))	x	inf
1.0ms	(fma.f64 x (.f64 x -2) (.f64 x 3))	x	-inf

rewrite42.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`log1p-expm1-u_binary64`
679×	`expm1-log1p-u_binary64`
147×	`prod-diff_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	162	23
2	1846	23

Stop Event

1×	node limit

Counts

2 → 41

simplify33.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
495×	`distribute-rgt-neg-in_binary64`
487×	`fma-neg_binary64`
428×	`distribute-lft-neg-in_binary64`
340×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	300
1	42	264
2	102	246
3	318	210
4	1031	210
5	2232	210
6	3763	210

Stop Event

1×	node limit

Counts

65 → 52

prune35.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	52	6	58

Error

0.0b

Counts

58 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))
✓	0.1b	(fma.f64 3 (.f64 x x) (.f64 (pow.f64 x 3) -2))
	26.1b	(-.f64 (cbrt.f64 (.f64 (pow.f64 x 6) 27)) (.f64 2 (pow.f64 x 3)))
	9.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
✓	0.2b	(.f64 x (fma.f64 x (.f64 x -2) (*.f64 x 3)))

Compiler

Compiled 710 to 515 computations (27.5% saved)

regimes52.0ms (3.5%)

Accuracy

Total 0.1b remaining (86.2%)

Threshold costs 0.1b (86.2%)

Counts

30 → 1

Compiler

Compiled 626 to 460 computations (26.5% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14

Stop Event

1×

saturated

end98.0ms (6.5%)

Stop Event

1×

fuel

Compiler

Compiled 91 to 68 computations (25.3% saved)

Details

analyze4.0ms (0.3%)

sample707.0ms (47.2%)

preprocess47.0ms (3.1%)

simplify36.0ms (2.4%)

prune3.0ms (0.2%)

localize6.0ms (0.4%)

series5.0ms (0.4%)

rewrite35.0ms (2.3%)

simplify38.0ms (2.5%)

prune48.0ms (3.2%)

localize6.0ms (0.4%)

series6.0ms (0.4%)

rewrite50.0ms (3.3%)

simplify66.0ms (4.4%)

prune60.0ms (4%)

localize5.0ms (0.4%)

series3.0ms (0.2%)

rewrite36.0ms (2.4%)

simplify33.0ms (2.2%)

prune31.0ms (2%)

localize5.0ms (0.4%)

series6.0ms (0.4%)

rewrite42.0ms (2.8%)

simplify33.0ms (2.2%)

prune35.0ms (2.3%)

regimes52.0ms (3.5%)

simplify2.0ms (0.2%)

end98.0ms (6.5%)

Profiling