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
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 (44.6%)

Results

646.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify40.0ms (2.5%)

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)

localize4.0ms (0.3%)

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 (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
2.0ms	(*.f64 x (fma.f64 x -2 3))

rewrite35.0ms (2.2%)

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

Calls

2 calls:

34.0ms	(*.f64 x (fma.f64 x -2 3))
34.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))

simplify33.0ms (2.1%)

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

prune44.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Error

0.0b

Counts

61 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	7.1b	(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 (.f64 x x) (-.f64 3 (*.f64 x 2)))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	16.4b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))

Compiler

Compiled 833 to 585 computations (29.8% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series8.0ms (0.5%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
3.0ms	(*.f64 2 (pow.f64 x 3))
2.0ms	(*.f64 3 (pow.f64 x 2))

rewrite50.0ms (3.1%)

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	30
1	214	28
2	2532	28

Stop Event

1×	node limit

Counts

3 → 76

Calls

3 calls:

48.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
48.0ms	(*.f64 2 (pow.f64 x 3))
48.0ms	(*.f64 3 (pow.f64 x 2))

simplify64.0ms (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

79 → 79

prune89.0ms (5.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Error

Counts

86 → 9

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	7.1b	(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 (.f64 x x) (-.f64 3 (*.f64 x 2)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	44.5b	(.f64 (-.f64 (.f64 (pow.f64 x 4) 9) (.f64 (pow.f64 x 6) 4)) (/.f64 1 (fma.f64 3 (.f64 x x) (*.f64 2 (pow.f64 x 3)))))
	15.7b	(-.f64 (sqrt.f64 (.f64 (pow.f64 x 4) 9)) (.f64 2 (pow.f64 x 3)))
	16.4b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
	0.9b	(.f64 x (pow.f64 (cbrt.f64 (.f64 x (fma.f64 x -2 3))) 3))

Compiler

Compiled 1729 to 1302 computations (24.7% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 x x) (-.f64 3 (*.f64 x 2)))

rewrite43.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`log1p-expm1-u_binary64`
799×	`expm1-log1p-u_binary64`
121×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	176	13
2	2173	13

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

42.0ms

(*.f64 (*.f64 x x) (-.f64 3 (*.f64 x 2)))

simplify30.0ms (1.9%)

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

33 → 27

prune29.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	29	7	36

Error

Counts

36 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	7.1b	(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 (.f64 x x) (-.f64 3 (*.f64 x 2)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	5.0b	(/.f64 (.f64 (-.f64 9 (.f64 (.f64 x x) 4)) (.f64 x x)) (+.f64 3 (*.f64 x 2)))
	7.7b	(/.f64 (.f64 (-.f64 27 (.f64 8 (pow.f64 x 3))) (.f64 x x)) (+.f64 9 (+.f64 (.f64 (.f64 x x) 4) (.f64 6 x))))

Compiler

Compiled 486 to 333 computations (31.5% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 x -2 3) (.f64 x x))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
✓	22.9b	(cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x)))

series56.0ms (3.5%)

Counts

3 → 28

Calls

3 calls:

42.0ms	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
11.0ms	(cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x)))
3.0ms	(.f64 (fma.f64 x -2 3) (.f64 x x))

rewrite44.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

685×	`log1p-expm1-u_binary64`
685×	`expm1-log1p-u_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`
120×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	184	35
2	1944	35

Stop Event

1×	node limit

Counts

3 → 88

Calls

3 calls:

43.0ms	(.f64 (fma.f64 x -2 3) (.f64 x x))
43.0ms	(pow.f64 (cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x))) 3)
43.0ms	(cbrt.f64 (.f64 (fma.f64 x -2 3) (.f64 x x)))

simplify40.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-def_binary64`
327×	`times-frac_binary64`
311×	`sub-neg_binary64`
237×	`associate-l_binary64`
230×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	711
1	326	663
2	1013	640
3	3972	637

Stop Event

1×	node limit

Counts

116 → 105

prune89.0ms (5.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	105	7	112

Error

Counts

112 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	7.1b	(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 (.f64 x x) (-.f64 3 (*.f64 x 2)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	5.0b	(/.f64 (.f64 (-.f64 9 (.f64 (.f64 x x) 4)) (.f64 x x)) (+.f64 3 (*.f64 x 2)))
	7.7b	(/.f64 (.f64 (-.f64 27 (.f64 8 (pow.f64 x 3))) (.f64 x x)) (+.f64 9 (+.f64 (.f64 (.f64 x x) 4) (.f64 6 x))))

Compiler

Compiled 2001 to 1529 computations (23.6% saved)

regimes57.0ms (3.6%)

Accuracy

Total 0.1b remaining (93.6%)

Threshold costs 0.1b (93.6%)

Counts

36 → 1

Compiler

Compiled 884 to 666 computations (24.7% saved)

simplify2.0ms (0.1%)

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

end91.0ms (5.8%)

Compiler: Compiled 117 to 85 computations (27.4% saved)

Details

analyze4.0ms (0.2%)

sample707.0ms (44.6%)

simplify40.0ms (2.5%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series5.0ms (0.3%)

rewrite35.0ms (2.2%)

simplify33.0ms (2.1%)

prune44.0ms (2.8%)

localize6.0ms (0.4%)

series8.0ms (0.5%)

rewrite50.0ms (3.1%)

simplify64.0ms (4%)

prune89.0ms (5.6%)

localize4.0ms (0.3%)

series3.0ms (0.2%)

rewrite43.0ms (2.7%)

simplify30.0ms (1.9%)

prune29.0ms (1.8%)

localize7.0ms (0.4%)

series56.0ms (3.5%)

rewrite44.0ms (2.8%)

simplify40.0ms (2.5%)

prune89.0ms (5.6%)

regimes57.0ms (3.6%)

simplify2.0ms (0.1%)

end91.0ms (5.8%)

Profiling