Details

analyze277.0ms (5.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (25.9%)

Results

1.0s	8256×	body	128	valid
154.0ms	1472×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
10×	`fma-def_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	35	10
3	41	10
4	39	10

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 46 to 33 computations (28.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	0.3b	(*.f64 y (sqrt.f64 z))

series23.0ms (0.5%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
11.0ms	(*.f64 y (sqrt.f64 z))

rewrite50.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

50× egg-rr

Counts

2 → 50

Calls

2 calls:

48.0ms	((.f64 y (sqrt.f64 z)) (+.f64 x (.f64 y (sqrt.f64 z))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	147	13
2	1850	13
3	5937	13
0	0	0
1	0	0

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

66 → 53

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	85
1	10	85
2	11	85
3	11	85

prune40.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	47	6	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Error

0.1b

Counts

54 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	29.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
	45.0b	(.f64 (/.f64 1 2) (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))))
	38.2b	(.f64 (/.f64 1 2) (/.f64 1 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (*.f64 y y))))))
	24.4b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
	27.3b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 z (*.f64 y y)))))
▶	0.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))

Compiler

Compiled 1065 to 567 computations (46.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3))
	0.3b	(*.f64 y (sqrt.f64 z))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)
✓	3.4b	(cbrt.f64 (*.f64 y (sqrt.f64 z)))

series999.0ms (21.1%)

Counts

3 → 65

Calls

3 calls:

513.0ms	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)
463.0ms	(cbrt.f64 (*.f64 y (sqrt.f64 z)))
23.0ms	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3))

rewrite55.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

95× egg-rr

Counts

3 → 95

Calls

2 calls:

54.0ms	((cbrt.f64 (.f64 y (sqrt.f64 z))) (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3) (+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	195	21
2	2295	21
3	5357	21
0	0	0
1	0	0

simplify209.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1160×	`unswap-sqr_binary64`
1068×	`sqr-pow_binary64`
568×	`cube-prod_binary64`
429×	`*-commutative_binary64`
361×	`pow-sqr_binary64`

Counts

160 → 102

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	476
1	40	476
2	83	476
3	199	476
4	678	476
5	983	476
6	973	476
7	1075	476
8	1198	476
9	1327	476
10	1493	476
11	3310	476
12	2662	476
13	2961	476
14	3222	476
15	3534	476
16	3957	476
17	4009	476
18	4122	476
19	4319	476
20	4497	476
21	4698	476
22	5465	476

prune102.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Error

0.0b

Counts

122 → 9

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	29.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
	30.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	45.0b	(.f64 (/.f64 1 2) (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))))
	38.2b	(.f64 (/.f64 1 2) (/.f64 1 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (*.f64 y y))))))
	24.4b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
✓	0.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))

Compiler

Compiled 2198 to 1226 computations (44.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y)))
✓	0.2b	(*.f64 (pow.f64 z 1/4) y)
✓	0.3b	(.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y))

series265.0ms (5.6%)

Counts

3 → 61

Calls

3 calls:

240.0ms	(*.f64 (pow.f64 z 1/4) y)
12.0ms	(.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y))
12.0ms	(+.f64 x (.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y)))

rewrite100.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

3 → 82

Calls

2 calls:

98.0ms	((.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y)) (.f64 (pow.f64 z 1/4) y) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	197	20
2	2368	20
3	4681	20
4	4922	20
0	0	0
1	0	0

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-neg_binary64`
635×	`log-prod_binary64`
512×	`div-sub_binary64`
480×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`

Counts

143 → 88

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	388
1	35	388
2	64	388
3	148	388
4	311	388
5	876	388
6	1679	388
7	4319	388
8	4611	388
9	4884	388

prune78.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	89	8	97

Error

0.0b

Counts

97 → 8

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	29.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
▶	0.2b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/8) (*.f64 (pow.f64 z 1/4) y)) x))
	24.4b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
	23.8b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 z 1/4) y) 3)))))
✓	0.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))

Compiler

Compiled 1646 to 982 computations (40.3% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y)) x)
	0.2b	(*.f64 (pow.f64 z 1/4) y)
✓	0.4b	(.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y))

series622.0ms (13.1%)

Counts

2 → 60

Calls

2 calls:

342.0ms	(.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y))
280.0ms	(fma.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y)) x)

rewrite55.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

38× egg-rr

Counts

2 → 38

Calls

2 calls:

53.0ms	((.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y)) (fma.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/4) y)) x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	229	16
2	2363	16
3	5523	16
0	0	0
1	0	0

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-l_binary64`
599×	`associate-r_binary64`
442×	`fma-neg_binary64`
331×	`exp-sum_binary64`
317×	`fma-def_binary64`

Counts

98 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	28	599
1	67	587
2	128	559
3	338	535
4	1024	499
5	3644	415
6	4701	415
7	4900	415

prune63.0ms (1.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	3	1	4
Picked	0	1	1
Done	0	3	3
Total	67	6	73

Error

0.0b

Counts

73 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 z 1/8) (.f64 y (pow.f64 z 3/8)) x))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
✓	0.2b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 z 1/8) (.f64 (pow.f64 z 1/8) (*.f64 (pow.f64 z 1/4) y)) x))
	23.8b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 z 1/4) y) 3)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))

Compiler

Compiled 1213 to 819 computations (32.5% saved)

regimes234.0ms (4.9%)

Accuracy

Total 0.1b remaining (76.4%)

Threshold costs 0.1b (76.4%)

Counts

29 → 1

Compiler

Compiled 3459 to 2623 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	17	12
2	15	12

end109.0ms (2.3%)

Compiler: Compiled 128 to 99 computations (22.7% saved)

Details

analyze277.0ms (5.8%)

sample1.2s (25.9%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite50.0ms (1.1%)

simplify8.0ms (0.2%)

prune40.0ms (0.8%)

localize10.0ms (0.2%)

series999.0ms (21.1%)

rewrite55.0ms (1.2%)

simplify209.0ms (4.4%)

prune102.0ms (2.2%)

localize10.0ms (0.2%)

series265.0ms (5.6%)

rewrite100.0ms (2.1%)

simplify85.0ms (1.8%)

prune78.0ms (1.6%)

localize18.0ms (0.4%)

series622.0ms (13.1%)

rewrite55.0ms (1.2%)

simplify79.0ms (1.7%)

prune63.0ms (1.3%)

regimes234.0ms (4.9%)

simplify2.0ms (0%)

end109.0ms (2.3%)

Profiling