Details

analyze462.0ms

Algorithm

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

sample18.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 42.0b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sum-log_binary64`
3×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`+-commutative_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

3 → 39

Calls

3 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))
25.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify70.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4933	605
1	4933	605

prune30.0ms

Filtered

36 candidates to 48 candidates (-33.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 18.2b

Counts

49 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.2b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64` `cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
8×	`cbrt-div_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

7.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
11.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
67.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
32.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
32.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5092	1826

prune49.0ms

Filtered

74 candidates to 86 candidates (-16.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	85	6	91

Merged error: 18.2b

Counts

91 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))))
0.5b	(cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
39.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`pow1/3_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))))
7.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))))
32.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
22.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5075	1521

prune43.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	74	6	80

Merged error: 18.2b

Counts

80 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.2b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
36.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4938	1128
1	4938	1128

prune40.0ms

Filtered

60 candidates to 64 candidates (-6.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	64	6	70

Merged error: 18.2b

Counts

70 → 6

regimes532.0ms

Accuracy

60.1% (7.8b remaining)

Error of 25.7b against oracle of 17.9b and baseline of 37.4b

bsearch29.0ms

Steps

Iters	Range		Point
7	2.8463148811402064e+47	7.155992921050486e+48	7.049438944300407e+48
11	-3.859164645758055e+111	-8.750619123260384e+88	-3.814994395619719e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample506.0ms

Algorithm

intervals

Results

331.0ms

8000×

body

valid

Details

analyze462.0ms

sample18.0ms

simplify6.0ms

prune3.0ms

localize8.0ms

rewrite18.0ms

series42.0ms

simplify70.0ms

prune30.0ms

localize13.0ms

rewrite33.0ms

series159.0ms

simplify57.0ms

prune49.0ms

localize15.0ms

rewrite25.0ms

series117.0ms

simplify38.0ms

prune43.0ms

localize17.0ms

rewrite28.0ms

series134.0ms

simplify57.0ms

prune40.0ms

regimes532.0ms

bsearch29.0ms

simplify2.0ms

end0.0ms

sample506.0ms

Profiling