Details

analyze72.0ms

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample12.0ms

Algorithm

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	3×	body	128	nan

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune1.0ms

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: 24.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) y)
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x x) y)
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

series83.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+.f64 (*.f64 x x) y)
54.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

simplify94.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4922	392
1	4922	392

prune20.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0.0b

Counts

33 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y))))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
54×	`add-sqr-sqrt_binary64`
38×	`sqrt-pow1_binary64`
32×	`sqrt-div_binary64`
31×	`pow1_binary64`
20×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

series263.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
57.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y))))
48.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
54.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

simplify68.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6029	2102

prune65.0ms

Filtered

79 candidates to 146 candidates (-84.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	6	150

Merged error: 0b

Counts

150 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64`
6×	`cbrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 61

Calls

4 calls:

5.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

series246.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
45.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
54.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
46.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

simplify68.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5044	1017

prune62.0ms

Filtered

61 candidates to 73 candidates (-19.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	73	6	79

Merged error: 0b

Counts

79 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
0.9b	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))) 4)
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))
23.2b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64` `cbrt-prod_binary64`
8×	`pow1_binary64`
6×	`sqrt-div_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `pow1/2_binary64` `flip-+_binary64`
2×	`cbrt-div_binary64` `pow1/3_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 76

Calls

4 calls:

5.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
8.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))) 4)
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

series366.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
163.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))) 4)
44.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
49.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

simplify89.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4895	1299
1	4895	1299

prune60.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	88	6	94

Merged error: 0b

Counts

94 → 6

regimes164.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.8b

bsearch27.0ms

Steps

Iters	Range		Point
8	4.4068412259979335e+80	4.951850941540697e+83	4.856068192842642e+83
9	-1.0550324997174567e+155	-3.327707734429613e+145	-1.3210370458038785e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	41
1	35	41

end0.0ms

sample318.0ms

Algorithm

intervals

Results

189.0ms	8000×	body	128	valid
3.0ms	152×	body	128	nan

Details

analyze72.0ms

sample12.0ms

simplify8.0ms

prune1.0ms

localize4.0ms

rewrite10.0ms

series83.0ms

simplify94.0ms

prune20.0ms

localize7.0ms

rewrite46.0ms

series263.0ms

simplify68.0ms

prune65.0ms

localize12.0ms

rewrite26.0ms

series246.0ms

simplify68.0ms

prune62.0ms

localize10.0ms

rewrite31.0ms

series366.0ms

simplify89.0ms

prune60.0ms

regimes164.0ms

bsearch27.0ms

simplify3.0ms

end0.0ms

sample318.0ms

Profiling