Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample34.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	58×	body	80	nan
1.0ms	25×	body	80	invalid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	807	21
1	807	21

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: 25.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
5.3b	(.f64 (.f64 x y) z)
9.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
28.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
5.0ms	(.f64 (.f64 x y) z)
10.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(-.f64 (.f64 z z) (.f64 t a))
29.0ms	(.f64 (.f64 x y) z)
127.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
50.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify69.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5333	1466

prune78.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 3.4b

Counts

88 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
2.3b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
28.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-r_binary64` `sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
31.0ms	(-.f64 (.f64 z z) (.f64 t a))
122.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
54.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify95.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5263	2515

prune72.0ms

Filtered

80 candidates to 123 candidates (-53.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 3.2b

Counts

132 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
1.1b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
28.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

22.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
20.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
30.0ms	(-.f64 (.f64 z z) (.f64 t a))
125.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
73.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5005	1891

prune67.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	102	9	111

Merged error: 3.2b

Counts

111 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(.f64 x (.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
1.8b	(.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
28.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
28.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log_binary64`
62×	`add-cbrt-cube_binary64`
61×	`associate-r_binary64`
60×	`sqrt-prod_binary64`
54×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
41×	`cbrt-unprod_binary64` `prod-exp_binary64`
27×	`cbrt-prod_binary64`
20×	`pow1_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`pow-prod-down_binary64` `associate-*r/_binary64`
8×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`div-inv_binary64`

Counts

4 → 156

Calls

4 calls:

27.0ms	(.f64 x (.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
33.0ms	(.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(.f64 x (.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
93.0ms	(.f64 (.f64 y (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
59.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
54.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify132.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4972	4767
1	4972	4767

prune104.0ms

Filtered

94 candidates to 168 candidates (-78.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	168	9	177

Merged error: 3.2b

Counts

177 → 9

regimes254.0ms

Accuracy

84.3% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 22.8b

bsearch49.0ms

Steps

Iters	Range		Point
7	3.816448003902394e+113	1.5293304887317915e+115	3.68902160281237e+114
6	-2.4850190238386238e+104	-2.5994497110014132e+103	-2.921133149674579e+103

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	79	73
1	79	73

end0.0ms

sample931.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
106.0ms	2202×	body	80	nan
43.0ms	861×	body	80	invalid

Details

analyze1.1s

sample34.0ms

simplify61.0ms

prune1.0ms

localize10.0ms

rewrite25.0ms

series236.0ms

simplify69.0ms

prune78.0ms

localize10.0ms

rewrite34.0ms

series249.0ms

simplify95.0ms

prune72.0ms

localize21.0ms

rewrite64.0ms

series300.0ms

simplify66.0ms

prune67.0ms

localize17.0ms

rewrite77.0ms

series347.0ms

simplify132.0ms

prune104.0ms

regimes254.0ms

bsearch49.0ms

simplify5.0ms

end0.0ms

sample931.0ms

Profiling