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

sample33.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
7.0ms	57×	body	80	nan
1.0ms	24×	body	80	invalid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
3.8b	(.f64 (.f64 x y) z)
8.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.4b	(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)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(-.f64 (.f64 z z) (.f64 t a))
28.0ms	(.f64 (.f64 x y) z)
122.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
51.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5333	1466

prune76.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 4.8b

Counts

88 → 8

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))
3.8b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms

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)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
27.0ms	(-.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)))

simplify99.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5263	2515

prune69.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	123	8	131

Merged error: 4.8b

Counts

131 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.2b	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
26.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
33×	`associate-r_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
16×	`cbrt-prod_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`associate-l_binary64`
6×	`cbrt-div_binary64` `pow1_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64`
2×	`pow1/3_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
19.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
339.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
93.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
88.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify99.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5061	4193

prune102.0ms

Filtered

94 candidates to 127 candidates (-35.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	126	9	135

Merged error: 4.8b

Counts

135 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b	(.f64 (.f64 x y) z)
8.7b	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`sqrt-div_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`associate-/r_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(.f64 (.f64 x y) z)
20.0ms	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
7.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (.f64 x y) z)
126.0ms	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
50.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
56.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5088	1702

prune56.0ms

Filtered

62 candidates to 93 candidates (-50.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	93	9	102

Merged error: 4.8b

Counts

102 → 9

regimes285.0ms

Accuracy

80.2% (3.8b remaining)

Error of 7.5b against oracle of 3.6b and baseline of 23.0b

bsearch55.0ms

Steps

Iters	Range		Point
9	8.886270356645134e+101	4.507142961649455e+108	3.600147263421176e+106
8	-8.340128957595745e+85	-2.1941850273914429e+83	-6.4410615914386545e+84

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	74	61
1	74	61

end0.0ms

sample863.0ms

Algorithm

intervals

Results

401.0ms	8000×	body	80	valid
99.0ms	2163×	body	80	nan
37.0ms	785×	body	80	invalid

Details

analyze1.1s

sample33.0ms

simplify60.0ms

prune1.0ms

localize10.0ms

rewrite25.0ms

series230.0ms

simplify71.0ms

prune76.0ms

localize10.0ms

rewrite33.0ms

series243.0ms

simplify99.0ms

prune69.0ms

localize17.0ms

rewrite35.0ms

series616.0ms

simplify99.0ms

prune102.0ms

localize13.0ms

rewrite40.0ms

series261.0ms

simplify71.0ms

prune56.0ms

regimes285.0ms

bsearch55.0ms

simplify4.0ms

end0.0ms

sample863.0ms

Profiling