Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	283×	body	80	valid
4.0ms	99×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune8.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 25.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.2b	(* (* x y) z)
8.7b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.5b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
77.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune376.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 3.8b

Counts

89 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.8b	(- (* z z) (* t a))
2.5b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.5b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (sqrt (- (* z z) (* t a))) z)
32.0ms	(- (* z z) (* t a))
78.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	512	1325
1	2358	1230
2	5002	1214

prune589.0ms

Filtered

144 candidates to 98 candidates (68.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	143	9	152

Merged error: 3.6b

Counts

152 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
2.8b	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
24.4b	(cbrt (- (* z z) (* t a)))
24.4b	(cbrt (- (* z z) (* t a)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

413×	`times-frac`
157×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
114×	`sqrt-prod`
63×	`cbrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
24×	`div-inv`
22×	`associate-/r*`
19×	`associate-/l*`
17×	`cbrt-undiv` `div-exp`
13×	`associate-/r/`
6×	`cbrt-div`
4×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `pow1/3` `sqrt-div` `clear-num`
1×	`associate-/l/`

Counts

4 → 284

Calls

4 calls:

24.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
12.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
6.0ms	(cbrt (- (* z z) (* t a)))
6.0ms	(cbrt (- (* z z) (* t a)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
60.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
78.0ms	(cbrt (- (* z z) (* t a)))
81.0ms	(cbrt (- (* z z) (* t a)))

simplify76.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1261	6499
1	5001	6166

prune1.4s

Filtered

296 candidates to 223 candidates (75.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	296	9	305

Merged error: 3.6b

Counts

305 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.2b	(* (* x y) z)
8.7b	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
23.5b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
30×	`add-cbrt-cube`
27×	`associate-r` `prod-exp`
20×	`add-sqr-sqrt`
19×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`cbrt-unprod`
12×	`sqrt-prod`
9×	`pow-prod-down`
6×	`div-exp` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--`
2×	`associate-l` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `un-div-inv` `div-inv`

Counts

4 → 101

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
14.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
78.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify75.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	515	839
1	3335	695
2	5001	670

prune328.0ms

Filtered

113 candidates to 63 candidates (55.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 3.6b

Counts

122 → 9

regimes750.0ms

Accuracy

81.9% (3.7b remaining)

Error of 6.7b against oracle of 3.0b and baseline of 23.4b

bsearch59.0ms

Steps

Iters	Range		Point
4	1.8581409902300446e+147	2.7314064417853037e+147	1.8854305355911464e+147
6	-3.70834960042386e+143	-3.734143760549916e+142	-1.3145474944288093e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	33	17
2	33	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

430.0ms	8882×	body	80	valid
139.0ms	2986×	body	80	nan

Details

sample43.0ms

simplify9.0ms

prune8.0ms

localize10.0ms

rewrite22.0ms

series192.0ms

simplify50.0ms

prune376.0ms

localize10.0ms

rewrite27.0ms

series248.0ms

simplify65.0ms

prune589.0ms

localize17.0ms

rewrite64.0ms

series405.0ms

simplify76.0ms

prune1.4s

localize11.0ms

rewrite29.0ms

series196.0ms

simplify75.0ms

prune328.0ms

regimes750.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample1.2s

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