Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	282×	body	80	valid
4.0ms	96×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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: 23.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.5b	(* (* x y) z)
9.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.4b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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

series208.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
84.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune219.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	8	89

Merged error: 3.3b

Counts

89 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.4b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ z (sqrt (- (* z z) (* t a))))
33.0ms	(- (* z z) (* t a))
86.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify67.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	431	1015
1	2166	912
2	5002	893

prune294.0ms

Filtered

124 candidates to 81 candidates (65.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Merged error: 3.3b

Counts

132 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
22.4b	(sqrt (- (* z z) (* t a)))
22.4b	(sqrt (- (* z z) (* t a)))
22.4b	(sqrt (- (* z z) (* t a)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
29×	`add-cbrt-cube`
23×	`prod-exp` `cbrt-unprod`
18×	`sqrt-div`
13×	`associate-r`
12×	`pow1` `cbrt-div`
11×	`add-sqr-sqrt`
9×	`flip3--` `sqrt-prod` `flip--`
8×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp` `associate-/r/`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-prod-down`
2×	`associate-*l/`
1×	`times-frac` `associate-l` `*-commutative` `div-inv`

Counts

4 → 90

Calls

4 calls:

20.0ms	(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
63.0ms	(sqrt (- (* z z) (* t a)))
67.0ms	(sqrt (- (* z z) (* t a)))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	503	1320
1	2570	1047
2	5001	953

prune319.0ms

Filtered

102 candidates to 68 candidates (66.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Merged error: 3.3b

Counts

111 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.5b	(* (* x y) z)
9.2b	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
22.4b	(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
16.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
92.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
71.0ms	(sqrt (- (* z z) (* t a)))

simplify88.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	518	840
1	3348	695
2	5003	670

prune197.0ms

Filtered

113 candidates to 62 candidates (54.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	113	9	122

Merged error: 3.3b

Counts

122 → 9

regimes362.0ms

Accuracy

87.1% (2.5b remaining)

Error of 6.2b against oracle of 3.7b and baseline of 23.2b

bsearch251.0ms

Steps

Iters	Range		Point
8	8.652172281318661e+117	1.0859828660130448e+121	4.0740761908068154e+120
10	4.663530970429285e-244	1.658596820250351e-230	4.0836093155324164e-232
10	-1.518437704233905e-153	-2.3395287029331725e-169	-2.005202403532717e-157
8	-6.572774097330817e+137	-2.1220637393417685e+133	-3.3604403558590137e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	42	24
2	42	24

end0.0ms

sample961.0ms

Algorithm

intervals

Results

456.0ms	8866×	body	80	valid
142.0ms	2937×	body	80	nan