Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	282×	body	80	valid
3.0ms	96×	body	80	nan

simplify14.0ms

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

localize14.0ms

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)))

rewrite26.0ms

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:

4.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
95.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
72.0ms	(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

prune238.0ms

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)))

rewrite31.0ms

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))
13.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ z (sqrt (- (* z z) (* t a))))
37.0ms	(- (* z z) (* t a))
97.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
71.0ms	(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (57.0ms)

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

prune275.0ms

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

localize20.0ms

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)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (* 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)))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (67.0ms)

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

prune340.0ms

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

localize15.0ms

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)))

rewrite32.0ms

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)
15.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
91.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify84.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (74.0ms)

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

prune205.0ms

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

regimes386.0ms

Accuracy

87.1% (2.5b remaining)

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

bsearch245.0ms

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

sample795.0ms

Algorithm

intervals

Results

340.0ms	8866×	body	80	valid
102.0ms	2937×	body	80	nan

Details

sample30.0ms

simplify14.0ms

prune3.0ms

localize14.0ms

rewrite26.0ms

series232.0ms

simplify60.0ms

prune238.0ms

localize11.0ms

rewrite31.0ms

series260.0ms

simplify68.0ms

prune275.0ms

localize20.0ms

rewrite36.0ms

series392.0ms

simplify79.0ms

prune340.0ms

localize15.0ms

rewrite32.0ms

series224.0ms

simplify84.0ms

prune205.0ms

regimes386.0ms

bsearch245.0ms

simplify2.0ms

end0.0ms

sample795.0ms

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