Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	289×	body	80	valid
5.0ms	97×	body	80	nan

simplify10.0ms

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

prune2.0ms

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: 26.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
6.3b	(* (* x y) z)
9.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.4b	(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:

3.0ms	(- (* z z) (* t a))
7.0ms	(* (* x y) z)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
57.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5001	510

prune403.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 3.6b

Counts

89 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
3.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
28.4b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (sqrt (- (* z z) (* t a))) z)
33.0ms	(- (* z z) (* t a))
81.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	519	1327
1	2378	1230
2	5001	1214

prune305.0ms

Filtered

144 candidates to 98 candidates (68.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	143	11	154

Merged error: 3.3b

Counts

154 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y)
1.3b	(/ x (/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y))
29.2b	(cbrt (- (* z z) (* t a)))
29.2b	(cbrt (- (* z z) (* t a)))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

7116×	`times-frac`
3072×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1926×	`cbrt-prod`
415×	`associate-/r*`
139×	`associate-/l*`
118×	`div-inv`
27×	`add-exp-log`
21×	`add-cbrt-cube`
16×	`cbrt-undiv` `div-exp`
4×	`pow1` `cbrt-div` `add-log-exp`
2×	`flip3--` `frac-2neg` `pow1/3` `clear-num` `flip--`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 2260

Calls

4 calls:

30.0ms	(/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y)
83.0ms	(/ x (/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y))
4.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y)
209.0ms	(/ x (/ (/ (/ (fabs (cbrt (- (* z z) (* t a)))) (cbrt z)) (cbrt z)) y))
83.0ms	(cbrt (- (* z z) (* t a)))
86.0ms	(cbrt (- (* z z) (* t a)))

simplify518.0ms

Algorithm

egg-herbie

Counts

2272 → 2272

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5001	57751

prune11.8s

Filtered

2272 candidates to 2103 candidates (92.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	2272	0	2272
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	2272	11	2283

Merged error: 3.3b

Counts

2283 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.7b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
28.4b	(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 227

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
21.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
81.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
53.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	817	2503
1	4028	2347
2	5001	2347

prune487.0ms

Filtered

239 candidates to 160 candidates (66.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	239	11	250

Merged error: 3.3b

Counts

250 → 11

regimes461.0ms

Accuracy

84.4% (3.1b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 23.1b

bsearch74.0ms

Steps

Iters	Range		Point
7	2.3213776524035136e+51	7.981098076133901e+52	8.676676205265586e+51
5	-1.5408390079967862e+112	-6.847226517557763e+111	-7.644117979862808e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	22
1	37	22
2	37	22

end0.0ms

sample987.0ms

Algorithm

intervals

Results

465.0ms	8845×	body	80	valid
150.0ms	2989×	body	80	nan

Details

sample35.0ms

simplify10.0ms

prune2.0ms

localize11.0ms

rewrite26.0ms

series198.0ms

simplify52.0ms

prune403.0ms

localize12.0ms

rewrite28.0ms

series250.0ms

simplify69.0ms

prune305.0ms

localize19.0ms

rewrite417.0ms

series553.0ms

simplify518.0ms

prune11.8s

localize14.0ms

rewrite50.0ms

series232.0ms

simplify106.0ms

prune487.0ms

regimes461.0ms

bsearch74.0ms

simplify2.0ms

end0.0ms

sample987.0ms

Profiling