Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	278×	body	80	valid
4.0ms	101×	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: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
7.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.7b	(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))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
83.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
87.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

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

prune207.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 2.5b

Counts

89 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
4.7b	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
27.6b	(cbrt (- (* z z) (* t a)))
27.6b	(cbrt (- (* z z) (* t a)))

rewrite49.0ms

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:

19.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
6.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
62.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
85.0ms	(cbrt (- (* z z) (* t a)))
86.0ms	(cbrt (- (* z z) (* t a)))

simplify75.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1261	6499
1	5001	6166

prune945.0ms

Filtered

296 candidates to 223 candidates (75.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	294	2	296
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	299	6	305

Merged error: 2.5b

Counts

305 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

2.6b	(* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z)))
2.9b	(/ (* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z))) (sqrt (cbrt (- (* z z) (* t a)))))
27.6b	(cbrt (- (* z z) (* t a)))
27.6b	(cbrt (- (* z z) (* t a)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
57×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `sqrt-prod`
10×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
6×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod`
5×	`div-inv`
4×	`add-log-exp`
3×	`flip3--` `associate-l` `associate-/r/` `flip--` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 132

Calls

4 calls:

14.0ms	(* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z)))
13.0ms	(/ (* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z))) (sqrt (cbrt (- (* z z) (* t a)))))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z)))
215.0ms	(/ (* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z))) (sqrt (cbrt (- (* z z) (* t a)))))
84.0ms	(cbrt (- (* z z) (* t a)))
85.0ms	(cbrt (- (* z z) (* t a)))

simplify135.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	769	1842
1	3914	1629
2	5002	1617

prune514.0ms

Filtered

144 candidates to 113 candidates (78.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	144	6	150

Merged error: 2.5b

Counts

150 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
7.7b	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
26.7b	(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:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
14.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
84.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
69.0ms	(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (69.0ms)

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

prune198.0ms

Filtered

113 candidates to 64 candidates (56.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	113	6	119

Merged error: 2.5b

Counts

119 → 6

regimes338.0ms

Accuracy

81.1% (3.8b remaining)

Error of 7.2b against oracle of 3.3b and baseline of 23.7b

bsearch90.0ms

Steps

Iters	Range		Point
8	6.054907010532053e+79	1.5527092960997059e+84	1.0904999292653473e+81
9	-1.1704368858821797e+54	-4.5216644823555906e+45	-3.743017489383575e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	36	11
2	36	11

end0.0ms

sample805.0ms

Algorithm

intervals

Results

339.0ms	8807×	body	80	valid
108.0ms	2890×	body	80	nan