Details

sample54.0ms

Algorithm

intervals

Results

19.0ms	278×	body	80	valid
7.0ms	101×	body	80	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	7

prune5.0ms

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

localize19.0ms

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)))

rewrite32.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
14.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* z z) (* t a))
37.0ms	(* (* x y) z)
83.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune253.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 2.5b

Counts

99 → 9

localize14.0ms

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` `expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `pow1/3` `sqrt-div` `clear-num`
1×	`associate-/l/`

Counts

4 → 292

Calls

4 calls:

16.0ms	(/ (/ (* 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))
4.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
68.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
80.0ms	(cbrt (- (* z z) (* t a)))
107.0ms	(cbrt (- (* z z) (* t a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1273	6567
1	5001	6234

prune886.0ms

Filtered

304 candidates to 231 candidates (76.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	307	6	313

Merged error: 2.5b

Counts

313 → 6

localize14.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 140

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)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z)))
195.0ms	(/ (* x (/ y (/ (fabs (cbrt (- (* z z) (* t a)))) z))) (sqrt (cbrt (- (* z z) (* t a)))))
82.0ms	(cbrt (- (* z z) (* t a)))
81.0ms	(cbrt (- (* z z) (* t a)))

simplify98.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	781	1910
1	3957	1697
2	5003	1685

prune467.0ms

Filtered

152 candidates to 119 candidates (78.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	152	6	158

Merged error: 2.5b

Counts

158 → 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)))

rewrite31.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `un-div-inv` `div-inv`

Counts

4 → 111

Calls

4 calls:

4.0ms	(- (* 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)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
81.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	540	888
1	3413	742
2	5002	713

prune222.0ms

Filtered

123 candidates to 75 candidates (61.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Merged error: 2.5b

Counts

129 → 6

regimes341.0ms

Accuracy

81.1% (3.8b remaining)

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

bsearch87.0ms

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

sample781.0ms

Algorithm

intervals

Results

341.0ms	8807×	body	80	valid
101.0ms	2890×	body	80	nan