Details

analyze1.1s

Algorithm: search

sample32.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	68×	body	80	nan
1.0ms	28×	body	80	invalid

simplify9.0ms

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

prune4.0ms

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: 26.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
7.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.4b	(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:

6.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
8.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
30.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune148.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 4.4b

Counts

89 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
2.9b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
28.4b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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))
8.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
3.0ms	(sqrt (- (* z z) (* t a)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
32.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	512	1325
1	2358	1230
2	5002	1214

prune149.0ms

Filtered

98 candidates to 144 candidates (-46.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	146	9	155

Merged error: 4.2b

Counts

155 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
28.4b	(sqrt (- (* z z) (* t a)))

rewrite46.0ms

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))
19.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
8.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
3.0ms	(sqrt (- (* z z) (* t a)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
30.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
18.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	814	2501
1	3992	2347
2	5002	2347

prune201.0ms

Filtered

158 candidates to 239 candidates (-51.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	238	10	248

Merged error: 4.2b

Counts

248 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

5.0b	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
28.4b	(sqrt (- (* z z) (* t a)))
28.4b	(sqrt (- (* z z) (* t a)))
28.4b	(sqrt (- (* z z) (* t a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 76

Calls

4 calls:

5.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
13.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	333	810
1	949	782
2	3424	763
3	5001	751

prune102.0ms

Filtered

70 candidates to 88 candidates (-25.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	88	10	98

Merged error: 4.2b

Counts

98 → 10

regimes809.0ms

Accuracy

81.2% (3.6b remaining)

Error of 6.9b against oracle of 3.2b and baseline of 22.6b

bsearch2.6s

Steps

Iters	Range		Point
7	1.3864021634740486e+29	3.521117398914688e+31	2.169925372179965e+30
7	-1.7654021977290096e+137	-1.4465544591472367e+135	-1.522257177777629e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	32	10
2	32	10

end0.0ms

analyze1.1s

Algorithm: search

sample958.0ms

Algorithm

intervals

Results

438.0ms	8000×	body	80	valid
116.0ms	2347×	body	80	nan
45.0ms	856×	body	80	invalid

Details

analyze1.1s

sample32.0ms

simplify9.0ms

prune4.0ms

localize11.0ms

rewrite24.0ms

series56.0ms

simplify50.0ms

prune148.0ms

localize10.0ms

rewrite25.0ms

series64.0ms

simplify61.0ms

prune149.0ms

localize10.0ms

rewrite46.0ms

series72.0ms

simplify104.0ms

prune201.0ms

localize15.0ms

rewrite18.0ms

series85.0ms

simplify106.0ms

prune102.0ms

regimes809.0ms

bsearch2.6s

simplify2.0ms

end0.0ms

analyze1.1s

sample958.0ms

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