Details

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 11.93407%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

19.0ms	256×	body	80	valid
3.0ms	56×	body	80	nan
1.0ms	24×	body	80	invalid

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

prune5.0ms

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: 23.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
4.9b	(* (* x y) z)
9.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b	(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))
4.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
34.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

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

prune142.0ms

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: 2.4b

Counts

89 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.8b	(- (* z z) (* t a))
2.0b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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)
5.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
31.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify67.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (53.0ms)

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

prune156.0ms

Filtered

99 candidates to 144 candidates (-45.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	145	10	155

Merged error: 2.4b

Counts

155 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
23.6b	(sqrt (- (* z z) (* t a)))
23.6b	(sqrt (- (* z z) (* t a)))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

417×	`times-frac`
284×	`add-sqr-sqrt`
210×	`cbrt-prod`
186×	`add-cube-cbrt` `*-un-lft-identity`
179×	`associate-r`
97×	`add-exp-log`
69×	`sqrt-prod`
61×	`add-cbrt-cube`
45×	`cbrt-undiv` `div-exp`
30×	`prod-exp` `cbrt-unprod`
24×	`unswap-sqr`
20×	`associate-l`
9×	`pow1`
8×	`div-inv`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`associate-/r/`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 316

Calls

4 calls:

97.0ms	(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
6.0ms	(sqrt (- (* z z) (* t a)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
19.0ms	(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2083	8844
1	5001	8266

prune308.0ms

Filtered

237 candidates to 328 candidates (-38.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	328	10	338

Merged error: 2.4b

Counts

338 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
0.8b	(- (* z z) (* t a))
2.0b	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
30×	`add-cbrt-cube`
29×	`add-sqr-sqrt`
17×	`prod-exp`
16×	`*-un-lft-identity` `div-exp`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
10×	`sqrt-div`
9×	`cbrt-undiv` `sqrt-prod` `cbrt-unprod`
7×	`pow1`
6×	`flip3--` `associate-l` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
4×	`frac-times` `associate-*l/`
3×	`rec-exp` `1-exp`
2×	`associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 108

Calls

4 calls:

11.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
4.0ms	(- (* z z) (* t a))
11.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
7.0ms	(- (* z z) (* t a))
31.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify67.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	539	1009
1	2688	885
2	5001	865

prune102.0ms

Filtered

77 candidates to 120 candidates (-55.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	120	10	130

Merged error: 2.4b

Counts

130 → 10

regimes800.0ms

Accuracy

84% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 23.1b

bsearch79.0ms

Steps

Iters	Range		Point
5	4.733393946842807e+64	1.8879565359672707e+65	1.8551308361141253e+65
9	-3.212479424722412e+154	-3.3196878575542664e+148	-2.4256844019273195e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	30	10
2	30	10

end0.0ms

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 11.93407%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

423.0ms	8000×	body	80	valid
75.0ms	1588×	body	80	nan
47.0ms	843×	body	80	invalid

Details

sample2.7s

simplify10.0ms

prune5.0ms

localize11.0ms

rewrite22.0ms

series61.0ms

simplify53.0ms

prune142.0ms

localize10.0ms

rewrite29.0ms

series65.0ms

simplify67.0ms

prune156.0ms

localize19.0ms

rewrite135.0ms

series77.0ms

simplify106.0ms

prune308.0ms

localize12.0ms

rewrite35.0ms

series65.0ms

simplify67.0ms

prune102.0ms

regimes800.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample3.5s

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