Details

sample3.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 24.612832%

Results

13.0ms	256×	body	80	valid
2.0ms	55×	body	80	nan
2.0ms	35×	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

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: 26.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
3.1b	(* (* x y) z)
10.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.8b	(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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
34.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(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

prune138.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

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: 3.4b

Counts

89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
2.0b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.8b	(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)
3.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
5.0ms	(sqrt (- (* z z) (* t a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
29.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (51.0ms)

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

prune150.0ms

Filtered

98 candidates to 144 candidates (-46.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Merged error: 3.4b

Counts

153 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.0b	(- (* z z) (* t a))
1.4b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite52.0ms

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:

9.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(- (* z z) (* t a))
23.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
11.0ms	(- (* z z) (* t a))
30.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (23.0ms)

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

prune199.0ms

Filtered

161 candidates to 239 candidates (-48.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	239	8	247

Merged error: 3.4b

Counts

247 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
1.0b	(- (* z z) (* t a))
1.6b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
400×	`add-sqr-sqrt`
399×	`add-cube-cbrt` `*-un-lft-identity`
147×	`sqrt-prod`
73×	`associate-/r*`
25×	`associate-/l*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`

Counts

4 → 433

Calls

4 calls:

9.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
4.0ms	(- (* z z) (* t a))
18.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
6.0ms	(sqrt (- (* z z) (* t a)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
7.0ms	(- (* z z) (* t a))
27.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
19.0ms	(sqrt (- (* z z) (* t a)))

simplify95.0ms

Algorithm

egg-herbie

Counts

445 → 445

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1598	6628
1	5002	6359

prune305.0ms

Filtered

305 candidates to 445 candidates (-45.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	444	1	445
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	446	7	453

Merged error: 3.4b

Counts

453 → 7

regimes718.0ms

Accuracy

83.2% (3.3b remaining)

Error of 6.7b against oracle of 3.4b and baseline of 22.9b

bsearch57.0ms

Steps

Iters	Range		Point
10	1.140968328812188e+131	8.4686327390831e+144	1.185451902408631e+143
5	-1.2384715879743401e+45	-4.121337431808632e+44	-7.979137958002804e+44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	31	10
2	31	10

end0.0ms

sample4.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 24.612832%

Results

429.0ms	8000×	body	80	valid
80.0ms	1545×	body	80	nan
47.0ms	832×	body	80	invalid

Details

sample3.9s

simplify9.0ms

prune5.0ms

localize10.0ms

rewrite22.0ms

series58.0ms

simplify53.0ms

prune138.0ms

localize10.0ms

rewrite29.0ms

series66.0ms

simplify65.0ms

prune150.0ms

localize10.0ms

rewrite52.0ms

series72.0ms

simplify106.0ms

prune199.0ms

localize11.0ms

rewrite65.0ms

series71.0ms

simplify95.0ms

prune305.0ms

regimes718.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample4.7s

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