Details

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 68.362832%

Results

18.0ms	279×	body	80	valid
2.0ms	50×	body	80	nan

simplify11.0ms

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: 25.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
8.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.6b	(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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
32.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

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

prune138.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 5.5b

Counts

89 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.1b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.6b	(sqrt (- (* z z) (* t a)))
25.6b	(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
48×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
15×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 141

Calls

4 calls:

8.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
27.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
55.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	661	1959
1	3424	1748
2	5002	1624

prune161.0ms

Filtered

100 candidates to 153 candidates (-53.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	152	11	163

Merged error: 5.5b

Counts

163 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

3.0ms	(sqrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (- (* z z) (* t a)))
23.0ms	(cbrt (- (* z z) (* t a)))
22.0ms	(cbrt (- (* z z) (* t a)))
25.0ms	(cbrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	209	545
1	624	515
2	2019	496
3	5001	471

prune135.0ms

Filtered

57 candidates to 66 candidates (-15.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	66	11	77

Merged error: 5.5b

Counts

77 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y))
5.1b	(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y)) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.6b	(sqrt (- (* z z) (* t a)))
25.6b	(sqrt (- (* z z) (* t a)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

445×	`times-frac`
307×	`add-sqr-sqrt`
249×	`sqrt-prod`
222×	`add-cube-cbrt` `*-un-lft-identity`
98×	`associate-l`
33×	`associate-r`
31×	`associate-/r*`
30×	`add-exp-log` `add-cbrt-cube`
20×	`unswap-sqr`
12×	`cbrt-undiv` `div-exp`
10×	`div-inv`
8×	`pow1` `sqrt-div`
6×	`prod-exp` `cbrt-unprod`
4×	`associate-/r/` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 347

Calls

4 calls:

11.0ms	(/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y))
64.0ms	(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y)) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y))
46.0ms	(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) y)) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))
17.0ms	(sqrt (- (* z z) (* t a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1300	5690
1	5001	5371

prune241.0ms

Filtered

232 candidates to 359 candidates (-54.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	358	1	359
Fresh	1	6	7
Picked	0	1	1
Done	0	3	3
Total	359	11	370

Merged error: 5.5b

Counts

370 → 11

regimes956.0ms

Accuracy

78% (4.5b remaining)

Error of 8.0b against oracle of 3.4b and baseline of 23.9b

bsearch53.0ms

Steps

Iters	Range		Point
7	168272709785.2424	28333139580135.332	27825563271391.047
7	-7.756758232943268e+83	-4.367743922778447e+82	-2.559585537453544e+83

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

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 68.362832%

Results

480.0ms	8819×	body	80	valid
75.0ms	1531×	body	80	nan

Details

sample1.7s

simplify11.0ms

prune4.0ms

localize11.0ms

rewrite22.0ms

series58.0ms

simplify51.0ms

prune138.0ms

localize13.0ms

rewrite48.0ms

series117.0ms

simplify82.0ms

prune161.0ms

localize23.0ms

rewrite15.0ms

series82.0ms

simplify58.0ms

prune135.0ms

localize13.0ms

rewrite106.0ms

series123.0ms

simplify72.0ms

prune241.0ms

regimes956.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling