Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
2.0ms	57×	body	80	nan
1.0ms	21×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	14
1	77	14

prune13.0ms

Filtered

1 candidates to 1 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: 21.0b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.2b	(- (* z z) (* t a))
1.7b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(- (* z z) (* t a))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
7.0ms	(sqrt (- (* z z) (* t a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(- (* z z) (* t a))
32.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	1238
1	4979	1238

prune136.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 2.6b

Counts

105 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

1.7b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
26.3b	(sqrt (- (* z z) (* t a)))
26.3b	(sqrt (- (* z z) (* t a)))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
37×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
21×	`pow1`
11×	`add-sqr-sqrt`
10×	`pow-prod-down`
9×	`cbrt-undiv` `div-exp` `sqrt-prod`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `flip--`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 86

Calls

4 calls:

31.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4936	1175
1	4936	1175

prune113.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Merged error: 2.6b

Counts

106 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (/ z (sqrt (- (* z z) (* t a)))))
26.3b	(sqrt (- (* z z) (* t a)))
26.3b	(sqrt (- (* z z) (* t a)))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4878	1292
1	4878	1292

prune129.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Merged error: 2.6b

Counts

99 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
1.2b	(- (* z z) (* t a))
1.6b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
31×	`pow1` `add-cbrt-cube`
27×	`prod-exp` `cbrt-unprod`
18×	`pow-prod-down`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`associate-l`
3×	`cbrt-undiv` `associate-*r/` `div-exp` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-r` `associate-l/` `-commutative` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 80

Calls

4 calls:

18.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
4.0ms	(- (* z z) (* t a))
11.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
4.0ms	(sqrt (- (* z z) (* t a)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
8.0ms	(- (* z z) (* t a))
42.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify35.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5393	1165

prune70.0ms

Filtered

55 candidates to 92 candidates (-67.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	91	10	101

Merged error: 2.6b

Counts

101 → 10

regimes845.0ms

Accuracy

86.9% (2.5b remaining)

Error of 5.8b against oracle of 3.2b and baseline of 22.6b

bsearch2.0s

Steps

Iters	Range		Point
4	2.93051759981468e+70	4.321380346599862e+70	4.277915885762825e+70
8	-2.229500273428656e+155	-5.2139214545012906e+150	-1.639453879920885e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	80
1	47	80

end0.0ms

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample1.0s

Algorithm

intervals

Results

470.0ms	8000×	body	80	valid
122.0ms	2223×	body	80	nan
48.0ms	850×	body	80	invalid

Details

analyze1.0s

sample31.0ms

simplify3.0ms

prune13.0ms

localize10.0ms

rewrite35.0ms

series75.0ms

simplify54.0ms

prune136.0ms

localize22.0ms

rewrite46.0ms

series80.0ms

simplify51.0ms

prune113.0ms

localize14.0ms

rewrite19.0ms

series89.0ms

simplify49.0ms

prune129.0ms

localize13.0ms

rewrite39.0ms

series99.0ms

simplify35.0ms

prune70.0ms

regimes845.0ms

bsearch2.0s

simplify2.0ms

end0.0ms

analyze1.0s

sample1.0s

Profiling