Details

analyze1.1s

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

sample35.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
2.0ms	48×	body	80	nan
1.0ms	25×	body	80	invalid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	805	14
1	805	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: 25.7b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.2b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
29.0b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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:

4.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
29.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune142.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 1.9b

Counts

105 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(* 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)))))))
29.0b	(sqrt (- (* z z) (* t a)))
29.0b	(sqrt (- (* z z) (* t a)))
29.0b	(sqrt (- (* z z) (* t a)))

rewrite47.0ms

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:

32.0ms	(* 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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 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)))))))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	6093	1175

prune115.0ms

Filtered

61 candidates to 98 candidates (-60.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Merged error: 1.9b

Counts

108 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.2b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
29.0b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
32.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5256	1640

prune135.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 1.9b

Counts

133 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (/ z (sqrt (- (* z z) (* t a)))))
29.0b	(sqrt (- (* z z) (* t a)))
29.0b	(sqrt (- (* z z) (* t a)))
29.0b	(sqrt (- (* z z) (* t a)))

rewrite20.0ms

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)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5570	1301

prune101.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	90	12	102

Merged error: 1.9b

Counts

102 → 12

regimes1.3s

Accuracy

80.6% (3.7b remaining)

Error of 7.3b against oracle of 3.6b and baseline of 22.6b

bsearch54.0ms

Steps

Iters	Range		Point
10	8.455732453445318e+58	2.4977611042190756e+73	3.430719117234428e+68
7	-5.919765987252031e+57	-9.261725486694637e+55	-6.57733640771942e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	42
1	70	42

end0.0ms

sample895.0ms

Algorithm

intervals

Results

424.0ms	8000×	body	80	valid
96.0ms	2130×	body	80	nan
45.0ms	841×	body	80	invalid

Details

analyze1.1s

sample35.0ms

simplify30.0ms

prune13.0ms

localize10.0ms

rewrite31.0ms

series69.0ms

simplify44.0ms

prune142.0ms

localize19.0ms

rewrite47.0ms

series73.0ms

simplify53.0ms

prune115.0ms

localize10.0ms

rewrite28.0ms

series62.0ms

simplify55.0ms

prune135.0ms

localize17.0ms

rewrite20.0ms

series85.0ms

simplify50.0ms

prune101.0ms

regimes1.3s

bsearch54.0ms

simplify2.0ms

end0.0ms

sample895.0ms

Profiling