Details

sample424.0ms

Algorithm

intervals

Results

329.0ms	89×	body	80	nan
54.0ms	283×	body	80	valid

simplify1.2s

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (408.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune23.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 21.1b

Counts

2 → 1

localize58.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
1.8b	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

13.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
16.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
8.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
11.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
36.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
26.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
40.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify166.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4877	1095
1	4877	1095

prune378.0ms

Filtered

58 candidates to 75 candidates (-29.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	8	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 6.1b

Counts

76 → 8

localize51.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
3.3b	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
4.4b	(* c (/ a b))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`sqrt-prod`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 91

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
18.0ms	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
13.0ms	(* c (/ a b))
8.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
33.0ms	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
10.0ms	(* c (/ a b))
33.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify87.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4961	1326
1	4961	1326

prune489.0ms

Filtered

78 candidates to 103 candidates (-32.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 6.1b

Counts

111 → 10

localize61.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
4.4b	(* c (/ a b))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

4 → 91

Calls

4 calls:

18.0ms	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
14.0ms	(* c (/ a b))
9.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
9.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ c (+ (* 2.0 (* c (/ a b))) (* b -2)))
10.0ms	(* c (/ a b))
34.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
30.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify96.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4954	1274
1	4954	1274

prune652.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	102	11	113

Merged error: 6.0b

Counts

113 → 11

localize68.0ms

Local error

Found 4 expressions with local error:

18.3b	(- (* (* (cbrt (sqrt (- (* b b) (* c (* 4.0 a))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
26.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

44.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* c (* 4.0 a))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
9.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
9.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
8.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* c (* 4.0 a))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) (cbrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
34.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
30.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
31.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify130.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4909	870
1	4909	870

prune426.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	11	80

Merged error: 6.0b

Counts

80 → 11

regimes664.0ms

Accuracy

91.8% (1.3b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 21.4b

bsearch81.0ms

Steps

Iters	Range		Point
5	1.1994113433831075e+59	2.551497614016684e+59	2.517726559601462e+59
4	-2.2327321462329562e+137	-1.3518192462889248e+137	-1.928713223890362e+137

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	164	156
1	164	156

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	8700×	body	80	valid
489.0ms	2933×	body	80	nan

Details

sample424.0ms

simplify1.2s

prune23.0ms

localize58.0ms

rewrite53.0ms

series130.0ms

simplify166.0ms

prune378.0ms

localize51.0ms

rewrite63.0ms

series106.0ms

simplify87.0ms

prune489.0ms

localize61.0ms

rewrite55.0ms

series106.0ms

simplify96.0ms

prune652.0ms

localize68.0ms

rewrite73.0ms

series129.0ms

simplify130.0ms

prune426.0ms

regimes664.0ms

bsearch81.0ms

simplify6.0ms

end0.0ms

sample2.8s

Profiling