Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	281×	body	80	valid
4.0ms	91×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	18
1	66	18
2	116	18
3	144	18
4	159	18
5	161	18
6	161	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize118.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	149	476
1	576	446
2	2486	444
3	5001	440

prune275.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.9b

localize118.0ms

Local error

Found 4 expressions with local error:

6.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

6.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	225	725
1	835	631
2	3414	609
3	5001	589

prune334.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize119.0ms

Local error

Found 4 expressions with local error:

6.5b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

6.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	363	835
1	1402	760
2	5001	731

prune404.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize124.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite12.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	202	609
1	639	571
2	2437	564
3	5001	562

prune352.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.8b

regimes215.0ms

Accuracy

92.3% (0.9b remaining)

Error of 8.9b against oracle of 7.9b and baseline of 20.2b

bsearch131.0ms

Steps

Iters	Range		Point
4	1.4117953071395708e+85	2.422703580179915e+85	1.810040537849194e+85
8	-3.7610221637517924e+157	-1.1271380753219535e+153	-1.358444129835255e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	60
1	49	60

end0.0ms

sample908.0ms

Algorithm

intervals

Results

492.0ms	8722×	body	80	valid
142.0ms	2794×	body	80	nan