Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	284×	body	80	valid
5.0ms	94×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

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)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (76.0ms)

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

prune269.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize120.0ms

Local error

Found 4 expressions with local error:

12.6b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

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:

11.0ms	(- (- 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)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (100.0ms)

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

prune325.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.4b

localize123.0ms

Local error

Found 4 expressions with local error:

6.0b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

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)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	368	805
1	1471	730
2	5001	697

prune372.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.4b

localize123.0ms

Local error

Found 4 expressions with local error:

23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series284.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	129	544
1	469	520
2	1914	516
3	5002	508

prune327.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.4b

regimes186.0ms

Accuracy

90.1% (1.3b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 20.3b

bsearch170.0ms

Steps

Iters	Range		Point
8	9.456042252142157e+48	5.633410846004884e+51	5.5792500737545097e+51
8	-8.652530131639494e+154	-4.1384699730603854e+150	-1.2327221365590868e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	59
1	55	59

end0.0ms

sample882.0ms

Algorithm

intervals

Results

481.0ms	8747×	body	80	valid
137.0ms	2875×	body	80	nan