Details

sample280.0ms

Algorithm

intervals

Results

6.0ms	201×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	21×	body	2560	valid
3.0ms	103×	body	80	nan
2.0ms	3×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

50.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune233.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	569	2100
1	2561	1900
2	5002	1763

prune275.0ms

Filtered

174 candidates to 86 candidates (49.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))
19.5b	(sqrt (- (* b_2 b_2) (* 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:

2.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	140	390
1	455	366
2	1490	364
3	5002	360

prune207.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt a)
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt a)
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	235	375
1	707	351
2	2346	346
3	5002	342

prune179.0ms

Filtered

65 candidates to 51 candidates (78.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.4b

regimes257.0ms

Accuracy

86.9% (3.7b remaining)

Error of 9.2b against oracle of 5.5b and baseline of 34.1b

bsearch84.0ms

Steps

Iters	Range	Point
2	3.9431530817676045e+109	4.557375181159837e+109	4.019930844191633e+109
10	9.294290849485744e-131	6.48544897696183e-121	1.9238883452280037e-130
3	-2.4188752133425037e+101	-1.756824163423226e+101	-2.377497022722549e+101

Iters

Range

Point

3.9431530817676045e+109

4.557375181159837e+109

4.019930844191633e+109

9.294290849485744e-131

6.48544897696183e-121

1.9238883452280037e-130

-2.4188752133425037e+101

-1.756824163423226e+101

-2.377497022722549e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	41	24
2	41	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

216.0ms	1102×	body	2560	valid
191.0ms	5848×	body	80	valid
144.0ms	920×	body	1280	valid
88.0ms	2883×	body	80	nan
54.0ms	453×	body	640	valid
24.0ms	103×	body	5120	valid
20.0ms	227×	body	320	valid
7.0ms	123×	body	160	valid