Details

Time bar (total: 5.0s)

sample297.0ms

Algorithm
intervals
Results
8.0ms189×body80valid
5.0ms28×body2560valid
5.0ms34×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
2.0ms7×body5120valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

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:
49.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705

prune245.0ms

Filtered
92 candidates to 69 candidates (75.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 200
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
145.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07293368
133203193
250013167

prune503.0ms

Filtered
212 candidates to 142 candidates (67.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.0b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.3b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
126×add-sqr-sqrt
125×*-un-lft-identity
77×add-cube-cbrt
32×add-exp-log
28×associate-/r*
24×distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
16×div-exp
15×sqrt-prod
12×distribute-rgt-neg-in
10×cbrt-undiv
6×prod-exp div-inv add-log-exp
5×pow1
4×associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ associate-/r/ associate-/l/
Counts
4 → 174
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
26.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
20.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
184.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
157.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07682476
135832301
250022278

prune427.0ms

Filtered
186 candidates to 119 candidates (64.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×add-cbrt-cube
7×div-exp
6×pow1
5×div-inv
3×cbrt-undiv flip3-- diff-log flip-- associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ inv-pow
Counts
4 → 169
Calls
4 calls:
29.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06212276
126632085
250011950

prune272.0ms

Filtered
181 candidates to 84 candidates (46.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes152.0ms

Accuracy

80.9% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 29.8b

bsearch79.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
1.3729799928425753e+84
9
-6.219842315709727e-116
-4.3103875869831393e-125
-3.16299820169664e-118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03817
14217
24217

end0.0ms

sample1.0s

Algorithm
intervals
Results
200.0ms5872×body80valid
200.0ms1048×body2560valid
146.0ms910×body1280valid
91.0ms2861×body80nan
54.0ms454×body640valid
26.0ms100×body5120valid
20.0ms219×body320valid
8.0ms123×body160valid