Details

Time bar (total: 4.9s)

sample291.0ms

Algorithm
intervals
Results
8.0ms181×body80valid
7.0ms32×body2560valid
6.0ms36×body1280valid
4.0ms111×body80nan
1.0ms10×body640valid
1.0ms12×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

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))))
1.4b
(- (* b_2 b_2) (* a c))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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:
11.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(- (* b_2 b_2) (* a c))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0358790
11261727
25001705

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
3.8b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

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:
4.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
140.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
165.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
07293368
133203193
250013167

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.5b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.8b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

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:
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
19.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* b_2 b_2) (* a c))
175.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07682476
135832301
250022278

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-exp-log
26×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
17×div-exp
13×add-cbrt-cube
10×add-log-exp
7×1-exp associate-/r*
6×pow1 prod-exp
5×cbrt-undiv div-inv
4×rec-exp sqrt-prod
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square pow-flip distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ cbrt-unprod inv-pow
Counts
4 → 104
Calls
4 calls:
12.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
8.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms
(- (* b_2 b_2) (* a c))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05211126
12188976
25002931

prune201.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

regimes201.0ms

Accuracy

78.7% (5.0b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 29.1b

bsearch69.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2445759453.473797
6
-1.6265262117742566e-90
-1.5703225997493665e-91
-4.247911584299811e-91

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03415
13615
23615

end0.0ms

sample1.1s

Algorithm
intervals
Results
233.0ms1098×body2560valid
213.0ms5841×body80valid
166.0ms933×body1280valid
98.0ms2922×body80nan
62.0ms450×body640valid
26.0ms101×body5120valid
23.0ms233×body320valid
7.0ms101×body160valid