Details

Time bar (total: 6.1s)

sample285.0ms

Algorithm
intervals
Results
7.0ms38×body2560valid
7.0ms196×body80valid
6.0ms91×body80nan
4.0ms27×body1280valid
1.0ms12×body640valid
0.0ms2×body5120valid
0.0ms5×body320valid
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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
0.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

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:
47.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
2.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0358790
11261727
25001705

prune240.0ms

Filtered
92 candidates to 69 candidates (75.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
2.0b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

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))
43.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* b_2 b_2) (* a c))
143.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
176.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07293368
133203193
250013167

prune500.0ms

Filtered
212 candidates to 142 candidates (67.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
1.9b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.0b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 485
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
187.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
160.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015368628
150017982

prune1.1s

Filtered
497 candidates to 298 candidates (60.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b
(- (* b_2 b_2) (* a c))
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
853×times-frac
514×add-sqr-sqrt
513×*-un-lft-identity
341×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
46×sqrt-prod
43×distribute-rgt-neg-in
41×div-inv
37×add-exp-log
29×div-exp
25×associate-/r*
16×add-cbrt-cube
13×associate-/l*
10×1-exp add-log-exp
8×cbrt-undiv
5×pow1
4×rec-exp
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ associate-/l/
Counts
4 → 438
Calls
4 calls:
33.0ms
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
450 → 450
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
016497618
150016860

prune399.0ms

Filtered
450 candidates to 120 candidates (26.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.3b

regimes187.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.3b against oracle of 5.2b and baseline of 29.2b

bsearch138.0ms

Steps
ItersRangePoint
8
2.531505514381809e+64
5.72577144612764e+68
2.4235533085097852e+67
9
-7.328840644673834e-256
-4.626257585305123e-261
-1.4397456618027265e-260
7
-4.788437381304621e+112
-1.2414549986870086e+111
-2.8688546137715554e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04022
14222
24222

end0.0ms

sample1.0s

Algorithm
intervals
Results
221.0ms1123×body2560valid
201.0ms5760×body80valid
137.0ms857×body1280valid
90.0ms2819×body80nan
55.0ms450×body640valid
31.0ms129×body5120valid
24.0ms255×body320valid
8.0ms123×body160valid