Details

Time bar (total: 5.7s)

sample279.0ms

Algorithm
intervals
Results
8.0ms196×body80valid
6.0ms31×body2560valid
5.0ms32×body1280valid
3.0ms113×body80nan
1.0ms11×body320valid
1.0ms4×body5120valid
1.0ms7×body640valid
0.0ms1×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
10.0ms
(/ (- (- 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)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11241910
25001901

prune255.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
3.7b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×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 → 184
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
152.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
185.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07252897
132102743
250032723

prune493.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
1.7b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.7b
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
25.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
119×add-sqr-sqrt
94×*-un-lft-identity
70×add-cube-cbrt
32×add-exp-log
25×associate-/r*
24×difference-of-squares
23×add-cbrt-cube
16×div-exp
15×sqrt-prod
12×distribute-lft-out--
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 → 162
Calls
4 calls:
6.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
15.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
164.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
133.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify89.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07732163
135601999
250011976

prune405.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
1.6b
(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
3.7b
(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
25.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
792×times-frac
491×add-sqr-sqrt
406×*-un-lft-identity
322×add-cube-cbrt
101×add-exp-log
84×difference-of-squares
67×div-exp
45×sqrt-prod
42×distribute-lft-out--
41×add-cbrt-cube div-inv
29×associate-/r/
25×associate-/l*
22×cbrt-undiv
18×prod-exp
16×flip3-- associate-/r* flip--
15×1-exp
6×rec-exp add-log-exp
5×pow1 cbrt-unprod
2×frac-2neg sqrt-div clear-num associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/
Counts
4 → 443
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
20.0ms
(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
34.0ms
(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
162.0ms
(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
128.0ms
(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
455 → 455
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
020918111
150017477

prune804.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.0b

regimes278.0ms

Accuracy

87.8% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.0b

bsearch111.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2445759453.473797
9
1.147231796899814e-295
2.5496030178102582e-290
6.634941373388381e-295
6
-7.692731713148582e+22
-5.509752788368676e+21
-9.346214526832347e+21

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03921
14121
24121

end0.0ms

sample997.0ms

Algorithm
intervals
Results
211.0ms1087×body2560valid
195.0ms5897×body80valid
138.0ms842×body1280valid
90.0ms2915×body80nan
56.0ms434×body640valid
30.0ms122×body5120valid
21.0ms228×body320valid
7.0ms116×body160valid