Details

Time bar (total: 5.0s)

sample276.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
6.0ms179×body80valid
5.0ms32×body1280valid
4.0ms89×body80nan
2.0ms15×body640valid
2.0ms7×body5120valid
1.0ms7×body320valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.3b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
22.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

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:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0368965
11241910
25001901

prune269.0ms

Filtered
103 candidates to 72 candidates (69.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.7b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.7b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×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 → 187
Calls
4 calls:
21.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
25.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
158.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
200.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07302960
132002803
250012783

prune507.0ms

Filtered
199 candidates to 148 candidates (74.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0b
(/ a (* a c))
22.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
103×add-exp-log
60×div-exp
41×add-cbrt-cube
34×times-frac
29×prod-exp
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
20×1-exp
18×cbrt-undiv
16×associate-/l*
9×cbrt-unprod
8×rec-exp
6×add-log-exp
5×pow1 associate-/r/
4×flip3-- sqrt-prod flip-- div-inv
2×frac-times frac-2neg sqrt-div associate-*r/ clear-num associate-/r* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*l/ associate-/l/ distribute-lft-out--
Counts
4 → 130
Calls
4 calls:
28.0ms
(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
18.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms
(/ a (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(/ a (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07471294
13857947
25001885

prune247.0ms

Filtered
142 candidates to 74 candidates (52.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b
(- (* b_2 b_2) (* a c))
0.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 83
Calls
4 calls:
20.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
38.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify127.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0314813
11002760
23949755
35001755

prune198.0ms

Filtered
95 candidates to 69 candidates (72.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

regimes215.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.4b

bsearch149.0ms

Steps
ItersRangePoint
10
2.531505514381809e+64
2.4051897841780437e+82
1.3017976234533476e+80
10
1.3073375047174026e-281
5.2835940265373795e-264
1.4444479783899298e-267
7
-4.788437381304621e+112
-4.459607117755996e+110
-4.419169890115165e+111

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03821
13821

end0.0ms

sample964.0ms

Algorithm
intervals
Results
198.0ms1047×body2560valid
190.0ms5916×body80valid
134.0ms897×body1280valid
91.0ms2837×body80nan
50.0ms419×body640valid
31.0ms133×body5120valid
22.0ms242×body320valid
7.0ms116×body160valid