Details

Time bar (total: 5.1s)

sample284.0ms

Algorithm
intervals
Results
8.0ms194×body80valid
7.0ms35×body2560valid
4.0ms27×body1280valid
3.0ms84×body80nan
2.0ms14×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×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: 34.0b

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 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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:
41.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
2.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11241910
25001901

prune248.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:
17.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
26.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
156.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms
(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

prune493.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
32×add-exp-log
26×difference-of-squares
25×associate-/r*
23×add-cbrt-cube
16×div-exp sqrt-prod
13×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 → 165
Calls
4 calls:
21.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
18.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
136.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08032218
136682058
250012035

prune409.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.7b
(/ a (* a c))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
7×sqrt-prod
6×pow1 add-log-exp
4×sqrt-div
3×flip3-- times-frac flip-- associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp difference-of-squares
1×sub-neg frac-2neg diff-log prod-exp clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out--
Counts
4 → 66
Calls
4 calls:
17.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms
(/ a (* a c))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(/ a (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0264447
1888411
23862404
35001402

prune219.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes233.0ms

Accuracy

89.5% (2.8b remaining)

Error of 8.2b against oracle of 5.4b and baseline of 31.9b

bsearch126.0ms

Steps
ItersRangePoint
6
1.1594993669073426e+93
1.3006782908792091e+94
1.9740449679534498e+93
7
-7.220328558483205e-277
-2.8795960734924236e-278
-1.3775573616595516e-277
8
-1.9687675883731564e+45
-2.9085012640544174e+42
-1.3726940620353851e+45

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04937
14937

end0.0ms

sample1.0s

Algorithm
intervals
Results
217.0ms1037×body2560valid
207.0ms5813×body80valid
151.0ms911×body1280valid
95.0ms2949×body80nan
61.0ms452×body640valid
31.0ms125×body5120valid
22.0ms222×body320valid
8.0ms126×body160valid