Details

Time bar (total: 4.9s)

sample47.0ms

Algorithm
intervals
Results
10.0ms179×body80valid
9.0ms34×body2560valid
6.0ms29×body1280valid
4.0ms85×body80nan
3.0ms17×body640valid
2.0ms5×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
72.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0400780
11529686
25002675

prune276.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74882
Fresh000
Picked011
Done000
Total74983

Merged error: 5.0b

Counts
83 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.3b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.1b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
25.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
142.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
171.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
79.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06472692
131142439
250012426

prune385.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1624166
Fresh167
Picked011
Done011
Total16312175

Merged error: 4.8b

Counts
175 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0b
(/ (* 3.0 a) (* 3.0 (* a c)))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0417636
12439522
25001492

prune174.0ms

Filtered
82 candidates to 54 candidates (65.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New80282
Fresh279
Picked101
Done022
Total831194

Merged error: 4.8b

Counts
94 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.0b
(- (* b b) (* (* 3.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×div-exp
8×pow1
7×add-cube-cbrt
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 82
Calls
4 calls:
12.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
42.0ms
(- (* b b) (* (* 3.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0432926
11830797
25003784

prune175.0ms

Filtered
94 candidates to 62 candidates (66.0%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New91394
Fresh268
Picked011
Done022
Total9312105

Merged error: 4.8b

Counts
105 → 12

regimes360.0ms

Accuracy

92.2% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 29.8b

bsearch171.0ms

Steps
ItersRangePoint
9
14028.172733867412
3007116902181.375
2947728123750.7354
8
-4.654091770266614e-259
-1.1349992526466847e-263
-1.3969863832568379e-263
8
-3.346688072492859e+118
-7.406473594041322e+115
-1.0306858894842368e+117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14626

end0.0ms

sample1.3s

Algorithm
intervals
Results
305.0ms1099×body2560valid
273.0ms5799×body80valid
199.0ms888×body1280valid
134.0ms2953×body80nan
80.0ms468×body640valid
38.0ms118×body5120valid
30.0ms214×body320valid
10.0ms111×body160valid