Details

Time bar (total: 4.7s)

sample50.0ms

Algorithm
intervals
Results
9.0ms33×body2560valid
9.0ms39×body1280valid
8.0ms166×body80valid
4.0ms22×body640valid
4.0ms77×body80nan
2.0ms12×body320valid
1.0ms2×body5120valid
0.0ms2×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: 35.8b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (* 3.0 a) c)
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0307469
11303428
25001417

prune178.0ms

Filtered
72 candidates to 52 candidates (72.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New621072
Fresh000
Picked011
Done000
Total621173

Merged error: 11.9b

Counts
73 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.0b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
174.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06472692
131142439
250012426

prune412.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New15610166
Fresh189
Picked101
Done101
Total15918177

Merged error: 10.7b

Counts
177 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3.0 a) c))
0.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.1b
(/ (* 3.0 a) (* 3.0 (* a c)))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

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:
3.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0417636
12439522
25001492

prune223.0ms

Filtered
82 candidates to 54 candidates (65.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New76682
Fresh61117
Picked101
Done000
Total8317100

Merged error: 6.9b

Counts
100 → 17

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.6b
(- (* b b) (* (* 3.0 a) c))
0.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

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:
13.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(- (* 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)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
49.0ms
(- (* b b) (* (* 3.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0432926
11830797
25003784

prune181.0ms

Filtered
94 candidates to 61 candidates (64.9%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New88694
Fresh8816
Picked011
Done000
Total9615111

Merged error: 6.2b

Counts
111 → 15

regimes368.0ms

Accuracy

93.1% (1.5b remaining)

Error of 8.9b against oracle of 7.4b and baseline of 29.7b

bsearch163.0ms

Steps
ItersRangePoint
8
2.6663703237532384e+123
2.0613724286176698e+127
1.1612125867005037e+127
7
-2.7658122324780073e-177
-4.963613050543331e-179
-5.591719996403657e-179
5
-2.783673024614503e+98
-8.233152822480874e+97
-2.720129631643668e+98

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05042
15042

end0.0ms

sample1.4s

Algorithm
intervals
Results
335.0ms1133×body2560valid
299.0ms5778×body80valid
214.0ms895×body1280valid
138.0ms2864×body80nan
86.0ms464×body640valid
41.0ms107×body5120valid
35.0ms248×body320valid
12.0ms110×body160valid