Details

Time bar (total: 7.3s)

sample1.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results
12.0ms38×body2560valid
10.0ms39×body1280valid
8.0ms158×body80valid
2.0ms10×body640valid
1.0ms7×body320valid
1.0ms13×body80nan
0.0ms8×body80invalid
0.0ms4×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.2b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.2b
(sqrt (- (* b b) (* 4.0 (* 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
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0394773
11501683
25002673

prune164.0ms

Filtered
63 candidates to 82 candidates (-30.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New711182
Fresh000
Picked101
Done000
Total721183

Merged error: 6.5b

Counts
83 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.4b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.2b
(sqrt (- (* b b) (* 4.0 (* 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:
9.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06352693
129742447
250012434

prune273.0ms

Filtered
111 candidates to 166 candidates (-49.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1642166
Fresh3710
Picked011
Done000
Total16710177

Merged error: 6.4b

Counts
177 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.2b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
12.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05251585
125501372
250011305

prune147.0ms

Filtered
70 candidates to 126 candidates (-80.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1251126
Fresh178
Picked011
Done011
Total12610136

Merged error: 6.4b

Counts
136 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div sum-log add-cbrt-cube distribute-lft-out
2×+-commutative neg-sub0 associate-+l- rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 60
Calls
4 calls:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0211596
1802556
23351536
35001532

prune138.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh077
Picked011
Done022
Total721082

Merged error: 6.4b

Counts
82 → 10

regimes477.0ms

Accuracy

84.1% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 32.6b

bsearch57.0ms

Steps
ItersRangePoint
8
4.0677208531155924e-94
2.3220863842839214e-90
4.101060593978102e-91
6
-6.29337037593488e+108
-4.021940037911578e+107
-1.145940795336922e+108

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample3.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results
332.0ms1087×body2560valid
278.0ms5080×body80valid
213.0ms868×body1280valid
91.0ms473×body640valid
38.0ms106×body5120valid
38.0ms258×body320valid
19.0ms345×body80nan
15.0ms287×body80invalid
14.0ms128×body160valid

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