Details

Time bar (total: 4.6s)

sample737.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.887207%

Guaranteed chance to sample good point: 86.240038%

Results
10.0ms188×body80valid
8.0ms32×body1280valid
7.0ms23×body2560valid
3.0ms14×body640valid
1.0ms10×body320valid
1.0ms2×body5120valid
0.0ms9×body80nan
0.0ms2×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.9b

Counts
2 → 1

localize12.0ms

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)))
0.7b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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)))
10.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* 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))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0394773
11501683
25002673

prune157.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 6.3b

Counts
83 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.7b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
14.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 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))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms
(- (* 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))))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0470914
12126788
25001776

prune138.0ms

Filtered
66 candidates to 92 candidates (-39.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New91192
Fresh167
Picked011
Done000
Total928100

Merged error: 6.2b

Counts
100 → 8

localize15.0ms

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)))
0.7b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series78.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05251585
125501372
250011305

prune149.0ms

Filtered
72 candidates to 126 candidates (-75.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1242126
Fresh156
Picked011
Done011
Total1259134

Merged error: 6.2b

Counts
134 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
3.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.4b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06262580
129912341
250032328

prune240.0ms

Filtered
105 candidates to 160 candidates (-52.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1591160
Fresh156
Picked011
Done022
Total1609169

Merged error: 6.2b

Counts
169 → 9

regimes284.0ms

Accuracy

82.1% (5.1b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 34.3b

bsearch62.0ms

Steps
ItersRangePoint
8
5.240988409583232e-06
0.002834971680837124
0.00011782405357240769
8
-5.768218291700969e+150
-9.419834664568275e+145
-2.3719932375833216e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03816
13816

end0.0ms

sample2.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.887207%

Guaranteed chance to sample good point: 86.240038%

Results
325.0ms5887×body80valid
322.0ms1048×body2560valid
212.0ms856×body1280valid
92.0ms441×body640valid
42.0ms114×body5120valid
34.0ms232×body320valid
21.0ms362×body80nan
12.0ms126×body160valid

Profiling

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