Details

Time bar (total: 7.0s)

sample67.0ms

Algorithm
intervals
Results
12.0ms44×body2560valid
12.0ms33×body1280valid
9.0ms188×body80valid
6.0ms105×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.8b

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)))
1.0b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:
12.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series437.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
57.0ms
(- (* b b) (* 4.0 (* a c)))
105.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0394773
11501683
25002673

prune400.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New721082
Fresh000
Picked101
Done000
Total731083

Merged error: 5.9b

Counts
83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.0b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
27.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

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:
11.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.0s

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
295.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
554.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
92.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06352693
129742447
250012434

prune932.0ms

Filtered
166 candidates to 111 candidates (33.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1651166
Fresh099
Picked011
Done000
Total16511176

Merged error: 5.8b

Counts
176 → 11

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)))
1.0b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:
15.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
58.0ms
(- (* b b) (* 4.0 (* a c)))
99.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
93.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0470914
12126788
25001776

prune361.0ms

Filtered
92 candidates to 65 candidates (29.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New91192
Fresh189
Picked011
Done011
Total9211103

Merged error: 5.8b

Counts
103 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
27.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
11.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
57.0ms
(- (* b b) (* 4.0 (* a c)))
99.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
91.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0380774
11335699
25001697

prune305.0ms

Filtered
84 candidates to 60 candidates (28.6%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New82284
Fresh268
Picked011
Done022
Total841195

Merged error: 5.8b

Counts
95 → 11

regimes438.0ms

Accuracy

83.3% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 32.8b

bsearch163.0ms

Steps
ItersRangePoint
9
1.4958858181332487e-84
1.457638978688563e-75
7.723146983287944e-82
10
-8.56091843340189e+161
-1.1976703346365243e+147
-1.0090011346354097e+152

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03114
13114

end0.0ms

sample1.6s

Algorithm
intervals
Results
319.0ms1089×body2560valid
303.0ms5799×body80valid
221.0ms910×body1280valid
143.0ms2913×body80nan
94.0ms496×body640valid
42.0ms116×body5120valid
32.0ms229×body320valid
9.0ms93×body160valid

Profiling

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