Details

Time bar (total: 5.2s)

sample60.0ms

Algorithm
intervals
Results
12.0ms44×body2560valid
9.0ms188×body80valid
7.0ms33×body1280valid
5.0ms105×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

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))
1.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.1b
(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))
11.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
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)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0396773
11550683
25002673

prune387.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh000
Picked101
Done000
Total74983

Merged error: 5.9b

Counts
83 → 9

localize16.0ms

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)))

rewrite48.0ms

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
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ (+ 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)))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series141.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06462693
131632447
250032434

prune962.0ms

Filtered
166 candidates to 111 candidates (33.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1651166
Fresh088
Picked011
Done000
Total16510175

Merged error: 5.8b

Counts
175 → 10

localize16.0ms

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)))

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)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
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)))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0472914
12176788
25001776

prune375.0ms

Filtered
92 candidates to 65 candidates (29.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New90292
Fresh178
Picked011
Done011
Total9111102

Merged error: 5.8b

Counts
102 → 11

localize10.0ms

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)))

rewrite25.0ms

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:
10.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0382774
11385699
25001697

prune300.0ms

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

regimes588.0ms

Accuracy

83.3% (4.5b remaining)

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

bsearch168.0ms

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
313.0ms1089×body2560valid
288.0ms5799×body80valid
213.0ms910×body1280valid
138.0ms2913×body80nan
91.0ms496×body640valid
41.0ms116×body5120valid
31.0ms229×body320valid
9.0ms93×body160valid

Profiling

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