Details

Time bar (total: 4.0s)

sample54.0ms

Algorithm
intervals
Results
10.0ms36×body2560valid
9.0ms184×body80valid
6.0ms23×body1280valid
4.0ms89×body80nan
3.0ms18×body640valid
1.0ms4×body5120valid
1.0ms6×body320valid
1.0ms8×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: 35.9b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.1b
(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)))

series67.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (+ (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)))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0396773
11550683
25002673

prune172.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New73982
Fresh000
Picked011
Done000
Total731083

Merged error: 5.7b

Counts
83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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))))
19.0ms
(/ (/ (+ 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)))

series132.0ms

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))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06462693
131632447
250032434

prune317.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1615166
Fresh358
Picked101
Done011
Total16511176

Merged error: 5.6b

Counts
176 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- distribute-rgt-neg-in flip3-+ neg-log flip-+
Counts
4 → 60
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms

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

simplify104.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0212558
1801538
23387526
35001522

prune248.0ms

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

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New72072
Fresh099
Picked011
Done011
Total721183

Merged error: 5.6b

Counts
83 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
0.7b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.8b
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ 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 → 72
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series84.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0486952
12894749
25002741

prune110.0ms

Filtered
58 candidates to 84 candidates (-44.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82284
Fresh358
Picked101
Done022
Total86995

Merged error: 5.6b

Counts
95 → 9

regimes457.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.0b

bsearch106.0ms

Steps
ItersRangePoint
7
7.012417207579252e+108
1.3633655355432952e+110
8.178847879023253e+109
9
6.029216363892667e-301
1.0518452559341914e-293
7.57507927592513e-301
9
-8.123118303304505e+80
-8.66777673642249e+74
-3.453036615513107e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04727
14927
24927

end0.0ms

sample1.6s

Algorithm
intervals
Results
331.0ms1105×body2560valid
307.0ms5835×body80valid
204.0ms853×body1280valid
149.0ms2894×body80nan
90.0ms472×body640valid
43.0ms112×body5120valid
35.0ms232×body320valid
12.0ms125×body160valid

Profiling

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