Details

Time bar (total: 3.5s)

sample50.0ms

Algorithm
intervals
Results
10.0ms196×body80valid
8.0ms26×body2560valid
6.0ms26×body1280valid
4.0ms75×body80nan
3.0ms16×body640valid
1.0ms4×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

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: 31.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

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

series90.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune169.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 6.3b

Counts
83 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite80.0ms

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:
14.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
20.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series133.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
06462693
131632447
250032434

prune268.0ms

Filtered
166 candidates to 111 candidates (33.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1633166
Fresh347
Picked011
Done000
Total1668174

Merged error: 6.2b

Counts
174 → 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))))))
1.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
21.3b
(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))))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series72.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* 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
05281585
125961372
250011305

prune147.0ms

Filtered
126 candidates to 71 candidates (43.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1260126
Fresh066
Picked011
Done011
Total1268134

Merged error: 6.2b

Counts
134 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (* b b) (* (* 4.0 a) c))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series46.0ms

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

simplify78.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0147474
1570446
22550444
35001442

prune121.0ms

Filtered
66 candidates to 50 candidates (24.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New66066
Fresh055
Picked011
Done022
Total66874

Merged error: 6.2b

Counts
74 → 8

regimes264.0ms

Accuracy

82.6% (4.8b remaining)

Error of 9.8b against oracle of 5.0b and baseline of 32.3b

bsearch55.0ms

Steps
ItersRangePoint
8
3.4713192377217875e-36
1.5663447360869123e-31
2.8203535769129045e-33
7
-6.682283173913537e+118
-3.724757707733592e+117
-2.4933470885408413e+118

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.6s

Algorithm
intervals
Results
305.0ms5853×body80valid
296.0ms999×body2560valid
227.0ms919×body1280valid
147.0ms3010×body80nan
78.0ms412×body640valid
44.0ms123×body5120valid
37.0ms261×body320valid
13.0ms131×body160valid

Profiling

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