Details

Time bar (total: 3.9s)

sample53.0ms

Algorithm
intervals
Results
10.0ms25×body2560valid
10.0ms196×body80valid
6.0ms27×body1280valid
4.0ms75×body80nan
3.0ms16×body640valid
1.0ms4×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.8b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
21.3b
(sqrt (- (* b b) (* (* 3.0 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) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms
(- (* b b) (* (* 3.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0391774
11518684
25001674

prune167.0ms

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: 6.4b

Counts
83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.6b
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite46.0ms

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) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series133.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06442693
131432447
250012434

prune312.0ms

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

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1624166
Fresh268
Picked011
Done011
Total16412176

Merged error: 6.3b

Counts
176 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0b
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
9.7b
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
21.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
54×add-cbrt-cube
40×div-exp
30×prod-exp
22×cbrt-undiv
20×add-sqr-sqrt
19×*-un-lft-identity
16×cbrt-unprod
8×times-frac 1-exp associate-/l* add-log-exp
7×add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 107
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
12.0ms
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series88.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
33.0ms
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
24.0ms
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07781660
140841318
250021306

prune179.0ms

Filtered
68 candidates to 119 candidates (-75.0%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1181119
Fresh189
Picked011
Done022
Total11912131

Merged error: 6.2b

Counts
131 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.2b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
21.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (* 3.0 a) c)
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series42.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* 3.0 a) c)
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0302468
11299428
25002417

prune88.0ms

Filtered
52 candidates to 72 candidates (-38.5%)
Pruning

12 alts after pruning (8 fresh and 4 done)

PrunedKeptTotal
New72072
Fresh088
Picked011
Done033
Total721284

Merged error: 6.2b

Counts
84 → 12

regimes674.0ms

Accuracy

82.5% (4.8b remaining)

Error of 9.8b against oracle of 5.0b and baseline of 32.4b

bsearch58.0ms

Steps
ItersRangePoint
8
3.4713192377217875e-36
1.5663447360869123e-31
2.8203535769129045e-33
7
-6.682283173913537e+118
-3.724757707733592e+117
-2.5592132314298372e+118

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03316
13316

end0.0ms

sample1.6s

Algorithm
intervals
Results
298.0ms5853×body80valid
293.0ms999×body2560valid
223.0ms922×body1280valid
152.0ms3009×body80nan
81.0ms408×body640valid
43.0ms122×body5120valid
37.0ms261×body320valid
13.0ms131×body160valid

Profiling

Loading profile data...