Details

Time bar (total: 2.7s)

analyze6.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
75%25%0%5
87.5%12.5%0%6
93.7%6.2%0%7
96.8%3.1%0%8
98.4%1.6%0%9
99.2%0.8%0%10
99.6%0.4%0%11
99.8%0.2%0%12
99.9%0.1%0%13
99.9%0.1%0.1%14

sample39.0ms

Algorithm
intervals
Results
10.0ms49×body640valid
7.0ms134×body80valid
7.0ms39×body320valid
5.0ms17×body1280valid
2.0ms17×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02215
12215

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 10.1b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.8b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l- associate-+l+
Counts
4 → 112
Calls
4 calls:
8.0ms
(/ 1.0 (+ x 1.0))
8.0ms
(/ 1.0 (- x 1.0))
29.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
56.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series17.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1.0 (+ x 1.0))
2.0ms
(/ 1.0 (- x 1.0))
3.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
9.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
051001596

prune199.0ms

Filtered
95 candidates to 124 candidates (-30.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1186124
Fresh000
Picked101
Done000
Total1196125

Merged error: 0.5b

Counts
125 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
2.8b
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
2.8b
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
2.8b
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
137×*-un-lft-identity
48×times-frac
32×distribute-lft-out
28×distribute-lft-out--
19×add-log-exp
12×frac-add
9×cbrt-prod
6×sum-log
5×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log flip3-- flip3-+ frac-sub add-cbrt-cube flip-- flip-+
3×+-commutative associate-+r- sub-neg associate-+r+ diff-log
1×pow1/3
Counts
4 → 91
Calls
4 calls:
32.0ms
(cbrt (+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
31.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
44.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
31.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))

series49.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(cbrt (+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
9.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
9.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
9.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049572386
149572386

prune288.0ms

Filtered
72 candidates to 103 candidates (-43.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1030103
Fresh055
Picked011
Done000
Total1036109

Merged error: 0.5b

Counts
109 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
14.0b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
38×cbrt-prod
34×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1 distribute-lft-out--
10×swap-sqr
9×flip3-- flip-- add-log-exp
8×pow1/3 associate-*r* associate-*l*
6×add-exp-log times-frac difference-of-squares
5×distribute-lft-out
4×frac-times add-cbrt-cube unswap-sqr
3×frac-add
2×associate-*r/ pow-prod-down associate-*l/ sum-log pow-sqr pow-prod-up
1×+-commutative pow2 associate-+l- sub-neg associate-+l+ flip3-+ pow-plus diff-log prod-exp *-commutative frac-sub cbrt-unprod flip-+
Counts
4 → 107
Calls
4 calls:
3.0ms
(cbrt (- x 1.0))
3.0ms
(cbrt (- x 1.0))
11.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
79.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series69.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(cbrt (- x 1.0))
15.0ms
(cbrt (- x 1.0))
16.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
24.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify49.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050381643

prune238.0ms

Filtered
87 candidates to 119 candidates (-36.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1190119
Fresh044
Picked011
Done011
Total1196125

Merged error: 0.5b

Counts
125 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
0.0b
(- (* 1.0 x) (* (+ 1.0 x) 2.0))
0.0b
(* x (- (* x x) (* 1.0 1.0)))
16.5b
(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-*r/
20×flip3-- flip--
16×frac-add
14×add-sqr-sqrt
12×frac-times
10×*-un-lft-identity
9×flip3-+ flip-+
8×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube add-log-exp
7×distribute-rgt-in sub-neg distribute-lft-in associate-*r*
6×associate-*l/
4×associate-+r+
2×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×+-commutative diff-log sum-log distribute-lft-out--
Counts
4 → 97
Calls
4 calls:
10.0ms
(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
3.0ms
(- (* 1.0 x) (* (+ 1.0 x) 2.0))
6.0ms
(* x (- (* x x) (* 1.0 1.0)))
11.0ms
(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series14.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
3.0ms
(- (* 1.0 x) (* (+ 1.0 x) 2.0))
6.0ms
(* x (- (* x x) (* 1.0 1.0)))
1.0ms
(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify49.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050922794

prune221.0ms

Filtered
86 candidates to 109 candidates (-26.7%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1090109
Fresh033
Picked011
Done022
Total1096115

Merged error: 0.5b

Counts
115 → 6

regimes52.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 10.1b

bsearch49.0ms

Steps
ItersRangePoint
7
44.21150822928992
2042.1563703702857
511.7848760495989
10
-265367843.15622452
-0.023916813597021216
-838439.3309523697

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04757
14757

end0.0ms

analyze6.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
75%25%0%5
87.5%12.5%0%6
93.7%6.2%0%7
96.8%3.1%0%8
98.4%1.6%0%9
99.2%0.8%0%10
99.6%0.4%0%11
99.8%0.2%0%12
99.9%0.1%0%13
99.9%0.1%0.1%14

sample765.0ms

Algorithm
intervals
Results
272.0ms1886×body640valid
160.0ms4122×body80valid
103.0ms944×body320valid
100.0ms550×body1280valid
36.0ms498×body160valid
0.0ms1×body80invalid

Profiling

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