Details

Time bar (total: 3.1s)

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

sample30.0ms

Algorithm
intervals
Results
9.0ms133×body80valid
9.0ms63×body640valid
3.0ms28×body320valid
2.0ms14×body1280valid
1.0ms18×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02215
12215

prune4.0ms

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: 9.9b

Counts
2 → 1

localize8.0ms

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)))

rewrite65.0ms

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:
5.0ms
(/ 1.0 (- x 1.0))
5.0ms
(/ 1.0 (+ x 1.0))
19.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
32.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series18.0ms

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))
10.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051001596

prune189.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1204124
Fresh000
Picked101
Done000
Total1214125

Merged error: 0.2b

Counts
125 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
0.6b
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
0.6b
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
19.0b
(+ (* (* (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (/ 1.0 (- x 1.0)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
153×cbrt-div
81×frac-times
63×frac-add
51×flip3-- frac-sub flip--
43×add-sqr-sqrt
40×*-un-lft-identity
30×cbrt-prod
27×associate-*l/
24×times-frac
15×associate-*r/
12×difference-of-squares
9×distribute-lft-out--
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 distribute-lft-out
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 137
Calls
4 calls:
17.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
17.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
20.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
73.0ms
(+ (* (* (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (/ 1.0 (- x 1.0)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
9.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
9.0ms
(cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
14.0ms
(+ (* (* (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (/ 1.0 (- x 1.0)))

simplify78.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
052368775

prune393.0ms

Filtered
89 candidates to 149 candidates (-67.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1481149
Fresh033
Picked101
Done000
Total1494153

Merged error: 0.2b

Counts
153 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
0.2b
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
6.4b
(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
14.4b
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
16×add-exp-log add-cbrt-cube
13×flip3-+ flip-+
12×frac-times
11×associate-/r/ associate-/l/
10×add-log-exp
9×times-frac
8×frac-add distribute-lft-out
5×associate-*r/ associate-*l/
4×pow1 cbrt-undiv add-sqr-sqrt add-cube-cbrt flip3-- div-exp prod-exp flip-- cbrt-unprod
3×+-commutative sum-log
2×sub-neg associate-+l+
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
18.0ms
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
17.0ms
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
24.0ms
(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
70.0ms
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

series32.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
3.0ms
(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
8.0ms
(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
18.0ms
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

simplify34.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
054012231

prune215.0ms

Filtered
78 candidates to 98 candidates (-25.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New97198
Fresh033
Picked011
Done000
Total975102

Merged error: 0.0b

Counts
102 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (* x x))
0.6b
(/ 2.0 (pow x 4))
1.7b
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (/ 2.0 (* x x)) (- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3))))) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
8.2b
(- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
62×times-frac
32×*-un-lft-identity
26×add-exp-log
24×add-cube-cbrt
23×add-cbrt-cube associate-/l/
21×frac-times unpow-prod-down frac-add
20×difference-of-squares
13×flip3-+ flip-+ sqr-pow
11×associate-/r/
9×flip3-- div-exp associate-/r* flip--
8×associate-*r/
7×cbrt-undiv associate-/l*
6×add-log-exp
5×associate-*l/ prod-exp frac-sub cbrt-unprod div-inv distribute-lft-out--
4×pow1 cube-prod
3×frac-2neg clear-num
1×pow-to-exp sub-neg diff-log pow-exp
Counts
4 → 158
Calls
4 calls:
4.0ms
(/ 2.0 (* x x))
5.0ms
(/ 2.0 (pow x 4))
111.0ms
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (/ 2.0 (* x x)) (- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3))))) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
49.0ms
(- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3)))

series23.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ 2.0 (* x x))
4.0ms
(/ 2.0 (pow x 4))
8.0ms
(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (/ 2.0 (* x x)) (- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3))))) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
9.0ms
(- (/ 2.0 (pow x 4)) (/ 2.0 (pow x 3)))

simplify65.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049783436
149783436

prune457.0ms

Filtered
123 candidates to 170 candidates (-38.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1664170
Fresh033
Picked101
Done011
Total1678175

Merged error: 0b

Counts
175 → 8

regimes70.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 28.6b

bsearch44.0ms

Steps
ItersRangePoint
8
0.0009046501007225119
3.194250034388108
0.915438559338819
10
-3.0494668563944933
-9.611769796425194e-12
-1.0137471735315313

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05478
15478

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

sample777.0ms

Algorithm
intervals
Results
281.0ms1910×body640valid
161.0ms4130×body80valid
106.0ms569×body1280valid
102.0ms929×body320valid
33.0ms462×body160valid
0.0ms1×body80invalid

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