Details

Time bar (total: 2.3s)

analyze119.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14

sample18.0ms

Algorithm
intervals
Results
6.0ms200×body80valid
2.0ms21×body640valid
2.0ms16×body320valid
1.0ms10×body1280valid
0.0ms9×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0165
1355
2745
31285
42525
53745
65145
76425
87775
910105
1016865
1150025

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.8b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
4.5b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r*
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg flip3-+ diff-log pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
6.0ms
(* (- 1.0 x) y)
7.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series22.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(* (- 1.0 x) y)
11.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0338401
11456359
25001359

prune105.0ms

Filtered
51 candidates to 72 candidates (-41.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New68472
Fresh000
Picked101
Done000
Total69473

Merged error: 0.2b

Counts
73 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.3b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
5.0ms
(/ y (+ y 1.0))
12.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series20.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(/ y (+ y 1.0))
6.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
11.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify78.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0400572
11790526
25001526

prune129.0ms

Filtered
70 candidates to 97 candidates (-38.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh033
Picked011
Done000
Total974101

Merged error: 0.2b

Counts
101 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ y 1.0))
0.5b
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
1.5b
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
4.3b
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
113×*-un-lft-identity
101×sqrt-prod
70×add-sqr-sqrt
61×add-cube-cbrt
25×distribute-lft-out
22×sqrt-div
20×associate-/r/
18×add-exp-log add-cbrt-cube
14×associate-/r* associate-/l*
11×flip3-+ flip-+
10×div-inv
7×cbrt-undiv div-exp
6×add-log-exp
5×pow1
3×associate-/l/ difference-of-squares
2×flip3-- frac-2neg associate-*l/ prod-exp clear-num flip-- cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 195
Calls
4 calls:
3.0ms
(sqrt (+ y 1.0))
19.0ms
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
15.0ms
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
31.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

series38.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ y 1.0))
7.0ms
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
13.0ms
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
13.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

simplify96.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07662435
131652150
250012138

prune327.0ms

Filtered
113 candidates to 207 candidates (-83.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2070207
Fresh022
Picked011
Done011
Total2074211

Merged error: 0.2b

Counts
211 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
0.0b
(- (/ 1 y) (/ x y))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×*-un-lft-identity
14×times-frac
6×add-log-exp difference-of-squares
5×div-inv distribute-lft-out--
4×add-cube-cbrt associate-+l+
3×sub-neg distribute-rgt-out--
2×pow1 add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
1×+-commutative flip3-- flip3-+ diff-log sum-log frac-sub flip-- flip-+ sub-div
Counts
2 → 43
Calls
2 calls:
16.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
13.0ms
(- (/ 1 y) (/ x y))

series9.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
4.0ms
(- (/ 1 y) (/ x y))

simplify77.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0224317
1627291
22875282
35001274

prune46.0ms

Filtered
33 candidates to 49 candidates (-48.5%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New48149
Fresh011
Picked011
Done022
Total48553

Merged error: 0.2b

Counts
53 → 5

regimes358.0ms

Accuracy

95.6% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03218
13218

end0.0ms

analyze78.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14

sample497.0ms

Algorithm
intervals
Results
181.0ms6153×body80valid
78.0ms700×body640valid
48.0ms333×body1280valid
45.0ms522×body320valid
19.0ms292×body160valid

Profiling

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