Details

Time bar (total: 2.8s)

analyze5.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14

sample34.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
3.0ms256×pre80true

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0502233

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 5) 5.0)
0.1b
(/ (pow (fabs x) 3) 3.0)
0.1b
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
1.0b
(sqrt PI)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
69×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
32×associate-*r/
24×unpow-prod-down
22×associate-*l*
19×add-exp-log associate-/l*
16×frac-add
13×sqrt-prod add-cbrt-cube
12×flip3-+ cube-prod flip-+
8×frac-times sqr-pow
7×pow1 div-exp
6×associate-/r*
4×cube-mult unpow3 add-log-exp
3×cbrt-undiv associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg pow-exp prod-exp clear-num cbrt-unprod
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 183
Calls
4 calls:
5.0ms
(/ (pow (fabs x) 5) 5.0)
5.0ms
(/ (pow (fabs x) 3) 3.0)
23.0ms
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
1.0ms
(sqrt PI)

series74.0ms

Counts
4 → 10
Calls
4 calls:
10.0ms
(/ (pow (fabs x) 5) 5.0)
7.0ms
(/ (pow (fabs x) 3) 3.0)
57.0ms
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.0ms
(sqrt PI)

simplify62.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052304238

prune539.0ms

Filtered
133 candidates to 193 candidates (-45.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1912193
Fresh101
Picked011
Done000
Total1923195

Merged error: 0b

Counts
195 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 7) 0.047619047619047616)
0.1b
(* (pow (fabs x) 5) 0.2)
0.1b
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))
0.1b
(* (pow (fabs x) 3) 0.6666666666666666)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
42×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down associate-*r* add-cbrt-cube
11×times-frac
10×prod-exp
6×pow1 sqr-pow
4×cube-prod *-commutative cbrt-unprod add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
5.0ms
(* (pow (fabs x) 7) 0.047619047619047616)
5.0ms
(* (pow (fabs x) 5) 0.2)
15.0ms
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))
6.0ms
(* (pow (fabs x) 3) 0.6666666666666666)

series75.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (pow (fabs x) 7) 0.047619047619047616)
9.0ms
(* (pow (fabs x) 5) 0.2)
47.0ms
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))
7.0ms
(* (pow (fabs x) 3) 0.6666666666666666)

simplify72.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
050142303

prune325.0ms

Filtered
94 candidates to 134 candidates (-42.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1331134
Fresh101
Picked101
Done011
Total1352137

Merged error: 0b

Counts
137 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 5) 0.2)
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.3b
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))) (sqrt PI))
1.0b
(sqrt PI)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
18×times-frac
16×add-exp-log
15×associate-*r* sqrt-prod
10×associate-*l* add-cbrt-cube
8×unpow-prod-down
7×unswap-sqr
6×prod-exp associate-/r*
5×pow1
4×cube-prod add-log-exp sqr-pow
3×associate-/l*
2×pow-to-exp pow-exp *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv cube-mult rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 unpow3 div-exp clear-num flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
5.0ms
(* (pow (fabs x) 5) 0.2)
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
13.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))) (sqrt PI))
1.0ms
(sqrt PI)

series63.0ms

Counts
4 → 10
Calls
4 calls:
9.0ms
(* (pow (fabs x) 5) 0.2)
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
46.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))) (sqrt PI))
0.0ms
(sqrt PI)

simplify46.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049402392
149402392

prune239.0ms

Filtered
79 candidates to 120 candidates (-51.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1200120
Fresh000
Picked011
Done011
Total1202122

Merged error: 0b

Counts
122 → 2

regimes62.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03233
13233

end0.0ms

analyze5.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14

sample923.0ms

Algorithm
intervals
Results
743.0ms8000×body80valid
80.0ms8001×pre80true
0.0ms1×body80invalid

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