Details

Time bar (total: 3.7s)

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

sample37.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
5.0ms256×pre80true

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0512933

prune13.0ms

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: 0.3b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 165
Calls
4 calls:
25.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
56.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
4.0ms
(sqrt PI)

series76.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
12.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify71.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049814037
149814037

prune430.0ms

Filtered
108 candidates to 175 candidates (-62.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1723175
Fresh011
Picked101
Done000
Total1734177

Merged error: 0.0b

Counts
177 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
23×associate-*l/
22×pow-prod-down
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 155
Calls
4 calls:
22.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
20.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series73.0ms

Counts
4 → 10
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
52.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify75.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049823941
149823941

prune443.0ms

Filtered
107 candidates to 165 candidates (-54.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1641165
Fresh123
Picked011
Done000
Total1654169

Merged error: 0.0b

Counts
169 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1.0 (/ (pow (fabs x) 7) 21.0))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(/ (pow (fabs x) 7) 21.0)
1.0b
(sqrt PI)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
50×times-frac
42×add-cube-cbrt *-un-lft-identity
35×add-exp-log associate-*l*
32×add-cbrt-cube
16×pow1
14×associate-*r/ prod-exp cbrt-unprod
13×sqrt-prod
12×unpow-prod-down frac-add
7×div-exp pow-prod-down associate-/l*
6×frac-times flip3-+ associate-*l/ flip-+
5×cbrt-undiv
4×associate-*r* add-log-exp sqr-pow
3×associate-/r* div-inv unswap-sqr
2×*-commutative
1×distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num
Counts
4 → 152
Calls
4 calls:
19.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1.0 (/ (pow (fabs x) 7) 21.0))))
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
5.0ms
(/ (pow (fabs x) 7) 21.0)
1.0ms
(sqrt PI)

series71.0ms

Counts
4 → 10
Calls
4 calls:
52.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1.0 (/ (pow (fabs x) 7) 21.0))))
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
11.0ms
(/ (pow (fabs x) 7) 21.0)
0.0ms
(sqrt PI)

simplify60.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049704217
149704217

prune476.0ms

Filtered
120 candidates to 162 candidates (-35.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1620162
Fresh022
Picked011
Done011
Total1624166

Merged error: 0.0b

Counts
166 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 21.0) (pow (fabs x) 7))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (* 1.0 (/ (+ (* 2.0 (/ (pow (fabs x) 3) 3.0)) (+ (* 2.0 (fabs x)) (+ (* 1.0 (/ (pow (fabs x) 5) 5.0)) (* (/ 1.0 21.0) (pow (fabs x) 7))))) (sqrt (sqrt PI)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log
49×add-sqr-sqrt
44×associate-*l*
39×times-frac
34×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
30×add-cbrt-cube
26×prod-exp
13×div-exp
12×cbrt-unprod
11×pow1
8×associate-*r*
6×cbrt-undiv unswap-sqr
5×unpow-prod-down
4×add-log-exp
3×rec-exp 1-exp associate-*r/ pow-prod-down sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ pow-exp *-commutative div-inv
1×frac-times
Counts
4 → 132
Calls
4 calls:
8.0ms
(* (/ 1.0 21.0) (pow (fabs x) 7))
33.0ms
(* (/ 1 (sqrt (sqrt PI))) (* 1.0 (/ (+ (* 2.0 (/ (pow (fabs x) 3) 3.0)) (+ (* 2.0 (fabs x)) (+ (* 1.0 (/ (pow (fabs x) 5) 5.0)) (* (/ 1.0 21.0) (pow (fabs x) 7))))) (sqrt (sqrt PI)))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series68.0ms

Counts
4 → 8
Calls
4 calls:
11.0ms
(* (/ 1.0 21.0) (pow (fabs x) 7))
56.0ms
(* (/ 1 (sqrt (sqrt PI))) (* 1.0 (/ (+ (* 2.0 (/ (pow (fabs x) 3) 3.0)) (+ (* 2.0 (fabs x)) (+ (* 1.0 (/ (pow (fabs x) 5) 5.0)) (* (/ 1.0 21.0) (pow (fabs x) 7))))) (sqrt (sqrt PI)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify83.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049432891
149432891

prune324.0ms

Filtered
92 candidates to 140 candidates (-52.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1391140
Fresh011
Picked101
Done112
Total1413144

Merged error: 0b

Counts
144 → 3

regimes72.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010649
110649

end0.0ms

sample939.0ms

Algorithm
intervals
Results
746.0ms8000×body80valid
86.0ms8000×pre80true

Profiling

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