Details

Time bar (total: 7.6s)

sample55.0ms

Algorithm
intervals
Results
38.0ms482×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

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
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite66.0ms

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
22×pow-prod-down
15×associate-*l/
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:
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) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
26.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series447.0ms

Counts
4 → 10
Calls
4 calls:
337.0ms
(* (/ 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)))))
58.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
52.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify62.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011964518
150013850

prune658.0ms

Filtered
165 candidates to 108 candidates (65.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1605165
Fresh000
Picked011
Done000
Total1606166

Merged error: 0b

Counts
166 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 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)))))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 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))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×associate-*l*
47×add-sqr-sqrt
40×associate-*l/
38×times-frac
36×frac-add
35×add-cube-cbrt *-un-lft-identity sqrt-div
31×frac-times associate-*r/
18×flip3-+ flip-+
13×pow1
11×add-exp-log add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 155
Calls
4 calls:
22.0ms
(* (sqrt (/ 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)))))
33.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 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))))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series914.0ms

Counts
4 → 8
Calls
4 calls:
528.0ms
(* (sqrt (/ 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)))))
386.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 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))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify91.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09348633
150017497

prune952.0ms

Filtered
163 candidates to 133 candidates (81.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1612163
Fresh224
Picked101
Done011
Total1645169

Merged error: 0b

Counts
169 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.3b
(* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4)))
1.0b
(sqrt PI)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
52×prod-exp
39×add-sqr-sqrt
34×sqrt-prod
31×add-cube-cbrt *-un-lft-identity
30×associate-*r*
29×associate-*l*
27×times-frac
20×add-cbrt-cube
17×unpow-prod-down pow-exp
10×cbrt-unprod
8×associate-*r/ div-exp
7×pow1 associate-*l/
5×pow-to-exp
4×rec-exp 1-exp cube-prod add-log-exp unswap-sqr
3×flip3-+ sqrt-div *-commutative flip-+ sqr-pow
2×frac-times div-inv
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 pow-prod-down
Counts
4 → 142
Calls
4 calls:
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
23.0ms
(* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4))
25.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4)))
2.0ms
(sqrt PI)

series951.0ms

Counts
4 → 10
Calls
4 calls:
51.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
522.0ms
(* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4))
378.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (* (sqrt 1.0) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7)))))) (pow (/ 1 PI) 1/4)))
0.0ms
(sqrt PI)

simplify115.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07272837
139252547
250022547

prune621.0ms

Filtered
152 candidates to 89 candidates (58.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1520152
Fresh033
Picked011
Done011
Total1525157

Merged error: 0b

Counts
157 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.1b
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
0.3b
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
1.0b
(sqrt PI)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
107×add-exp-log
72×prod-exp
52×pow1
51×add-cbrt-cube
40×pow-prod-up
28×cbrt-unprod
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
15×times-frac
14×associate-*r*
9×div-exp sqrt-prod
8×pow2 pow-to-exp pow-plus pow-exp pow-sqr
7×associate-*r/
6×associate-*l/ frac-add associate-/r* associate-/l/
5×cbrt-undiv
4×pow-prod-down add-log-exp
3×flip3-+ flip-+
2×associate-*l* *-commutative div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l*
Counts
4 → 138
Calls
4 calls:
13.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
12.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
35.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
1.0ms
(sqrt PI)

series464.0ms

Counts
4 → 10
Calls
4 calls:
59.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
60.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
344.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
0.0ms
(sqrt PI)

simplify118.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08052243
138121671
250011504

prune370.0ms

Filtered
148 candidates to 72 candidates (48.6%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1471148
Fresh202
Picked011
Done112
Total1503153

Merged error: 0b

Counts
153 → 3

regimes146.0ms

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
03725
13725

end0.0ms

sample1.1s

Algorithm
intervals
Results
960.0ms13929×body80valid