Details

Time bar (total: 7.3s)

sample50.0ms

Algorithm
intervals
Results
34.0ms437×body80valid

simplify106.0ms

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

localize25.0ms

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) (* (* (* (* (* (* (fabs x) (fabs x)) (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)

rewrite67.0ms

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:
22.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
24.0ms
(* (/ 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)))
1.0ms
(sqrt PI)

series447.0ms

Counts
4 → 10
Calls
4 calls:
64.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
338.0ms
(* (/ 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)))))
45.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify61.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011964518
150023785

prune835.0ms

Filtered
165 candidates to 108 candidates (65.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1614165
Fresh000
Picked101
Done000
Total1624166

Merged error: 0b

Counts
166 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
29×associate-*r*
25×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down 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
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
16.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

series458.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* 0.2 (pow (fabs x) 5))
73.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
279.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))
46.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

simplify85.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05931430
127951324
250021320

prune464.0ms

Filtered
134 candidates to 87 candidates (64.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh033
Picked011
Done000
Total1344138

Merged error: 0b

Counts
138 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) (cbrt 1.0)) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
43×add-cbrt-cube
34×add-sqr-sqrt
31×times-frac
27×sqrt-prod
26×associate-*l*
21×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
14×cbrt-undiv div-exp associate-*r*
13×pow1
6×unswap-sqr
4×pow-prod-down add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 121
Calls
4 calls:
12.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
33.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) (cbrt 1.0)) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series399.0ms

Counts
4 → 8
Calls
4 calls:
32.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
367.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt PI))) (/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) (cbrt 1.0)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify103.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06913865
133942991
250012734

prune518.0ms

Filtered
129 candidates to 79 candidates (61.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh022
Picked011
Done011
Total1294133

Merged error: 0b

Counts
133 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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
(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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)))))) (sqrt (+ (+ (+ (* 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)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
202×associate-*l/
180×sqrt-div frac-add
126×frac-times
90×flip3-+ flip-+
54×associate-*r/
46×add-sqr-sqrt
39×add-exp-log add-cbrt-cube
36×associate-*l*
31×times-frac
29×add-cube-cbrt *-un-lft-identity
23×sqrt-prod
21×pow1
19×prod-exp cbrt-unprod
13×associate-*r*
10×pow-prod-down
6×unswap-sqr
5×cbrt-undiv div-exp
4×add-log-exp
3×*-commutative
2×div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 231
Calls
4 calls:
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
23.0ms
(* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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
(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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)))))) (sqrt (+ (+ (+ (* 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))))))
2.0ms
(sqrt PI)

series713.0ms

Counts
4 → 10
Calls
4 calls:
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
324.0ms
(* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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))))))
339.0ms
(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (+ (+ (* 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)))))) (sqrt (+ (+ (+ (* 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)

simplify302.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
0131628321
1493126324
2500226292

prune1.2s

Filtered
241 candidates to 151 candidates (62.7%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2410241
Fresh011
Picked011
Done022
Total2414245

Merged error: 0b

Counts
245 → 4

regimes104.0ms

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
03819
13819

end0.0ms

sample1.1s

Algorithm
intervals
Results
950.0ms13908×body80valid