Details

Time bar (total: 8.0s)

sample59.0ms

Algorithm
intervals
Results
42.0ms454×body80valid

simplify107.0ms

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

rewrite103.0ms

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:
55.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
23.0ms
(* (/ 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)))
2.0ms
(sqrt PI)

series444.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
326.0ms
(* (/ 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)))))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify64.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013384946
150014033

prune618.0ms

Filtered
175 candidates to 109 candidates (62.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1696175
Fresh000
Picked101
Done000
Total1706176

Merged error: 0b

Counts
176 → 6

localize24.0ms

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 (pow (fabs x) 6)) (fabs x)) 21.0)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite64.0ms

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
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
7×associate-*l/
6×frac-times flip3-+ associate-*r/ associate-*r* flip-+
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 distribute-lft-out
Counts
4 → 156
Calls
4 calls:
25.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
18.0ms
(* (/ 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) 6)) (fabs x)) 21.0)))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series429.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
324.0ms
(* (/ 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) 6)) (fabs x)) 21.0)))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify57.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011923891
150023235

prune620.0ms

Filtered
166 candidates to 108 candidates (65.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1642166
Fresh325
Picked011
Done000
Total1675172

Merged error: 0b

Counts
172 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l/
37×add-sqr-sqrt
36×associate-*l* frac-add
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/
17×prod-exp cbrt-unprod
14×flip3-+ flip-+
13×sqrt-prod
10×pow-prod-down
7×associate-*r*
6×pow-plus pow-prod-up
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 151
Calls
4 calls:
6.0ms
(* (* (fabs x) (fabs x)) (fabs x))
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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series542.0ms

Counts
4 → 10
Calls
4 calls:
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))
470.0ms
(* (/ 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 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify68.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012335351
150014795

prune749.0ms

Filtered
161 candidates to 112 candidates (69.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1610161
Fresh033
Picked011
Done011
Total1615166

Merged error: 0b

Counts
166 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.5b
(* (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 (pow (fabs x) 6)) (fabs x)) 21.0)))) (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 (pow (fabs x) 6)) (fabs x)) 21.0)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
364×sqrt-div
337×frac-times
336×frac-add
181×associate-*r/
168×flip3-+ flip-+
154×associate-*l/
64×pow1
30×sqrt-pow1
27×add-exp-log add-cbrt-cube
26×pow-prod-down
21×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity associate-*l*
13×prod-exp cbrt-unprod
12×pow1/2
10×sqrt-prod pow-prod-up
9×times-frac
6×pow-sqr
5×associate-*r*
4×swap-sqr add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt div-inv unswap-sqr
Counts
4 → 308
Calls
4 calls:
12.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
38.0ms
(* (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 (pow (fabs x) 6)) (fabs x)) 21.0)))) (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 (pow (fabs x) 6)) (fabs x)) 21.0)))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series420.0ms

Counts
4 → 8
Calls
4 calls:
50.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
370.0ms
(* (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 (pow (fabs x) 6)) (fabs x)) 21.0)))) (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 (pow (fabs x) 6)) (fabs x)) 21.0)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify414.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
0114641885
1438741248
2500141032

prune1.6s

Filtered
316 candidates to 171 candidates (54.1%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New3160316
Fresh022
Picked011
Done022
Total3165321

Merged error: 0b

Counts
321 → 5

regimes84.0ms

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
04133
14133

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s13961×body80valid