Details

Time bar (total: 3.3s)

analyze5.0ms

Algorithm
search

sample35.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
3.0ms256×pre80true

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize31.0ms

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)

rewrite61.0ms

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:
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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
22.0ms
(* (/ 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)

series73.0ms

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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
13.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
7.0ms
(* (/ 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 (27.0ms)

IterNodesCost
011964518
150013850

prune384.0ms

Filtered
108 candidates to 165 candidates (-52.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1605165
Fresh000
Picked101
Done000
Total1615166

Merged error: 0b

Counts
166 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
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))))))

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
(* 0.047619047619047616 (pow (fabs x) 7))
5.0ms
(* 0.2 (pow (fabs x) 5))
8.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
15.0ms
(* (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))))))

series74.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
12.0ms
(* 0.2 (pow (fabs x) 5))
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
44.0ms
(* (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))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05931430
127951324
250021320

prune325.0ms

Filtered
87 candidates to 134 candidates (-54.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1322134
Fresh404
Picked011
Done000
Total1363139

Merged error: 0b

Counts
139 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×times-frac
16×add-exp-log
15×sqrt-prod
10×add-cbrt-cube
8×unpow-prod-down
7×unswap-sqr
6×associate-*l* 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
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
13.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) (sqrt PI))
1.0ms
(sqrt PI)

series63.0ms

Counts
4 → 10
Calls
4 calls:
12.0ms
(* 0.2 (pow (fabs x) 5))
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
44.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify61.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04021503
117991400
250011397

prune448.0ms

Filtered
76 candidates to 120 candidates (-57.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1191120
Fresh101
Picked011
Done011
Total1203123

Merged error: 0b

Counts
123 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×add-exp-log
12×add-cube-cbrt *-un-lft-identity associate-*r*
11×add-cbrt-cube
6×pow1 sqrt-prod
4×unpow-prod-down cube-prod prod-exp add-log-exp unswap-sqr
3×times-frac associate-*l* associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp cbrt-unprod associate-/l/ sqr-pow
1×cube-mult pow-to-exp frac-2neg flip3-+ unpow3 pow-exp clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 80
Calls
4 calls:
9.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
19.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series51.0ms

Counts
4 → 8
Calls
4 calls:
7.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
44.0ms
(/ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify48.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0318907
11338773
25001769

prune170.0ms

Filtered
58 candidates to 88 candidates (-51.7%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New88088
Fresh000
Picked011
Done022
Total88391

Merged error: 0b

Counts
91 → 3

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03819
13819

end0.0ms

analyze5.0ms

Algorithm
search

sample966.0ms

Algorithm
intervals
Results
783.0ms8000×body80valid
83.0ms8000×pre80true

Profiling

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