Details

Time bar (total: 22.4s)

sample66.0ms

Algorithm
intervals
Results
39.0ms428×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (210.0ms)

IterNodesCost
02867
16967
222848
387537
4415537
done500237

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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)))) (* (/ 1.0 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)

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
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 → 135
Calls
4 calls:
19.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.8s
(* (/ 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)))))
99.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series637.0ms

Counts
4 → 10
Calls
4 calls:
46.0ms
(* (* (fabs x) (fabs x)) (fabs x))
534.0ms
(* (/ 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)))))
57.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify783.0ms

Counts
145 → 145
Iterations

Useful iterations: done (770.0ms)

IterNodesCost
02836867
110095325
done50014175

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize27.0ms

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
(* 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))))))

rewrite347.0ms

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:
12.0ms
(* 0.2 (pow (fabs x) 5))
25.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
27.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
278.0ms
(* (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))))))

series632.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* 0.2 (pow (fabs x) 5))
101.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
50.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
410.0ms
(* (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))))))

simplify2.2s

Counts
134 → 134
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02282601
16402455
230582296
done50012292

prune849.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

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 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
9.2b
(sqrt (pow (fabs x) 7))
9.2b
(sqrt (pow (fabs x) 7))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×sqrt-prod
22×*-un-lft-identity
21×add-cube-cbrt
19×associate-*l*
15×associate-*r*
12×unpow-prod-down
11×add-exp-log times-frac
8×add-cbrt-cube unswap-sqr
6×pow1 rem-sqrt-square sqr-pow
4×cube-prod prod-exp add-log-exp
3×sqrt-div
2×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ *-commutative cbrt-unprod flip-+
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 pow-prod-down associate-*l/ pow-exp div-inv
Counts
4 → 110
Calls
4 calls:
16.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
247.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (* 0.047619047619047616 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
3.0ms
(sqrt (pow (fabs x) 7))
3.0ms
(sqrt (pow (fabs x) 7))

series681.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
457.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (* 0.047619047619047616 (sqrt (pow (fabs x) 7))) (sqrt (pow (fabs x) 7)))))))
97.0ms
(sqrt (pow (fabs x) 7))
75.0ms
(sqrt (pow (fabs x) 7))

simplify1.7s

Counts
122 → 122
Iterations

Useful iterations: 2 (420.0ms)

IterNodesCost
01792806
15142279
225222138
done50012138

prune909.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (pow (fabs x) 7/2)) (sqrt (pow (fabs x) 7/2)))
9.2b
(sqrt (pow (fabs x) 7))
17.3b
(sqrt (pow (fabs x) 7/2))
17.3b
(sqrt (pow (fabs x) 7/2))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
56×add-sqr-sqrt
32×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
18×sqr-pow
16×unswap-sqr
12×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×rem-sqrt-square sqrt-pow1 pow1/2
6×add-exp-log add-cbrt-cube
4×add-log-exp
3×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
34.0ms
(* (sqrt (pow (fabs x) 7/2)) (sqrt (pow (fabs x) 7/2)))
10.0ms
(sqrt (pow (fabs x) 7))
3.0ms
(sqrt (pow (fabs x) 7/2))
3.0ms
(sqrt (pow (fabs x) 7/2))

series1.0s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (sqrt (pow (fabs x) 7/2)) (sqrt (pow (fabs x) 7/2)))
95.0ms
(sqrt (pow (fabs x) 7))
248.0ms
(sqrt (pow (fabs x) 7/2))
565.0ms
(sqrt (pow (fabs x) 7/2))

simplify1.5s

Counts
140 → 140
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01101747
12131193
28791149
done50001134

prune894.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02733
13833
done3833

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.9s14049×body80valid