Details

Time bar (total: 27.8s)

sample151.0ms

Algorithm
intervals
Results
123.0ms473×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

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)

rewrite2.0s

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:
21.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.9s
(* (/ 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)))))
81.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series575.0ms

Counts
4 → 10
Calls
4 calls:
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))
490.0ms
(* (/ 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
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.0s

Counts
145 → 145
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02836867
19365041
244943885
done50013849

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* 0.2 (pow (fabs x) 5))
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))

rewrite404.0ms

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:
22.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
25.0ms
(* 0.2 (pow (fabs x) 5))
328.0ms
(* (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))))))
25.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

series603.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
68.0ms
(* 0.2 (pow (fabs x) 5))
392.0ms
(* (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))))))
62.0ms
(* 0.6666666666666666 (pow (fabs x) 3))

simplify1.6s

Counts
134 → 134
Iterations

Useful iterations: 2 (519.0ms)

IterNodesCost
02282601
15942449
219642292
done50002292

prune875.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize76.0ms

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) (* (* (* (* (pow (pow (fabs x) 3) 1) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.4s

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:
33.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.3s
(* (/ 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) (* (* (* (* (pow (pow (fabs x) 3) 1) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
72.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series601.0ms

Counts
4 → 10
Calls
4 calls:
47.0ms
(* (* (fabs x) (fabs x)) (fabs x))
506.0ms
(* (/ 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) (* (* (* (* (pow (pow (fabs x) 3) 1) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
47.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.1s

Counts
145 → 145
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02866723
19415041
245933885
done50003849

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (pow (fabs x) (+ 4 1)) (/ 1.0 5.0))) (* 2.0 (fabs x))))
0.2b
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
35×associate-*l*
33×times-frac
30×add-cube-cbrt *-un-lft-identity
22×add-exp-log
16×sqrt-prod
15×associate-*r*
14×add-cbrt-cube
11×unswap-sqr
8×pow1 prod-exp
5×unpow-prod-down cube-prod
4×div-exp cbrt-unprod add-log-exp
3×sqr-pow
2×cbrt-undiv frac-times pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ associate-*l/ pow-exp *-commutative flip-+ div-inv
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down
Counts
4 → 124
Calls
4 calls:
319.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (pow (fabs x) (+ 4 1)) (/ 1.0 5.0))) (* 2.0 (fabs x))))
36.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
2.0ms
(sqrt PI)
3.0ms
(sqrt PI)

series430.0ms

Counts
4 → 8
Calls
4 calls:
345.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (pow (fabs x) (+ 4 1)) (/ 1.0 5.0))) (* 2.0 (fabs x))))
85.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.9s

Counts
132 → 132
Iterations

Useful iterations: 2 (612.0ms)

IterNodesCost
02222782
16682564
227602365
done50012365

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes139.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02733
13833
done3833

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s14065×body80valid