Details

Time bar (total: 11.0s)

sample72.0ms

Algorithm
intervals
Results
50.0ms476×body80valid

simplify100.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

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))
62.0ms
(* (/ 2.0 3.0) (* (* (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) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0ms
(sqrt PI)

series427.0ms

Counts
4 → 10
Calls
4 calls:
28.0ms
(* (* (fabs x) (fabs x)) (fabs x))
51.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
348.0ms
(* (/ 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)))))
0.0ms
(sqrt PI)

simplify51.0ms

Counts
145 → 145

prune684.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite256.0ms

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))
13.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
14.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
212.0ms
(* (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))))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* 0.2 (pow (fabs x) 5))
77.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
52.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
306.0ms
(* (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))))))

simplify78.0ms

Counts
134 → 134

prune593.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
0.1b
(* 0.047619047619047616 (pow (fabs x) 7/2))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.2b
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
42×add-exp-log
29×associate-*r*
28×prod-exp
23×*-un-lft-identity associate-*l*
22×add-cube-cbrt
16×sqrt-prod
15×add-cbrt-cube
11×unpow-prod-down times-frac unswap-sqr
9×pow-to-exp pow-exp
6×pow1 cbrt-unprod
5×sqr-pow
4×cube-prod *-commutative add-log-exp
3×sqrt-div
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 → 127
Calls
4 calls:
27.0ms
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
13.0ms
(* 0.047619047619047616 (pow (fabs x) 7/2))
16.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
210.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
92.0ms
(* 0.047619047619047616 (pow (fabs x) 7/2))
46.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
311.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))))))

simplify82.0ms

Counts
139 → 139

prune635.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.3b
(* (sqrt (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))))))
0.3b
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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)))))))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
65×sqrt-prod
53×add-sqr-sqrt
44×associate-*l*
31×*-un-lft-identity
30×add-cube-cbrt sqrt-div
23×associate-*r*
21×add-exp-log
20×times-frac
15×add-cbrt-cube
12×unswap-sqr
11×pow1 frac-times associate-*r/
10×prod-exp
8×unpow-prod-down
6×flip3-+ cbrt-unprod flip-+
5×distribute-rgt-in distribute-lft-in
4×cube-prod pow-prod-down associate-*l/ *-commutative add-log-exp sqr-pow
2×pow-to-exp pow-exp div-inv
1×cube-mult unpow3
Counts
4 → 150
Calls
4 calls:
13.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
13.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
212.0ms
(* (sqrt (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))))))
234.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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)))))))

series952.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
52.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
509.0ms
(* (sqrt (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))))))
312.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (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)))))))

simplify101.0ms

Counts
162 → 162

prune808.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes232.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.4s14074×body80valid