Details

Time bar (total: 34.7s)

sample95.0ms

Algorithm
intervals
Results
65.0ms473×body80valid

simplify2.1s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize76.0ms

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)

rewrite3.2s

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:
2.0s
(* (/ 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)))))
996.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
114.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series658.0ms

Counts
4 → 10
Calls
4 calls:
520.0ms
(* (/ 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)))))
75.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
62.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify795.0ms

Counts
165 → 165

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize32.0ms

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
(* 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))))))

rewrite406.0ms

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:
24.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
18.0ms
(* 0.2 (pow (fabs x) 5))
15.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
341.0ms
(* (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))))))

series679.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
89.0ms
(* 0.2 (pow (fabs x) 5))
76.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
413.0ms
(* (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))))))

simplify1.5s

Counts
134 → 134

prune849.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite6.9s

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×associate-*l*
47×add-sqr-sqrt
40×associate-*l/
38×times-frac
36×frac-add
35×add-cube-cbrt *-un-lft-identity sqrt-div
31×frac-times associate-*r/
18×flip3-+ flip-+
13×pow1
11×add-exp-log add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 155
Calls
4 calls:
1.9s
(* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
5.0s
(* (sqrt (/ 1.0 (sqrt PI))) (* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series1.3s

Counts
4 → 8
Calls
4 calls:
784.0ms
(* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
503.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify782.0ms

Counts
163 → 163

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
0.1b
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
0.3b
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
1.0b
(sqrt PI)

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
71×add-exp-log
42×prod-exp
35×add-cbrt-cube
23×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×cbrt-unprod
15×times-frac
14×associate-*r*
13×associate-*l*
12×pow1
9×div-exp sqrt-prod
7×associate-*r/
6×pow-to-exp associate-*l/ frac-add pow-exp associate-/r* associate-/l/
5×cbrt-undiv pow-prod-up
4×unpow-prod-down cube-prod add-log-exp unswap-sqr
3×flip3-+ flip-+
2×*-commutative div-inv sqr-pow
1×pow2 cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow-plus pow1/2 unpow3 pow-prod-down clear-num pow-sqr associate-/l*
Counts
4 → 127
Calls
4 calls:
37.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
107.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
3.0s
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
3.0ms
(sqrt PI)

series690.0ms

Counts
4 → 10
Calls
4 calls:
69.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
117.0ms
(* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))
504.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (+ (/ (* 2.0 (pow (fabs x) 3)) 3.0) (* 2.0 (fabs x)))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) 1.0) (sqrt PI))
0.0ms
(sqrt PI)

simplify2.2s

Counts
137 → 137

prune786.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.5s

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.5s14127×body80valid