Details

Time bar (total: 42.8s)

sample111.0ms

Algorithm
intervals
Results
93.0ms425×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2001
42001
31089
2240
174
028

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×add-exp-log
36×associate-*l*
35×pow1 add-cbrt-cube
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
19×prod-exp
17×cbrt-unprod
14×associate-*l/ sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+ unswap-sqr
5×div-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp pow3
Counts
4 → 143
Calls
4 calls:
14.0ms
(* (* (fabs x) (fabs x)) (fabs x))
1.7s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
48.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series473.0ms

Counts
4 → 10
Calls
4 calls:
31.0ms
(* (* (fabs x) (fabs x)) (fabs x))
390.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
52.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.8s

Counts
153 → 153
Iterations
IterNodes
done2002
22002
11013
0285

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 5) 1/5)
0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.1b
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (/ 1 PI)))
0.2b
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×pow1
25×add-exp-log
22×add-cbrt-cube
21×associate-*r*
19×*-un-lft-identity
18×add-cube-cbrt
16×associate-*l* sqrt-prod
13×prod-exp
11×times-frac cbrt-unprod
10×pow-prod-down
8×unswap-sqr
5×pow-prod-up
4×unpow-prod-down *-commutative insert-posit16 add-log-exp
3×sqrt-div
2×frac-times flip3-+ associate-*l/ flip-+ sqr-pow
1×pow2 pow-to-exp pow-plus cube-unmult pow-exp associate-*r/ pow-sqr div-inv
Counts
4 → 113
Calls
4 calls:
11.0ms
(* (pow (fabs x) 5) 1/5)
28.0ms
(* (fabs x) (* (fabs x) (fabs x)))
2.2s
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (/ 1 PI)))
62.0ms
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (pow (fabs x) 5) 1/5)
35.0ms
(* (fabs x) (* (fabs x) (fabs x)))
377.0ms
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (/ 1 PI)))
45.0ms
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))

simplify1.7s

Counts
125 → 125
Iterations
IterNodes
done2004
32004
21917
1472
0203

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI)))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite5.2s

Algorithm
rewrite-expression-head
Rules
163×add-sqr-sqrt
159×sqrt-prod
144×times-frac
122×*-un-lft-identity
72×add-cube-cbrt
40×associate-*r*
31×associate-*l*
28×add-exp-log unswap-sqr
19×distribute-lft-out
18×add-cbrt-cube
9×associate-/r* div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×cbrt-unprod insert-posit16 associate-/l* add-log-exp associate-/l/
3×div-inv
2×rem-sqrt-square rec-exp sqrt-pow1 flip3-+ pow1/2 1-exp frac-add flip-+
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 218
Calls
4 calls:
2.7s
(/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI)))
2.5s
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series952.0ms

Counts
4 → 8
Calls
4 calls:
597.0ms
(/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI)))
354.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (/ (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) 21) (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 2 (fabs x))) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.7s

Counts
226 → 226
Iterations
IterNodes
done2001
22001
1741
0244

prune4.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.2b
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))
0.2b
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI))))
0.3b
(* (* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI))))

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
65×sqrt-prod
40×associate-*r*
37×add-sqr-sqrt
34×pow1
30×sqrt-div
26×*-un-lft-identity
25×add-cbrt-cube add-exp-log add-cube-cbrt
20×times-frac
13×pow-prod-down prod-exp cbrt-unprod
11×frac-times associate-*l/
10×associate-*l*
6×flip3-+ flip-+ unswap-sqr
5×pow-prod-up
4×associate-*r/ *-commutative insert-posit16 add-log-exp
2×div-inv
1×pow2 pow-plus cube-unmult pow-sqr
Counts
4 → 137
Calls
4 calls:
13.0ms
(* (fabs x) (* (fabs x) (fabs x)))
54.0ms
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))
2.1s
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI))))
2.3s
(* (* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI))))

series1.3s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (fabs x) (* (fabs x) (fabs x)))
65.0ms
(* 2/3 (* (fabs x) (* (fabs x) (fabs x))))
726.0ms
(* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI))))
417.0ms
(* (* (+ (+ (+ (* 2/3 (* (fabs x) (* (fabs x) (fabs x)))) (* 1/21 (pow (fabs x) 7))) (* 2 (fabs x))) (* (pow (fabs x) 5) 1/5)) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI))))

simplify1.4s

Counts
149 → 149
Iterations
IterNodes
done2005
22005
1587
0229

prune3.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done36
136
025

end0.0ms

sample5.0s

Algorithm
intervals
Results
4.7s13996×body80valid