Details

Time bar (total: 25.3s)

sample143.0ms

Algorithm
intervals
Results
106.0ms456×body80valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: done (3.8s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

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)

rewrite3.0s

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:
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)))))
958.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
73.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series635.0ms

Counts
4 → 10
Calls
4 calls:
495.0ms
(* (/ 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)))))
73.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
67.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify932.0ms

Counts
165 → 165
Iterations

Useful iterations: done (925.0ms)

IterNodesCost
03427956
111065828
done50004727

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
0.2b
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b
(sqrt PI)

rewrite398.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
48×associate-*l*
45×times-frac
38×add-cube-cbrt *-un-lft-identity
35×add-exp-log
22×associate-*r*
20×associate-*r/
19×add-cbrt-cube
17×unswap-sqr
16×frac-add
14×prod-exp
13×sqrt-prod
12×flip3-+ flip-+
11×associate-*l/
10×unpow-prod-down
8×frac-times
7×pow1 div-exp
6×cbrt-unprod sqr-pow
5×cube-prod
4×pow-to-exp pow-exp add-log-exp
3×cbrt-undiv *-commutative div-inv
1×distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down
Counts
4 → 166
Calls
4 calls:
25.0ms
(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
299.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
55.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
2.0ms
(sqrt PI)

series619.0ms

Counts
4 → 10
Calls
4 calls:
87.0ms
(* (/ 1.0 21.0) (pow (fabs x) (* 2 3)))
476.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
55.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify926.0ms

Counts
176 → 176
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
03676018
112475162
done50014818

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (/ (* (pow (fabs x) 6) 1.0) (sqrt 21.0))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
0.2b
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b
(sqrt PI)

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
48×associate-*l*
45×times-frac
38×add-cube-cbrt *-un-lft-identity
36×associate-*r/
35×add-exp-log
32×frac-add
23×associate-*r*
19×associate-*l/ add-cbrt-cube
17×unswap-sqr
16×frac-times flip3-+ flip-+
14×prod-exp
13×sqrt-prod
10×unpow-prod-down
7×pow1 div-exp
6×cbrt-unprod sqr-pow
5×cube-prod
4×pow-to-exp pow-exp add-log-exp
3×cbrt-undiv *-commutative div-inv
1×unpow-prod-up distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down
Counts
4 → 175
Calls
4 calls:
34.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
212.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (/ (* (pow (fabs x) 6) 1.0) (sqrt 21.0))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
51.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0ms
(sqrt PI)

series764.0ms

Counts
4 → 10
Calls
4 calls:
49.0ms
(* (/ 1.0 5.0) (pow (fabs x) (+ 3 1)))
661.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (fabs x) (+ (* (/ 1.0 5.0) (pow (fabs x) (+ 3 1))) (* (/ 1 (sqrt 21.0)) (/ (* (pow (fabs x) 6) 1.0) (sqrt 21.0))))) (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3)))))
54.0ms
(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms
(sqrt PI)

simplify930.0ms

Counts
185 → 185
Iterations

Useful iterations: done (919.0ms)

IterNodesCost
04057321
114186256
done50005913

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 5) 5.0)
0.1b
(/ (pow (fabs x) 3) 3.0)
0.3b
(/ (+ (* 1.0 (+ (/ (pow (fabs x) 7) 21.0) (/ (pow (fabs x) 5) 5.0))) (* 2.0 (+ (/ (pow (fabs x) 3) 3.0) (fabs x)))) (/ (sqrt PI) 1.0))
1.0b
(sqrt PI)

rewrite463.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
122×add-sqr-sqrt
121×add-cube-cbrt *-un-lft-identity
39×sqrt-prod
28×associate-/r*
24×unpow-prod-down
22×associate-/l*
19×add-exp-log
13×add-cbrt-cube
12×cube-prod associate-*r/
9×div-exp
8×frac-add associate-/l/ sqr-pow
7×div-inv
6×flip3-+ flip-+
5×pow1 cbrt-undiv
4×cube-mult unpow3 add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 237
Calls
4 calls:
9.0ms
(/ (pow (fabs x) 5) 5.0)
10.0ms
(/ (pow (fabs x) 3) 3.0)
432.0ms
(/ (+ (* 1.0 (+ (/ (pow (fabs x) 7) 21.0) (/ (pow (fabs x) 5) 5.0))) (* 2.0 (+ (/ (pow (fabs x) 3) 3.0) (fabs x)))) (/ (sqrt PI) 1.0))
1.0ms
(sqrt PI)

series598.0ms

Counts
4 → 10
Calls
4 calls:
83.0ms
(/ (pow (fabs x) 5) 5.0)
53.0ms
(/ (pow (fabs x) 3) 3.0)
462.0ms
(/ (+ (* 1.0 (+ (/ (pow (fabs x) 7) 21.0) (/ (pow (fabs x) 5) 5.0))) (* 2.0 (+ (/ (pow (fabs x) 3) 3.0) (fabs x)))) (/ (sqrt PI) 1.0))
0.0ms
(sqrt PI)

simplify2.2s

Counts
247 → 247
Iterations

Useful iterations: 2 (838.0ms)

IterNodesCost
04308177
19447779
235387520
done50017520

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes244.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03144
14640
done4640

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.1s13874×body80valid