Details

Time bar (total: 25.6s)

sample72.0ms

Algorithm
intervals
Results
54.0ms463×body80valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: done (3.4s)

IterNodesCost
02867
16967
222848
386437
4308737
done500033

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2.0 3.0) (* (* (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)))))
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:
940.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
91.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
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)))))
1.0ms
(sqrt PI)

series589.0ms

Counts
4 → 10
Calls
4 calls:
62.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
68.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
459.0ms
(* (/ 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)

simplify846.0ms

Counts
165 → 165
Iterations

Useful iterations: done (835.0ms)

IterNodesCost
03427956
111085828
done50004727

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI)))
0.3b
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
123×sqrt-prod
78×times-frac
75×add-sqr-sqrt
58×associate-*l*
53×add-cube-cbrt *-un-lft-identity
30×add-exp-log add-cbrt-cube
15×associate-*r/
13×associate-*r*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1 frac-add associate-/l/
7×unswap-sqr
6×flip3-+ flip-+
4×add-log-exp
3×associate-*l/ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 169
Calls
4 calls:
147.0ms
(/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI)))
184.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series1.1s

Counts
4 → 8
Calls
4 calls:
707.0ms
(/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI)))
411.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (sqrt 1.0) (+ (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* 2.0 (fabs x))) (* (fabs x) (+ (/ (* 1.0 (pow (fabs x) (+ 3 1))) 5.0) (* (/ 1.0 21.0) (pow (fabs x) (* 2 3))))))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.8s

Counts
177 → 177
Iterations

Useful iterations: 2 (528.0ms)

IterNodesCost
02448997
17377861
235186460
done50006460

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (/ (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (fabs x) (+ 2.0 (+ (/ (* 1.0 (pow (fabs x) 4)) 5.0) (* (/ 1.0 21.0) (pow (fabs x) 6)))))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
191×sqrt-prod
122×times-frac
90×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
61×associate-*l*
40×associate-*r*
22×add-exp-log add-cbrt-cube
9×pow1
8×unswap-sqr
7×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×associate-/r/
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l/ div-inv
2×flip3-+ sqrt-div frac-add flip-+
1×frac-times pow-prod-down *-commutative
Counts
4 → 170
Calls
4 calls:
267.0ms
(* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (/ (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (fabs x) (+ 2.0 (+ (/ (* 1.0 (pow (fabs x) 4)) 5.0) (* (/ 1.0 21.0) (pow (fabs x) 6)))))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series494.0ms

Counts
4 → 6
Calls
4 calls:
493.0ms
(* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (/ (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt PI)))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (+ (* (/ 2.0 3.0) (pow (fabs x) 3)) (* (fabs x) (+ 2.0 (+ (/ (* 1.0 (pow (fabs x) 4)) 5.0) (* (/ 1.0 21.0) (pow (fabs x) 6)))))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.9s

Counts
176 → 176
Iterations

Useful iterations: 2 (931.0ms)

IterNodesCost
03248732
18017907
232926804
done50016804

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 3) 3.0)
0.1b
(/ (pow (fabs x) 5) 5.0)
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)

rewrite356.0ms

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:
14.0ms
(/ (pow (fabs x) 3) 3.0)
8.0ms
(/ (pow (fabs x) 5) 5.0)
311.0ms
(/ (+ (* 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)

series519.0ms

Counts
4 → 10
Calls
4 calls:
47.0ms
(/ (pow (fabs x) 3) 3.0)
79.0ms
(/ (pow (fabs x) 5) 5.0)
394.0ms
(/ (+ (* 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 (722.0ms)

IterNodesCost
04308177
19457779
235357520
done50017520

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes316.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02867
14167
done4167

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.9s14085×body80valid