Details

Time bar (total: 1.0m)

sample151.0ms

Algorithm
intervals
Results
123.0ms444×body80valid

simplify897.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
31089
2240
174
028

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (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)

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
76×prod-exp
75×add-cbrt-cube
48×associate-*l*
46×add-sqr-sqrt
44×cbrt-unprod
40×times-frac
36×pow1
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
15×div-exp associate-*l/
14×sqrt-prod
12×frac-add
9×cbrt-undiv
6×frac-times rec-exp flip3-+ 1-exp associate-*r/ flip-+
5×associate-*r* unswap-sqr
4×insert-posit16 add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 173
Calls
4 calls:
590.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.6s
(* (/ 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)))
1.0ms
(sqrt PI)

series469.0ms

Counts
4 → 10
Calls
4 calls:
56.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
364.0ms
(* (/ 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)))))
48.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.2s

Counts
183 → 183
Iterations
IterNodes
done2000
11215
0354

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2/3 (* (fabs x) (fabs x))) (fabs x))
0.2b
(* 2/3 (* (fabs x) (fabs x)))
0.3b
(/ (+ (* (* 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (fabs x)) (+ (* 2 (fabs x)) (+ (* (* 2/3 (* (fabs x) (fabs x))) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5)))) (sqrt PI))
1.0b
(sqrt PI)

rewrite4.2s

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×pow1
18×times-frac
15×sqrt-prod
9×pow-prod-down prod-exp cbrt-unprod
6×associate-/r*
4×associate-*r* associate-*l* insert-posit16 add-log-exp
3×associate-/l*
2×*-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ div-inv unswap-sqr
Counts
4 → 98
Calls
4 calls:
61.0ms
(* (* 2/3 (* (fabs x) (fabs x))) (fabs x))
13.0ms
(* 2/3 (* (fabs x) (fabs x)))
4.1s
(/ (+ (* (* 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (fabs x)) (+ (* 2 (fabs x)) (+ (* (* 2/3 (* (fabs x) (fabs x))) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5)))) (sqrt PI))
1.0ms
(sqrt PI)

series441.0ms

Counts
4 → 10
Calls
4 calls:
47.0ms
(* (* 2/3 (* (fabs x) (fabs x))) (fabs x))
47.0ms
(* 2/3 (* (fabs x) (fabs x)))
347.0ms
(/ (+ (* (* 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (fabs x)) (+ (* 2 (fabs x)) (+ (* (* 2/3 (* (fabs x) (fabs x))) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5)))) (sqrt PI))
0.0ms
(sqrt PI)

simplify1.2s

Counts
108 → 108
Iterations
IterNodes
done2003
21492
1406
0160

prune684.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
11×pow1
9×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×times-frac associate-*l* pow-prod-down associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/l/
1×clear-num associate-/r* frac-2neg flip3-+ associate-*r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 72
Calls
4 calls:
20.0ms
(* 2/3 (* (fabs x) (fabs x)))
3.9s
(/ (+ (* (* 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (fabs x)) (+ (* 2 (fabs x)) (+ (* (* 2/3 (* (fabs x) (fabs x))) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series419.0ms

Counts
4 → 8
Calls
4 calls:
37.0ms
(* 2/3 (* (fabs x) (fabs x)))
381.0ms
(/ (+ (* (* 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (fabs x)) (+ (* 2 (fabs x)) (+ (* (* 2/3 (* (fabs x) (fabs x))) (fabs x)) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) 1/5)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.1s

Counts
80 → 80
Iterations
IterNodes
done2006
21273
1345
0125

prune577.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.9s

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
141×sqrt-prod
126×times-frac
78×*-un-lft-identity
66×add-cube-cbrt
31×associate-*r* associate-*l*
28×add-exp-log unswap-sqr
18×add-cbrt-cube
9×associate-/r* div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×cbrt-unprod insert-posit16 add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 197
Calls
4 calls:
17.6s
(/ (+ (+ (+ (* 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))))) (* 2 (fabs x))) (* (* 1/5 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fabs x))) (* (* (fabs x) (* (fabs x) (fabs x))) 2/3)) (sqrt (sqrt PI)))
18.3s
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (+ (+ (* 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))))) (* 2 (fabs x))) (* (* 1/5 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fabs x))) (* (* (fabs x) (* (fabs x) (fabs x))) 2/3)) (sqrt (sqrt PI))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series976.0ms

Counts
4 → 8
Calls
4 calls:
629.0ms
(/ (+ (+ (+ (* 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))))) (* 2 (fabs x))) (* (* 1/5 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fabs x))) (* (* (fabs x) (* (fabs x) (fabs x))) 2/3)) (sqrt (sqrt PI)))
346.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (+ (+ (* 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))))) (* 2 (fabs x))) (* (* 1/5 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fabs x))) (* (* (fabs x) (* (fabs x) (fabs x))) 2/3)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.1s

Counts
205 → 205
Iterations
IterNodes
done2000
1690
0233

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes327.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done46
146
028

end0.0ms

sample4.3s

Algorithm
intervals
Results
4.1s13875×body80valid