Details

Time bar (total: 1.5m)

sample99.0ms

Algorithm
intervals
Results
42.0ms256×body80valid
36.0ms228×body80nan

simplify922.0ms

Calls
1 calls:
Slowest
910.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune63.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize213.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* (* v v) PI)))
0.2b
(* (* v -6) v)
0.2b
(* (* v v) PI)
0.0b
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×sqrt-prod
18×associate-/r/
9×associate-/r* div-inv
8×flip3-- flip--
6×add-cbrt-cube add-exp-log associate-/l*
4×pow1 insert-posit16 add-log-exp
2×clear-num frac-2neg sqrt-div associate-*l* *-commutative
1×cbrt-undiv flip3-+ div-exp flip-+ associate-/l/
Calls
4 calls:
Slowest
16.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
13.0ms
(* (* v -6) v)
5.0ms
(* (* v v) PI)
4.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series587.0ms

Calls
4 calls:
Slowest
284.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* (* v -6) v))))
172.0ms
(/ 4/3 (- PI (* (* v v) PI)))
79.0ms
(* (* v -6) v)
44.0ms
(* (* v v) PI)

simplify36.4s

Calls
103 calls:
Slowest
1.6s
(/ (* (* (/ 4/3 (- PI (* (* v v) PI))) (/ 4/3 (- PI (* (* v v) PI)))) (/ 4/3 (- PI (* (* v v) PI)))) (* (* (sqrt (+ 2 (* (* v -6) v))) (sqrt (+ 2 (* (* v -6) v)))) (sqrt (+ 2 (* (* v -6) v)))))
1.5s
(/ (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI)))) (sqrt (sqrt (+ 2 (* (* v -6) v)))))
1.4s
(+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI))))
1.4s
(/ (/ 4/3 (- (pow PI 3) (pow (* (* v v) PI) 3))) (sqrt (sqrt (+ 2 (* (* v -6) v)))))
1.3s
(/ (/ 4/3 (- (pow PI 3) (pow (* (* v v) PI) 3))) (sqrt (* (cbrt (+ 2 (* (* v -6) v))) (cbrt (+ 2 (* (* v -6) v))))))

prune3.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* v -6) v)
0.2b
(* (* v v) PI)
0.0b
(/ 1 (/ (- PI (* (* v v) PI)) 4/3))
0.0b
(/ (/ 1 (/ (- PI (* (* v v) PI)) 4/3)) (sqrt (+ 2 (* (* v -6) v))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×sqrt-prod
10×associate-/r* associate-/r/ div-inv
9×add-exp-log
6×add-cbrt-cube
5×pow1 associate-/l*
4×insert-posit16 add-log-exp
2×rec-exp clear-num frac-2neg sqrt-div div-exp associate-*l* *-commutative
1×cbrt-undiv flip3-+ flip-+ pow-flip inv-pow associate-/l/
Calls
4 calls:
Slowest
29.0ms
(/ (/ 1 (/ (- PI (* (* v v) PI)) 4/3)) (sqrt (+ 2 (* (* v -6) v))))
25.0ms
(/ 1 (/ (- PI (* (* v v) PI)) 4/3))
5.0ms
(* (* v -6) v)
5.0ms
(* (* v v) PI)

series450.0ms

Calls
4 calls:
Slowest
258.0ms
(/ (/ 1 (/ (- PI (* (* v v) PI)) 4/3)) (sqrt (+ 2 (* (* v -6) v))))
112.0ms
(/ 1 (/ (- PI (* (* v v) PI)) 4/3))
47.0ms
(* (* v v) PI)
32.0ms
(* (* v -6) v)

simplify24.5s

Calls
91 calls:
Slowest
843.0ms
(/ (/ 1 (/ (- PI (* (* v v) PI)) 4/3)) (sqrt (+ 2 (* (* v -6) v))))
825.0ms
(- (- (log (/ (- PI (* (* v v) PI)) 4/3))) (log (sqrt (+ 2 (* (* v -6) v)))))
764.0ms
(/ (sqrt (/ 1 (/ (- PI (* (* v v) PI)) 4/3))) (sqrt (sqrt (+ 2 (* (* v -6) v)))))
709.0ms
(- (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 7) PI))) (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 3) PI))) (* 4/3 (/ (sqrt -1/6) (* (pow v 5) PI))))) (+ (* 1/1944 (/ 1 (* (pow v 7) (* PI (pow (sqrt -1/6) 3))))) (+ (* 4/81 (/ 1 (* (pow v 7) (* PI (sqrt -1/6))))) (* 1/27 (/ 1 (* (pow v 5) (* PI (sqrt -1/6))))))))
699.0ms
(/ (/ 1 (/ (- PI (* (* v v) PI)) 4/3)) (sqrt (sqrt (+ 2 (* (* v -6) v)))))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* v -6) v)
0.2b
(* (* v v) PI)
0.0b
(/ 4/3 (* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI))))
0.0b
(* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×frac-times associate-*l* associate-/r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 flip3-+ flip3-- add-cbrt-cube add-exp-log flip-+ flip--
4×associate-*l/ associate-*r/ insert-posit16 add-log-exp
3×associate-*r* *-commutative sqrt-prod
2×distribute-rgt-in sub-neg distribute-lft-in
1×clear-num associate-/r* frac-2neg pow-prod-down prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
15.0ms
(* (* v -6) v)
12.0ms
(* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI)))
6.0ms
(* (* v v) PI)
3.0ms
(/ 4/3 (* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI))))

series986.0ms

Calls
4 calls:
Slowest
513.0ms
(/ 4/3 (* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI))))
172.0ms
(* (* v -6) v)
151.0ms
(* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI)))
139.0ms
(* (* v v) PI)

simplify14.0s

Calls
48 calls:
Slowest
1.0s
(- (+ (* 1/1944 (/ 1 (* (pow v 7) (* PI (pow (sqrt -1/6) 3))))) (+ (* 4/81 (/ 1 (* (pow v 7) (* PI (sqrt -1/6))))) (* 1/27 (/ 1 (* (pow v 5) (* PI (sqrt -1/6))))))) (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 7) PI))) (+ (* 4/3 (/ (sqrt -1/6) (* (pow v 3) PI))) (* 4/3 (/ (sqrt -1/6) (* (pow v 5) PI))))))
870.0ms
(* (sqrt (- 2 (* (* v -6) v))) (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI)))))
790.0ms
(* (sqrt (+ 2 (* (* v -6) v))) (- PI (* (* v v) PI)))
705.0ms
(* (sqrt (+ (pow 2 3) (pow (* (* v -6) v) 3))) (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI))))
662.0ms
(* (sqrt (- 2 (* (* v -6) v))) (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI)))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.4s7970×body80nan
2.4s8000×body80valid