Details

Time bar (total: 3.2m)

sample107.0ms

Algorithm
intervals
Results
51.0ms256×body80valid
36.0ms241×body80nan

simplify182.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
182.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
134×*-un-lft-identity
111×add-sqr-sqrt
109×add-cube-cbrt
57×sqrt-prod
25×distribute-rgt-out--
21×add-cbrt-cube add-exp-log associate-/l*
18×associate-/r/
14×pow1
10×associate-/r*
9×div-inv
8×flip3-- flip--
6×pow-prod-down prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*r* associate-*l* insert-posit16 add-log-exp
2×clear-num frac-2neg sqrt-div *-commutative unswap-sqr
1×flip3-+ flip-+ associate-/l/
Counts
4 → 224
Calls
4 calls:
Slowest
22.0ms
(* (* v v) PI)
16.0ms
(* -6 (* v v))
15.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* -6 (* v v)))))
6.0ms
(/ 4/3 (- PI (* (* v v) PI)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
428.0ms
(/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ 2 (* -6 (* v v)))))
111.0ms
(/ 4/3 (- PI (* (* v v) PI)))
46.0ms
(* -6 (* v v))
29.0ms
(* (* v v) PI)

simplify48.8s

Counts
358 → 236
Calls
358 calls:
Slowest
655.0ms
(/ (/ 1 (- PI (* (* v v) PI))) (sqrt (+ 2 (* -6 (* v v)))))
563.0ms
(/ (/ 4/3 (- (* PI PI) (* (* (* v v) PI) (* (* v v) PI)))) (* (cbrt (sqrt (+ 2 (* -6 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))
499.0ms
(- (+ (* 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))))))
458.0ms
(* (* (* -6 (* v v)) (* -6 (* v v))) (* -6 (* v v)))
458.0ms
(- (+ (* 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))))))))

prune2.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) PI) (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3)))
1.0b
(/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3))
0.3b
(* (* v v) (sqrt (+ 2 (* (* v v) -6))))
0.2b
(* (* v v) -6)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
613×times-frac
342×*-un-lft-identity
235×add-sqr-sqrt
232×add-cube-cbrt
138×cbrt-prod
110×distribute-rgt-out--
59×sqrt-prod
45×div-inv
40×associate-/r*
37×add-exp-log
29×add-cbrt-cube
14×pow1 cbrt-undiv sqrt-div div-exp
12×associate-/l*
9×associate-*r* associate-/l/
8×prod-exp associate-*r/ cbrt-unprod
7×flip3-+ flip-+
6×pow-prod-down
4×frac-sub insert-posit16 add-log-exp
3×unswap-sqr
2×clear-num frac-2neg associate-*l* *-commutative sub-div
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 413
Calls
4 calls:
Slowest
65.0ms
(/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3))
34.0ms
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) PI) (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3)))
31.0ms
(* (* v v) (sqrt (+ 2 (* (* v v) -6))))
24.0ms
(* (* v v) -6)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
706.0ms
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) PI) (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3)))
388.0ms
(/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3))
143.0ms
(* (* v v) (sqrt (+ 2 (* (* v v) -6))))
56.0ms
(* (* v v) -6)

simplify2.2m

Counts
697 → 425
Calls
697 calls:
Slowest
748.0ms
(* (* (* (* v v) v) (* (* v v) v)) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6)))))
746.0ms
(* (* (* (* v v) (* v v)) (* v v)) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6)))))
658.0ms
(/ (/ (cbrt 4/3) (sqrt PI)) (/ (* (cbrt (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6)))))) (cbrt (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))))) 1))
621.0ms
(/ (* (cbrt (/ (* (cbrt 4/3) (cbrt 4/3)) PI)) (cbrt (/ (* (cbrt 4/3) (cbrt 4/3)) PI))) (/ (* (cbrt (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6)))))) (cbrt (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))))) 1))
615.0ms
(* (* (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3)) (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3))) (/ (- (sqrt (+ 2 (* (* v v) -6))) (* (* v v) (sqrt (+ 2 (* (* v v) -6))))) (cbrt 4/3)))

prune4.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s8000×body80valid
1.0s8073×body80nan