Details

Time bar (total: 41.7s)

sample93.0ms

Algorithm
intervals
Results
38.0ms256×body80valid
36.0ms260×body80nan

simplify253.0ms

Calls
1 calls:
Slowest
253.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* v (* PI v))))
0.3b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×sqrt-prod
16×associate-/r/
9×associate-/r* div-inv
8×flip3-- flip--
6×add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative
1×cbrt-undiv div-exp associate-*r* associate-/l/
Calls
4 calls:
Slowest
8.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
2.0ms
(* v (* PI v))
2.0ms
(/ 4/3 (- PI (* v (* PI v))))
0.0ms
(* PI v)

series593.0ms

Calls
4 calls:
Slowest
438.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
98.0ms
(/ 4/3 (- PI (* v (* PI v))))
29.0ms
(* v (* PI v))
28.0ms
(* PI v)

simplify17.2s

Calls
101 calls:
Slowest
568.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) 1)
555.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
533.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (sqrt (sqrt (fma (* v -6) v 2))))
529.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (sqrt (* (cbrt (fma (* v -6) v 2)) (cbrt (fma (* v -6) v 2)))))
526.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (sqrt 1))

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b
(* PI (- (* PI PI) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
1.0b
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
0.3b
(* PI v)
0.3b
(* PI v)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
12×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative associate-/l*
2×sub-neg prod-diff associate-*r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- difference-of-squares
Calls
4 calls:
Slowest
95.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
7.0ms
(* PI (- (* PI PI) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
0.0ms
(* PI v)
0.0ms
(* PI v)

series825.0ms

Calls
4 calls:
Slowest
382.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
376.0ms
(* PI (- (* PI PI) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
33.0ms
(* PI v)
33.0ms
(* PI v)

simplify16.8s

Calls
72 calls:
Slowest
740.0ms
(* PI (- (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
542.0ms
(/ (* (* (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (* (* (sqrt (fma (* v -6) v 2)) (sqrt (fma (* v -6) v 2))) (sqrt (fma (* v -6) v 2))))
436.0ms
(* (fma (- (* (* v (* PI v)) v)) (* (* v (* PI v)) v) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))) PI)
412.0ms
(/ (sqrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (sqrt (* (cbrt (fma (* v -6) v 2)) (cbrt (fma (* v -6) v 2)))))
388.0ms
(- (+ (* (pow PI 2) (sqrt 1/2)) (+ (* 3/4 (/ (* (pow v 2) (pow PI 2)) (sqrt 1/2))) (+ (* 3 (/ (* (pow v 4) (pow PI 2)) (sqrt 1/2))) (+ (* (pow v 4) (* (pow PI 2) (sqrt 1/2))) (* (pow v 2) (* (pow PI 2) (sqrt 1/2))))))) (* 9/32 (/ (* (pow v 4) (pow PI 2)) (pow (sqrt 1/2) 3))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.6s8025×body80nan
1.2s8000×body80valid