Details

Time bar (total: 57.9s)

sample71.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
26.0ms240×body80nan

simplify284.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
283.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* v (* PI v))))
0.3b
(* PI v)
0.2b
(* v (* PI v))
0.0b
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
98×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
18×add-cbrt-cube add-exp-log associate-/l*
16×associate-/r/
11×pow1
9×associate-/r* div-inv
8×flip3-- flip--
6×associate-*l*
4×expm1-log1p-u cbrt-undiv div-exp associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative
1×unswap-sqr associate-/l/
Counts
4 → 203
Calls
4 calls:
Slowest
30.0ms
(* v (* PI v))
12.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
6.0ms
(/ 4/3 (- PI (* v (* PI v))))
5.0ms
(* PI v)

series597.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
94.0ms
(/ 4/3 (- PI (* v (* PI v))))
29.0ms
(* PI v)
26.0ms
(* v (* PI v))

simplify34.7s

Counts
259 → 215
Calls
259 calls:
Slowest
649.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
555.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
539.0ms
(/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))
478.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
444.0ms
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v)))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))

prune2.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×associate-/r* sqrt-prod
10×add-cbrt-cube add-exp-log
9×associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×fma-udef
Counts
4 → 113
Calls
4 calls:
Slowest
7.0ms
(/ 4/3 PI)
4.0ms
(/ (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI)) (sqrt (fma (* v -6) v 2)))
4.0ms
(/ 4/3 PI)
0.0ms
(fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI))

series544.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
425.0ms
(/ (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI)) (sqrt (fma (* v -6) v 2)))
119.0ms
(fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI))
0.0ms
(/ 4/3 PI)
0.0ms
(/ 4/3 PI)

simplify15.0s

Counts
102 → 121
Calls
102 calls:
Slowest
784.0ms
(/ (* (* (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI)) (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI))) (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI))) (* (* (sqrt (fma (* v -6) v 2)) (sqrt (fma (* v -6) v 2))) (sqrt (fma (* v -6) v 2))))
490.0ms
(- (+ (* 4/3 (/ (sqrt -1/6) (* v PI))) (+ (* 4/3 (/ (* v (sqrt -1/6)) PI)) (* 4/3 (/ (* (pow v 3) (sqrt -1/6)) PI)))) (+ (* 1/27 (/ v (* PI (sqrt -1/6)))) (+ (* 1/1944 (/ 1 (* v (* PI (pow (sqrt -1/6) 3))))) (* 4/81 (/ 1 (* v (* PI (sqrt -1/6))))))))
435.0ms
(- (+ (* 4 (/ (pow v 4) (* PI (sqrt 1/2)))) (+ (/ (pow v 2) (* PI (sqrt 1/2))) (+ (* 4/3 (/ (sqrt 1/2) PI)) (+ (* 4/3 (/ (* (pow v 2) (sqrt 1/2)) PI)) (* 4/3 (/ (* (pow v 4) (sqrt 1/2)) PI)))))) (* 3/8 (/ (pow v 4) (* PI (pow (sqrt 1/2) 3)))))
372.0ms
(- (+ (* 1/27 (/ v (* PI (sqrt -1/6)))) (+ (* 1/1944 (/ 1 (* v (* PI (pow (sqrt -1/6) 3))))) (* 4/81 (/ 1 (* v (* PI (sqrt -1/6))))))) (+ (* 4/3 (/ (sqrt -1/6) (* v PI))) (+ (* 4/3 (/ (* v (sqrt -1/6)) PI)) (* 4/3 (/ (* (pow v 3) (sqrt -1/6)) PI)))))
365.0ms
(/ (sqrt (fma (/ 4/3 PI) (fma (* v v) (* v v) (* v v)) (/ 4/3 PI))) (sqrt (sqrt (fma (* v -6) v 2))))

prune1.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.5s8069×body80nan
1.3s8000×body80valid