Details

Time bar (total: 3.5m)

sample106.0ms

Algorithm
intervals
Results
36.0ms284×body80nan
35.0ms256×body80valid

simplify217.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
217.0ms
(/ 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

localize28.0ms

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)))

rewrite61.0ms

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
17.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
14.0ms
(* v (* PI v))
13.0ms
(/ 4/3 (- PI (* v (* PI v))))
12.0ms
(* PI v)

series674.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
490.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
117.0ms
(/ 4/3 (- PI (* v (* PI v))))
37.0ms
(* PI v)
30.0ms
(* v (* PI v))

simplify35.8s

Counts
259 → 215
Calls
259 calls:
Slowest
880.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
600.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
485.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
480.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
473.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))

prune2.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* v (* PI v))))
1.0b
(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
0.3b
(* PI v)
0.1b
(* v (* PI v))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
870×times-frac
405×add-sqr-sqrt
403×*-un-lft-identity add-cube-cbrt
180×sqrt-prod
98×associate-/r*
55×associate-/r/
34×add-exp-log
30×div-inv
25×flip3-- flip--
22×add-cbrt-cube
16×div-exp
12×pow1
7×cbrt-undiv
6×associate-*l* associate-/l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg *-commutative
1×pow-flip inv-pow unswap-sqr
Counts
4 → 485
Calls
4 calls:
Slowest
34.0ms
(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
14.0ms
(* v (* PI v))
14.0ms
(/ 4/3 (- PI (* v (* PI v))))
11.0ms
(* PI v)

series735.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
529.0ms
(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
137.0ms
(/ 4/3 (- PI (* v (* PI v))))
42.0ms
(* v (* PI v))
27.0ms
(* PI v)

simplify2.7m

Counts
734 → 497
Calls
734 calls:
Slowest
812.0ms
(/ (cbrt 1) (/ (sqrt (cbrt (fma (* v -6) v 2))) (+ PI (* v (* PI v)))))
768.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
764.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))) (/ 1 (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v))))))))
690.0ms
(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
635.0ms
(/ (sqrt 1) (/ (sqrt (fma (* v -6) v 2)) (/ (cbrt 4/3) (cbrt (- PI (* v (* PI v)))))))

prune5.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.3s8138×body80nan
1.1s8000×body80valid