Details

sample73.0ms

Algorithm

intervals

Results

35.0ms	259×	body	80	nan
22.0ms	256×	body	80	valid

simplify248.0ms

Calls

1 calls:

Slowest

248.0ms

(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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/`

Calls

4 calls:

Slowest

26.0ms	(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
16.0ms	(* v (* PI v))
7.0ms	(/ 4/3 (- PI (* v (* PI v))))
6.0ms	(* PI v)

series668.0ms

Calls

4 calls:

Slowest

465.0ms	(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
134.0ms	(/ 4/3 (- PI (* v (* PI v))))
37.0ms	(* PI v)
32.0ms	(* v (* PI v))

simplify34.3s

Calls

259 calls:

Slowest

672.0ms	(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
569.0ms	(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
531.0ms	(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
493.0ms	(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
483.0ms	(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize52.0ms

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))

rewrite92.0ms

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`

Calls

4 calls:

Slowest

35.0ms	(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
21.0ms	(* v (* PI v))
14.0ms	(/ 4/3 (- PI (* v (* PI v))))
11.0ms	(* PI v)

series692.0ms

Calls

4 calls:

Slowest

501.0ms	(/ 1 (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
115.0ms	(/ 4/3 (- PI (* v (* PI v))))
46.0ms	(* PI v)
31.0ms	(* v (* PI v))

simplify2.6m

Calls

734 calls:

Slowest

813.0ms	(/ 1 (/ (sqrt (cbrt (fma (* v -6) v 2))) (/ (sqrt 4/3) (- PI (* v (* PI v))))))
781.0ms	(/ (cbrt 1) (/ (sqrt (fma (* v -6) v 2)) (/ 4/3 (- PI (* v (* PI v))))))
692.0ms	(/ (sqrt 1) (/ (sqrt (sqrt (fma (* v -6) v 2))) (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))))
615.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt (fma (* v -6) v 2)) (cbrt (fma (* v -6) v 2)))) (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))))
598.0ms	(/ 1 (/ (sqrt (fma (* v -6) v 2)) (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))))

prune6.3s

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	(/ 4/3 (sqrt (- PI (* v (* PI v)))))
1.0b	(sqrt (- PI (* v (* PI v))))
1.0b	(sqrt (- PI (* v (* PI v))))
0.3b	(* PI v)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `sqrt-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `associate-l` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Calls

4 calls:

Slowest

11.0ms	(* PI v)
9.0ms	(sqrt (- PI (* v (* PI v))))
8.0ms	(/ 4/3 (sqrt (- PI (* v (* PI v)))))
5.0ms	(sqrt (- PI (* v (* PI v))))

series579.0ms

Calls

4 calls:

Slowest

293.0ms	(/ 4/3 (sqrt (- PI (* v (* PI v)))))
133.0ms	(sqrt (- PI (* v (* PI v))))
116.0ms	(sqrt (- PI (* v (* PI v))))
36.0ms	(* PI v)

simplify8.6s

Calls

83 calls:

Slowest

580.0ms	(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
576.0ms	(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
513.0ms	(sqrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))))
383.0ms	(+ (* 1/2 (* (pow v 4) (sqrt (/ 1 PI)))) (+ (* 2/3 (* (pow v 2) (sqrt (/ 1 PI)))) (* 4/3 (sqrt (/ 1 PI)))))
325.0ms	(* (* (* PI PI) PI) (* (* v v) v))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.2s	8122×	body	80	nan