Details

Time bar (total: 35.6s)

sample105.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
37.0ms239×body80nan

simplify222.0ms

Calls
1 calls:
Slowest
222.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4/3 (- PI (* v (* PI v))))
0.2b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(sqrt (fma (* v -6) v 2))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* sqrt-prod
2×associate-/r/ *-commutative
1×rem-sqrt-square clear-num frac-2neg flip3-- pow1/2 associate-*r* div-inv flip--
Calls
4 calls:
Slowest
1.0ms
(* v (* PI v))
1.0ms
(sqrt (fma (* v -6) v 2))
1.0ms
(/ 4/3 (- PI (* v (* PI v))))
0.0ms
(* PI v)

series144.0ms

Calls
4 calls:
Slowest
51.0ms
(/ 4/3 (- PI (* v (* PI v))))
37.0ms
(* PI v)
30.0ms
(* v (* PI v))
26.0ms
(sqrt (fma (* v -6) v 2))

simplify2.5s

Calls
21 calls:
Slowest
468.0ms
(- (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))) (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))))
386.0ms
(- (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))) (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))))
316.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
286.0ms
(- (sqrt 2) (+ (* 9/2 (/ (pow v 4) (pow (sqrt 2) 3))) (* 3 (/ (pow v 2) (sqrt 2)))))
257.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))

prune776.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(* 4/3 (/ 1 (- PI (* v (* PI v)))))
0.0b
(/ 1 (- PI (* v (* PI v))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-*r*
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×flip3-- div-inv flip--
1×rec-exp clear-num frac-2neg associate-*r/ un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
3.0ms
(* 4/3 (/ 1 (- PI (* v (* PI v)))))
3.0ms
(* v (* PI v))
2.0ms
(/ 1 (- PI (* v (* PI v))))
1.0ms
(* PI v)

series211.0ms

Calls
4 calls:
Slowest
75.0ms
(/ 1 (- PI (* v (* PI v))))
64.0ms
(* 4/3 (/ 1 (- PI (* v (* PI v)))))
43.0ms
(* PI v)
28.0ms
(* v (* PI v))

simplify2.3s

Calls
26 calls:
Slowest
298.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
288.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
287.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))
233.0ms
(+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI))))
224.0ms
(- (+ (/ 1 (* (pow v 2) PI)) (+ (/ 1 (* (pow v 4) PI)) (/ 1 (* (pow v 6) PI)))))

prune760.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (- PI (* v (* PI v))))
1.0b
(sqrt (- PI (* v (* PI v))))
1.0b
(/ (/ 1 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))
0.2b
(* PI v)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
29×add-sqr-sqrt
27×*-un-lft-identity add-cube-cbrt sqrt-prod
20×sqrt-div
16×associate-/r/
10×flip3-- flip--
8×add-exp-log div-inv
7×pow1
6×associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u pow1/2 insert-posit16 log1p-expm1-u add-log-exp
3×pow-div
2×rem-sqrt-square div-exp pow-flip
1×cbrt-undiv rec-exp clear-num frac-2neg *-commutative inv-pow associate-/l/
Calls
4 calls:
Slowest
6.0ms
(/ (/ 1 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))
1.0ms
(sqrt (- PI (* v (* PI v))))
1.0ms
(sqrt (- PI (* v (* PI v))))
0.0ms
(* PI v)

series222.0ms

Calls
4 calls:
Slowest
66.0ms
(sqrt (- PI (* v (* PI v))))
62.0ms
(sqrt (- PI (* v (* PI v))))
54.0ms
(/ (/ 1 (sqrt (- PI (* v (* PI v))))) (sqrt (- PI (* v (* PI v)))))
40.0ms
(* PI v)

simplify15.7s

Calls
117 calls:
Slowest
610.0ms
(/ (sqrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (sqrt (sqrt (- PI (* v (* PI v))))))
459.0ms
(/ (/ 1 (sqrt (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))) (sqrt 1))
457.0ms
(/ 1 (sqrt (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))))
438.0ms
(/ (/ 1 (sqrt (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))) 1)
410.0ms
(sqrt (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
0.1b
(* 6 (* v v))
0.0b
(* (* 3 PI) (- 1 (* v v)))
0.0b
(sqrt (- 2 (* 6 (* v v))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r/
8×flip3-- sqrt-div associate-/r/ flip--
7×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u frac-times associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l/ *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg pow1/2 associate-*l* pow-prod-down prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
9.0ms
(* (* 3 PI) (- 1 (* v v)))
9.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
2.0ms
(sqrt (- 2 (* 6 (* v v))))
2.0ms
(* 6 (* v v))

series348.0ms

Calls
4 calls:
Slowest
202.0ms
(/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
99.0ms
(* (* 3 PI) (- 1 (* v v)))
37.0ms
(sqrt (- 2 (* 6 (* v v))))
11.0ms
(* 6 (* v v))

simplify6.5s

Calls
39 calls:
Slowest
419.0ms
(- (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))) (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))))
417.0ms
(sqrt (- (* 2 2) (* (* 6 (* v v)) (* 6 (* v v)))))
392.0ms
(- (+ (* 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))))))
392.0ms
(- (+ (* 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))))))))
360.0ms
(- (+ (/ 1 (* v (sqrt -6))) (* v (sqrt -6))) (* 1/2 (/ 1 (* (pow v 3) (pow (sqrt -6) 3)))))

prune884.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s8000×body80valid
1.1s7930×body80nan