Details

Time bar (total: 1.1m)

sample111.0ms

Algorithm
intervals
Results
53.0ms259×body80nan
39.0ms256×body80valid

simplify219.0ms

Calls
1 calls:
Slowest
218.0ms
(/ 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

localize29.0ms

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)))

rewrite13.0ms

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))
1.0ms
(/ 4/3 (- PI (* v (* PI v))))
0.0ms
(* PI v)

series677.0ms

Calls
4 calls:
Slowest
505.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
107.0ms
(/ 4/3 (- PI (* v (* PI v))))
43.0ms
(* v (* PI v))
22.0ms
(* PI v)

simplify16.9s

Calls
101 calls:
Slowest
498.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (sqrt (* (cbrt (fma (* v -6) v 2)) (cbrt (fma (* v -6) v 2)))))
493.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
480.0ms
(/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))
475.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) 1)
473.0ms
(/ (/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3))) (sqrt (sqrt (fma (* v -6) v 2))))

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize63.0ms

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)

rewrite83.0ms

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
71.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
10.0ms
(* PI (- (* PI PI) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
0.0ms
(* PI v)
0.0ms
(* PI v)

series740.0ms

Calls
4 calls:
Slowest
358.0ms
(* PI (- (* PI PI) (* (* (* v (* PI v)) v) (* (* v (* PI v)) v))))
330.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
30.0ms
(* PI v)
21.0ms
(* PI v)

simplify15.5s

Calls
72 calls:
Slowest
513.0ms
(- (pow PI 3) (* (pow v 6) (pow PI 3)))
472.0ms
(/ (* (* (+ (* 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))))
410.0ms
(- (+ (* (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))))
364.0ms
(- (+ (/ (* (pow PI 2) (sqrt -1/6)) v) (+ (* (pow v 3) (* (pow PI 2) (sqrt -1/6))) (* v (* (pow PI 2) (sqrt -1/6))))) (+ (* 1/27 (/ (pow PI 2) (* v (sqrt -1/6)))) (+ (* 1/36 (/ (* v (pow PI 2)) (sqrt -1/6))) (* 1/2592 (/ (pow PI 2) (* v (pow (sqrt -1/6) 3)))))))
361.0ms
(/ (cbrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (sqrt (fma (* v -6) v 2)))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
78×sqrt-prod
54×times-frac
42×add-sqr-sqrt
41×*-un-lft-identity add-cube-cbrt
21×associate-/r/
15×associate-/r*
11×div-inv
10×flip3-- flip--
6×add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×sqrt-div
1×cbrt-undiv rem-sqrt-square sqrt-undiv pow1/2 div-exp
Calls
4 calls:
Slowest
9.0ms
(/ (sqrt (fma (* v -6) v 2)) (sqrt (/ 4/3 (- PI (* v (* PI v))))))
1.0ms
(/ 4/3 (- PI (* v (* PI v))))
1.0ms
(sqrt (/ 4/3 (- PI (* v (* PI v)))))
1.0ms
(/ 4/3 (- PI (* v (* PI v))))

series1.0s

Calls
4 calls:
Slowest
467.0ms
(/ (sqrt (fma (* v -6) v 2)) (sqrt (/ 4/3 (- PI (* v (* PI v))))))
333.0ms
(sqrt (/ 4/3 (- PI (* v (* PI v)))))
106.0ms
(/ 4/3 (- PI (* v (* PI v))))
102.0ms
(/ 4/3 (- PI (* v (* PI v))))

simplify20.1s

Calls
156 calls:
Slowest
483.0ms
(/ (sqrt 1) (sqrt (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))))
423.0ms
(- (+ (* (/ (* (sqrt 6) (pow v 2)) (sqrt 4/3)) (sqrt PI)) (* (/ 1 (* (sqrt 4/3) (* (sqrt 6) (pow v 2)))) (sqrt PI))) (+ (* 4 (* (/ 1 (* (sqrt 4/3) (sqrt 6))) (sqrt PI))) (* 8 (* (/ 1 (* (sqrt 4/3) (* (pow (sqrt 6) 3) (pow v 2)))) (sqrt PI)))))
420.0ms
(/ 1 (sqrt (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v)))))))
406.0ms
(sqrt (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))))
382.0ms
(- (+ (* (/ (* (sqrt 6) (pow v 2)) (sqrt 4/3)) (sqrt PI)) (* (/ 1 (* (sqrt 4/3) (* (sqrt 6) (pow v 2)))) (sqrt PI))) (+ (* 4 (* (/ 1 (* (sqrt 4/3) (sqrt 6))) (sqrt PI))) (* 8 (* (/ 1 (* (sqrt 4/3) (* (pow (sqrt 6) 3) (pow v 2)))) (sqrt PI)))))

prune1.9s

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

sample3.0s

Algorithm
intervals
Results
1.6s8000×body80valid
1.1s8122×body80nan