Details

Time bar (total: 2.8m)

sample106.0ms

Algorithm
intervals
Results
45.0ms293×body80nan
39.0ms256×body80valid

simplify211.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
210.0ms
(/ 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

localize23.0ms

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)))

rewrite78.0ms

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
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
26.0ms
(* v (* PI v))
9.0ms
(* PI v)
6.0ms
(/ 4/3 (- PI (* v (* PI v))))

series651.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
487.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
99.0ms
(/ 4/3 (- PI (* v (* PI v))))
44.0ms
(* v (* PI v))
21.0ms
(* PI v)

simplify34.6s

Counts
259 → 215
Calls
259 calls:
Slowest
696.0ms
(- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI))))))
597.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
579.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
520.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (sqrt (sqrt (fma (* v -6) v 2))))
497.0ms
(+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
738×times-frac
441×sqrt-prod
387×add-sqr-sqrt
386×*-un-lft-identity add-cube-cbrt
315×cbrt-prod
42×associate-/l*
22×sqrt-div
20×associate-/r/
11×flip3-- div-inv flip--
9×associate-/r* add-exp-log
8×add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×pow1/3
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 493
Calls
4 calls:
Slowest
22.0ms
(/ (/ (cbrt 4/3) (sqrt (- PI (* v (* PI v))))) (sqrt (cbrt (fma (* v -6) v 2))))
10.0ms
(sqrt (- PI (* v (* PI v))))
1.0ms
(cbrt (fma (* v -6) v 2))
1.0ms
(cbrt (fma (* v -6) v 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
632.0ms
(/ (/ (cbrt 4/3) (sqrt (- PI (* v (* PI v))))) (sqrt (cbrt (fma (* v -6) v 2))))
208.0ms
(cbrt (fma (* v -6) v 2))
182.0ms
(cbrt (fma (* v -6) v 2))
127.0ms
(sqrt (- PI (* v (* PI v))))

simplify1.7m

Counts
836 → 505
Calls
836 calls:
Slowest
656.0ms
(/ (cbrt 4/3) (sqrt (- (pow PI 3) (pow (* v (* PI v)) 3))))
578.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
551.0ms
(/ (sqrt (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v)))))) (sqrt (cbrt (fma (* v -6) v 2))))
547.0ms
(/ (/ (* (cbrt (cbrt 4/3)) (cbrt (cbrt 4/3))) (* (cbrt (sqrt (- PI (* v (* PI v))))) (cbrt (sqrt (- PI (* v (* PI v))))))) (* (cbrt (sqrt (cbrt (fma (* v -6) v 2)))) (cbrt (sqrt (cbrt (fma (* v -6) v 2))))))
505.0ms
(/ (/ 1 (sqrt (- PI (* v (* PI v))))) (sqrt (cbrt (cbrt (fma (* v -6) v 2)))))

prune9.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (fma (* v -6) v 2))
1.0b
(cbrt (fma (* v -6) v 2))
1.0b
(sqrt (- PI (* v (* PI v))))
1.0b
(sqrt (- PI (* v (* PI v))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow1/3 flip--
Counts
4 → 64
Calls
4 calls:
Slowest
10.0ms
(sqrt (- PI (* v (* PI v))))
10.0ms
(sqrt (- PI (* v (* PI v))))
1.0ms
(cbrt (fma (* v -6) v 2))
1.0ms
(cbrt (fma (* v -6) v 2))

series600.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(cbrt (fma (* v -6) v 2))
180.0ms
(cbrt (fma (* v -6) v 2))
117.0ms
(sqrt (- PI (* v (* PI v))))
111.0ms
(sqrt (- PI (* v (* PI v))))

simplify5.6s

Counts
32 → 76
Calls
32 calls:
Slowest
645.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
642.0ms
(- (+ (* 1/2 (/ PI (* v (sqrt (- PI))))) (* v (sqrt (- PI)))) (* 1/8 (/ (pow PI 2) (* (pow v 3) (pow (sqrt (- PI)) 3)))))
601.0ms
(sqrt (- (pow PI 3) (pow (* v (* PI v)) 3)))
312.0ms
(- (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 2))) (* 1/81 (/ (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 4)))))
304.0ms
(- (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 2))) (* 1/81 (/ (exp (* 1/3 (- (log -6) (* 2 (log (/ -1 v)))))) (pow v 4)))))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize111.0ms

Local error

Found 4 expressions with local error:

1.0b
(* PI (- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v))))))
0.3b
(* PI v)
0.3b
(* PI v)
0.3b
(* PI v)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×associate-*r*
12×pow1 *-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
4×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in
2×sub-neg prod-diff associate-*r/
1×flip3-- flip-- difference-of-squares
Counts
4 → 93
Calls
4 calls:
Slowest
42.0ms
(* PI (- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v))))))
8.0ms
(* PI v)
5.0ms
(* PI v)
5.0ms
(* PI v)

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(* PI (- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v))))))
30.0ms
(* PI v)
23.0ms
(* PI v)
21.0ms
(* PI v)

simplify6.5s

Counts
58 → 105
Calls
58 calls:
Slowest
605.0ms
(sqrt (- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v))))))
581.0ms
(cbrt (- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v))))))
507.0ms
(+ (* (* PI PI) (* PI PI)) (+ (* (* (* PI (* v (* v v))) (* PI (* v (* v v)))) (* (* PI (* v (* v v))) (* PI (* v (* v v))))) (* (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v)))))))
474.0ms
(- (* PI PI) (* (* PI (* v (* v v))) (* PI (* v (* v v)))))
368.0ms
(- PI (* PI (* v (* v v))))

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.3s8019×body80nan
1.2s8000×body80valid