Details

Time bar (total: 3.5m)

sample81.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
33.0ms241×body80nan

simplify276.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
276.0ms
(/ 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

localize39.0ms

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)))

rewrite57.0ms

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
13.0ms
(/ 4/3 (- PI (* v (* PI v))))
13.0ms
(* v (* PI v))
12.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
10.0ms
(* PI v)

series614.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(/ (/ 4/3 (- PI (* v (* PI v)))) (sqrt (fma (* v -6) v 2)))
113.0ms
(/ 4/3 (- PI (* v (* PI v))))
31.0ms
(* v (* PI v))
23.0ms
(* PI v)

simplify33.9s

Counts
259 → 215
Calls
259 calls:
Slowest
561.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (sqrt (fma (* v -6) v 2))))
554.0ms
(/ 4/3 (- (pow PI 3) (pow (* v (* PI v)) 3)))
493.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (sqrt (sqrt (fma (* v -6) v 2))))
486.0ms
(/ (/ 4/3 (- (* PI PI) (* (* v (* PI v)) (* v (* PI v))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
472.0ms
(/ (/ (* (cbrt 4/3) (cbrt 4/3)) (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v)))))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))

prune2.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI v)
0.1b
(* v (* PI v))
0.0b
(/ (/ 1 (/ (- PI (* v (* PI v))) 4/3)) (sqrt (fma (* v -6) v 2)))
0.0b
(/ 1 (/ (- PI (* v (* PI v))) 4/3))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
801×times-frac
386×add-sqr-sqrt
384×*-un-lft-identity add-cube-cbrt
135×sqrt-prod
47×associate-/l*
41×add-exp-log
34×div-inv
25×add-cbrt-cube
21×div-exp
19×associate-/r*
12×pow1
9×cbrt-undiv
8×associate-/r/
6×associate-*l*
4×expm1-log1p-u rec-exp 1-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×pow-flip inv-pow unswap-sqr associate-/l/
Counts
4 → 459
Calls
4 calls:
Slowest
30.0ms
(/ (/ 1 (/ (- PI (* v (* PI v))) 4/3)) (sqrt (fma (* v -6) v 2)))
27.0ms
(* v (* PI v))
17.0ms
(/ 1 (/ (- PI (* v (* PI v))) 4/3))
14.0ms
(* PI v)

series603.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
442.0ms
(/ (/ 1 (/ (- PI (* v (* PI v))) 4/3)) (sqrt (fma (* v -6) v 2)))
102.0ms
(/ 1 (/ (- PI (* v (* PI v))) 4/3))
29.0ms
(* PI v)
28.0ms
(* v (* PI v))

simplify2.2m

Counts
715 → 471
Calls
715 calls:
Slowest
792.0ms
(/ (/ 1 (/ (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v))))) (* (cbrt 4/3) (cbrt 4/3)))) (sqrt (* (cbrt (fma (* v -6) v 2)) (cbrt (fma (* v -6) v 2)))))
762.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v))))) (sqrt 4/3))) (sqrt (sqrt (fma (* v -6) v 2))))
596.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt 4/3) (cbrt 4/3)))) (* (cbrt (sqrt (fma (* v -6) v 2))) (cbrt (sqrt (fma (* v -6) v 2)))))
574.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- PI (* v (* PI v)))) (cbrt (- PI (* v (* PI v))))) (sqrt 4/3)))
566.0ms
(/ (/ (sqrt 1) (/ (cbrt (- PI (* v (* PI v)))) (cbrt 4/3))) (sqrt (sqrt (fma (* v -6) v 2))))

prune5.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
257×times-frac
163×add-sqr-sqrt
152×*-un-lft-identity
126×add-cube-cbrt
67×associate-*l*
54×add-exp-log
50×difference-of-squares
34×add-cbrt-cube
26×div-exp
25×associate-/l*
16×associate-/r/
14×cbrt-undiv associate-/r*
11×div-inv
10×prod-exp
8×flip3-- flip--
7×pow1
6×sqrt-prod cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×associate-*l/ associate-/l/
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 283
Calls
4 calls:
Slowest
46.0ms
(* (/ (/ 1 (- 1 (* v v))) PI) 4/3)
26.0ms
(/ (* (/ (/ 1 (- 1 (* v v))) PI) 4/3) (sqrt (fma (* v -6) v 2)))
13.0ms
(/ (/ 1 (- 1 (* v v))) PI)
9.0ms
(/ 1 (- 1 (* v v)))

series877.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
570.0ms
(/ (* (/ (/ 1 (- 1 (* v v))) PI) 4/3) (sqrt (fma (* v -6) v 2)))
141.0ms
(* (/ (/ 1 (- 1 (* v v))) PI) 4/3)
126.0ms
(/ (/ 1 (- 1 (* v v))) PI)
40.0ms
(/ 1 (- 1 (* v v)))

simplify29.2s

Counts
324 → 295
Calls
324 calls:
Slowest
773.0ms
(/ (* (* (* (/ (/ 1 (- 1 (* v v))) PI) 4/3) (* (/ (/ 1 (- 1 (* v v))) PI) 4/3)) (* (/ (/ 1 (- 1 (* v v))) PI) 4/3)) (* (* (sqrt (fma (* v -6) v 2)) (sqrt (fma (* v -6) v 2))) (sqrt (fma (* v -6) v 2))))
653.0ms
(* (* (* (/ (/ 1 (- 1 (* v v))) PI) (/ (/ 1 (- 1 (* v v))) PI)) (/ (/ 1 (- 1 (* v v))) PI)) (* (* 4/3 4/3) 4/3))
551.0ms
(/ (* (/ (* (* (/ 1 (- 1 (* v v))) (/ 1 (- 1 (* v v)))) (/ 1 (- 1 (* v v)))) (* (* PI PI) PI)) (* (* 4/3 4/3) 4/3)) (* (* (sqrt (fma (* v -6) v 2)) (sqrt (fma (* v -6) v 2))) (sqrt (fma (* v -6) v 2))))
490.0ms
(/ (/ 1 (- (* 1 1) (* (* v v) (* v v)))) (sqrt PI))
475.0ms
(/ (* (* (/ 1 (- 1 (* v v))) (/ 1 (- 1 (* v v)))) (/ 1 (- 1 (* v v)))) (* (* PI PI) PI))

prune3.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.4s8000×body80valid
1.1s7875×body80nan