Details

Time bar (total: 3.1m)

sample47.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
15.0ms273×body80nan

simplify6.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
6.0ms
(/ a (- (acos a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
1 → 56
Calls
1 calls:
Slowest
10.0ms
(/ a (- (acos a)))

series56.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
56.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 59
Calls
77 calls:
Slowest
204.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
69.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
43.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
42.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
35.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune375.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (/ (- (acos a)) a))
0.2b
(/ (- (acos a)) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/r*
16×neg-mul-1
15×add-exp-log
13×associate-/l*
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv
3×pow1
2×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 219
Calls
2 calls:
Slowest
7.0ms
(/ 1 (/ (- (acos a)) a))
5.0ms
(/ (- (acos a)) a)

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(/ (- (acos a)) a)
35.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.2s

Counts
326 → 225
Calls
326 calls:
Slowest
451.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
411.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
396.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
383.0ms
(/ (sqrt 1) (/ (- (acos a)) a))
350.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×neg-mul-1 add-exp-log
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 582
Calls
2 calls:
Slowest
27.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
45.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.4m

Counts
1031 → 588
Calls
1031 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
993.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
646.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
623.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
594.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))

prune3.8s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
1.0b
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
0.4b
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
0.0b
(* (acos a) (acos a))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
1965×times-frac
673×add-sqr-sqrt
671×*-un-lft-identity add-cube-cbrt
570×cbrt-prod
153×distribute-lft-neg-in distribute-rgt-neg-in
76×div-inv
75×associate-/l*
51×neg-mul-1
37×add-exp-log
21×add-cbrt-cube
18×div-exp
14×associate-/r*
11×pow1
9×cbrt-undiv
5×prod-exp
4×insert-posit16 add-log-exp
3×rec-exp 1-exp swap-sqr associate-*r* associate-*l* cbrt-unprod
2×cbrt-div clear-num frac-2neg associate-/l/
1×pow2 pow-plus pow1/3 pow-prod-down associate-/r/ pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 773
Calls
4 calls:
Slowest
14.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
11.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
9.0ms
(* (acos a) (acos a))
5.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
45.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
44.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
23.0ms
(* (acos a) (acos a))

simplify1.3m

Counts
1311 → 785
Calls
1311 calls:
Slowest
447.0ms
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (acos a))
360.0ms
(/ (cbrt (/ (/ 1 (sqrt (acos a))) (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
346.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
345.0ms
(/ (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))
290.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune4.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample906.0ms

Algorithm
intervals
Results
459.0ms8000×body80valid
287.0ms7988×body80nan