Details

Time bar (total: 1.1m)

sample36.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
10.0ms259×body80nan

simplify4.0ms

Calls
1 calls:
Slowest
4.0ms
(/ a (- (acos a)))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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
Calls
1 calls:
Slowest
5.0ms
(/ a (- (acos a)))

series28.0ms

Calls
1 calls:
Slowest
28.0ms
(/ a (- (acos a)))

simplify858.0ms

Calls
77 calls:
Slowest
160.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
62.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
44.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
38.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
30.0ms
(* -1 (/ a (acos a)))

prune408.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite25.0ms

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
Calls
2 calls:
Slowest
10.0ms
(/ (- (acos a)) a)
8.0ms
(/ 1 (/ (- (acos a)) a))

series94.0ms

Calls
2 calls:
Slowest
53.0ms
(/ (- (acos a)) a)
41.0ms
(/ 1 (/ (- (acos a)) a))

simplify13.3s

Calls
326 calls:
Slowest
517.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
381.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
346.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
339.0ms
(/ (sqrt 1) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
296.0ms
(/ 1 (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (- (acos a)) a))
0.6b
(cbrt (/ (- (acos a)) a))
0.6b
(cbrt (/ (- (acos a)) a))
0.5b
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
262×cbrt-prod
228×times-frac
176×add-sqr-sqrt
164×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
43×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
28.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
2.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))

series999.0ms

Calls
4 calls:
Slowest
292.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
237.0ms
(cbrt (/ (- (acos a)) a))
236.0ms
(cbrt (/ (- (acos a)) a))
233.0ms
(cbrt (/ (- (acos a)) a))

simplify8.3s

Calls
311 calls:
Slowest
550.0ms
(exp (* 1/3 (+ (log (/ -1 a)) (log (acos a)))))
313.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
312.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
259.0ms
(* (cbrt -1) (exp (* 1/3 (+ (log (/ 1 a)) (log (acos a))))))
254.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))

prune3.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (- (acos a)) a))
0.6b
(cbrt (/ (- (acos a)) a))
0.6b
(cbrt (/ (- (acos a)) a))
0.5b
(* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
1078×times-frac
660×add-sqr-sqrt
602×cbrt-prod
572×*-un-lft-identity
492×add-cube-cbrt
153×distribute-rgt-neg-in
136×swap-sqr
135×distribute-lft-neg-in
116×associate-*r* associate-*l*
49×unswap-sqr
45×neg-mul-1
44×add-exp-log
21×div-inv
19×pow1
16×div-exp prod-exp
14×pow-flip
12×add-cbrt-cube
9×pow1/3
8×rec-exp 1-exp inv-pow
7×cbrt-div
6×pow-prod-up
4×cbrt-undiv pow-prod-down associate-/r/ pow-sqr cbrt-unprod insert-posit16 add-log-exp
1×pow2 frac-times pow-plus associate-*l/ associate-*r/ un-div-inv *-commutative
Calls
4 calls:
Slowest
44.0ms
(* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
3.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))

series920.0ms

Calls
4 calls:
Slowest
298.0ms
(* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
217.0ms
(cbrt (/ (- (acos a)) a))
211.0ms
(cbrt (/ (- (acos a)) a))
193.0ms
(cbrt (/ (- (acos a)) a))

simplify30.4s

Calls
769 calls:
Slowest
676.0ms
(* (* (* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ 1 (cbrt (/ (- (acos a)) a)))) (* (* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ 1 (cbrt (/ (- (acos a)) a)))))
617.0ms
(* (* (* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ (* (* 1 1) 1) (/ (- (acos a)) a)))
333.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
301.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (cbrt (/ (- (acos a)) a))) (cbrt (cbrt (/ (- (acos a)) a))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (cbrt (/ (- (acos a)) a))) (cbrt (cbrt (/ (- (acos a)) a))))))
296.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))

prune6.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
618.0ms8000×body80valid
409.0ms8107×body80nan