Details

Time bar (total: 1.2m)

sample42.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
13.0ms259×body80nan

simplify4.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

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×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
1 calls:
Slowest
9.0ms
(/ a (- (acos a)))

series33.0ms

Calls
1 calls:
Slowest
33.0ms
(/ a (- (acos a)))

simplify1.1s

Calls
77 calls:
Slowest
227.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
90.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
39.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
39.0ms
(* -1 (/ a (acos a)))
37.0ms
(* -1 (/ a (acos a)))

prune529.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Calls
2 calls:
Slowest
8.0ms
(/ 1 (/ (- (acos a)) a))
6.0ms
(/ (- (acos a)) a)

series101.0ms

Calls
2 calls:
Slowest
63.0ms
(/ (- (acos a)) a)
38.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.2s

Calls
326 calls:
Slowest
530.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
490.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
411.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
356.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
324.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

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)))

rewrite29.0ms

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×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u 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
16.0ms
(* (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))

series935.0ms

Calls
4 calls:
Slowest
291.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
231.0ms
(cbrt (/ (- (acos a)) a))
223.0ms
(cbrt (/ (- (acos a)) a))
190.0ms
(cbrt (/ (- (acos a)) a))

simplify8.8s

Calls
311 calls:
Slowest
383.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
381.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
335.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
261.0ms
(* (cbrt -1) (exp (* 1/3 (+ (log (/ 1 a)) (log (acos a))))))
248.0ms
(* (pow (cbrt -1) 2) (exp (* 1/3 (+ (* 2 (log (/ 1 a))) (log (pow (acos a) 2))))))

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize38.0ms

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))))

rewrite78.0ms

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×expm1-log1p-u cbrt-undiv pow-prod-down associate-/r/ pow-sqr cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×pow2 frac-times pow-plus associate-*l/ associate-*r/ un-div-inv *-commutative
Calls
4 calls:
Slowest
49.0ms
(* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
4.0ms
(cbrt (/ (- (acos a)) a))
3.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))

series974.0ms

Calls
4 calls:
Slowest
296.0ms
(* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
275.0ms
(cbrt (/ (- (acos a)) a))
212.0ms
(cbrt (/ (- (acos a)) a))
192.0ms
(cbrt (/ (- (acos a)) a))

simplify33.8s

Calls
769 calls:
Slowest
1.1s
(* (* (* (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ 1 (cbrt (/ (- (acos a)) a)))) (/ (* (* 1 1) 1) (/ (- (acos a)) a)))
769.0ms
(* (* (* (/ 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)))))
412.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
401.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))
359.0ms
(* (exp (* 1/3 (- (log (acos a)) (log a)))) (cbrt -1))

prune7.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes148.0ms

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
610.0ms8000×body80valid
425.0ms8107×body80nan