Details

Time bar (total: 2.4m)

sample49.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
18.0ms241×body80nan

simplify4.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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)))

series44.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
44.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
90 → 59
Calls
90 calls:
Slowest
311.0ms
(* (* (/ a (- (acos a))) (/ a (- (acos a)))) (/ a (- (acos a))))
249.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
73.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
45.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
34.0ms
(/ (* (cbrt a) (cbrt a)) (- 1))

prune435.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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
11.0ms
(/ (- (acos a)) a)
11.0ms
(/ 1 (/ (- (acos a)) a))

series95.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(/ 1 (/ (- (acos a)) a))
47.0ms
(/ (- (acos a)) a)

simplify18.3s

Counts
359 → 225
Calls
359 calls:
Slowest
608.0ms
(* (* (/ 1 (/ (- (acos a)) a)) (/ 1 (/ (- (acos a)) a))) (/ 1 (/ (- (acos a)) a)))
508.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
440.0ms
(* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a))
419.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
384.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))

prune1.7s

Pruning

12 alts after pruning (10 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)))

rewrite51.0ms

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
22.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series40.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.7m

Counts
1061 → 588
Calls
1061 calls:
Slowest
1.1s
(/ (/ (* (cbrt 1) (cbrt 1)) (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
1.0s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
729.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (sqrt a)))
721.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
709.0ms
(/ (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (* (cbrt a) (cbrt a))))

prune4.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×add-cbrt-cube prod-exp
15×*-un-lft-identity
14×times-frac add-cube-cbrt
13×associate-*r*
10×associate-*l*
9×rec-exp 1-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l* unswap-sqr
2×pow-prod-down associate-*r/ associate-/r/ un-div-inv insert-posit16 div-inv pow-flip add-log-exp
1×distribute-lft-neg-out clear-num associate-/r* neg-mul-1 frac-2neg *-commutative inv-pow
Counts
2 → 86
Calls
2 calls:
Slowest
19.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
11.0ms
(* (- (acos a)) (/ 1 a))

series101.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
64.0ms
(* (- (acos a)) (/ 1 a))
37.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify9.7s

Counts
96 → 92
Calls
96 calls:
Slowest
700.0ms
(* (* (/ 1 (* (- (acos a)) (/ 1 a))) (/ 1 (* (- (acos a)) (/ 1 a)))) (/ 1 (* (- (acos a)) (/ 1 a))))
662.0ms
(* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)))
498.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
332.0ms
(* (- (acos a)) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
321.0ms
(* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))

prune600.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
635.0ms8000×body80valid
512.0ms8062×body80nan