Details

Time bar (total: 1.8m)

sample32.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
10.0ms251×body80nan

simplify3.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
3.0ms
(/ a (- (acos a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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
9.0ms
(/ a (- (acos a)))

series53.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
53.0ms
(/ a (- (acos a)))

simplify996.0ms

Counts
77 → 59
Calls
77 calls:
Slowest
182.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
57.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
40.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
35.0ms
(* -1 (/ a (acos a)))
35.0ms
(* -1 (/ a (acos a)))

prune332.0ms

Pruning

8 alts after pruning (7 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)

rewrite24.0ms

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
9.0ms
(/ (- (acos a)) a)
8.0ms
(/ 1 (/ (- (acos a)) a))

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(/ (- (acos a)) a)
40.0ms
(/ 1 (/ (- (acos a)) a))

simplify13.3s

Counts
326 → 225
Calls
326 calls:
Slowest
452.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
428.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
350.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
342.0ms
(/ 1 (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
328.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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
16.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
11.0ms
(* (- (acos a)) (/ 1 a))

series90.0ms

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

simplify3.0s

Counts
64 → 92
Calls
64 calls:
Slowest
423.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
186.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))))
170.0ms
(- 0 (log (* (- (acos a)) (/ 1 a))))
156.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))))
138.0ms
(- (log 1) (log (* (- (acos a)) (/ 1 a))))

prune555.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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
18.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
5.0ms
(/ 1 (- (acos a)))

series48.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
38.0ms
(/ (/ 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)))
780.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
554.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
548.0ms
(/ (/ 1 (- (sqrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
540.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune3.5s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
469.0ms8000×body80valid
391.0ms8057×body80nan