Details

Time bar (total: 2.4m)

sample54.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
18.0ms279×body80nan

simplify6.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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

series56.0ms

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

simplify1.0s

Calls
77 calls:
Slowest
235.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
74.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
50.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
41.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
35.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune346.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.2b
(/ (- (acos a)) a)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
146×*-un-lft-identity
144×add-sqr-sqrt add-cube-cbrt
52×distribute-rgt-neg-in
51×distribute-lft-neg-in
40×associate-/r*
25×associate-/l*
17×neg-mul-1
16×associate-/r/
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv clear-num
3×pow1 frac-2neg remove-double-div
2×rec-exp 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg pow-flip inv-pow
Calls
2 calls:
Slowest
24.0ms
(/ 1 (/ (- (acos a)) a))
11.0ms
(/ (- (acos a)) a)

series110.0ms

Calls
2 calls:
Slowest
67.0ms
(/ (- (acos a)) a)
44.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.1s

Calls
343 calls:
Slowest
835.0ms
(/ (* (* 1 1) 1) (* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a)))
461.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
433.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
385.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
348.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))

prune1.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
556×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
141×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
47×neg-mul-1
46×add-exp-log
43×associate-/l*
36×associate-/r*
34×div-exp
16×add-cbrt-cube associate-/l/
9×cbrt-undiv rec-exp 1-exp associate-/r/
4×clear-num frac-2neg
3×pow1
2×insert-posit16 add-log-exp
1×pow-flip inv-pow
Calls
2 calls:
Slowest
17.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series46.0ms

Calls
2 calls:
Slowest
41.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.4m

Calls
1051 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
685.0ms
(/ (/ 1 (sqrt (acos a))) (/ 1 a))
593.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
587.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
578.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))

prune3.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
210×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×div-inv
26×add-exp-log
22×associate-/r* associate-/l*
17×div-exp
16×add-cbrt-cube
9×cbrt-undiv associate-/r/ associate-/l/
4×clear-num frac-2neg
2×pow1 rec-exp 1-exp insert-posit16 add-log-exp
Calls
2 calls:
Slowest
10.0ms
(/ (/ -1 (acos a)) (/ 1 a))
7.0ms
(/ -1 (acos a))

series32.0ms

Calls
2 calls:
Slowest
26.0ms
(/ (/ -1 (acos a)) (/ 1 a))
5.0ms
(/ -1 (acos a))

simplify31.5s

Calls
418 calls:
Slowest
830.0ms
(/ (* (* (/ -1 (acos a)) (/ -1 (acos a))) (/ -1 (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
711.0ms
(/ (* (* -1 -1) -1) (* (* (acos a) (acos a)) (acos a)))
595.0ms
(/ (* (* (/ -1 (acos a)) (/ -1 (acos a))) (/ -1 (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))
520.0ms
(/ (/ (* (cbrt -1) (cbrt -1)) (sqrt (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
520.0ms
(/ (/ (sqrt -1) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
544.0ms8000×body80valid
479.0ms8028×body80nan