Details

Time bar (total: 3.4m)

sample46.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
15.0ms292×body80nan

simplify3.0ms

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

prune4.0ms

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)))

rewrite8.0ms

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
7.0ms
(/ a (- (acos a)))

series43.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
43.0ms
(/ a (- (acos a)))

simplify1.6s

Counts
90 → 59
Calls
90 calls:
Slowest
428.0ms
(* (* (/ a (- (acos a))) (/ a (- (acos a)))) (/ a (- (acos a))))
165.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
72.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
56.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
55.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))

prune461.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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
15.0ms
(/ 1 (/ (- (acos a)) a))
11.0ms
(/ (- (acos a)) a)

series70.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(/ (- (acos a)) a)
28.0ms
(/ 1 (/ (- (acos a)) a))

simplify17.7s

Counts
359 → 225
Calls
359 calls:
Slowest
726.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
552.0ms
(* (* (/ 1 (/ (- (acos a)) a)) (/ 1 (/ (- (acos a)) a))) (/ 1 (/ (- (acos a)) a)))
505.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
485.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
405.0ms
(* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite63.0ms

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
23.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series42.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
36.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.6m

Counts
1061 → 588
Calls
1061 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
642.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))
629.0ms
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
619.0ms
(/ (/ 1 (- (sqrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
595.0ms
(/ (/ 1 (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune3.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
1.0b
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
0.4b
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
0.0b
(* (acos a) (acos a))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
1965×times-frac
673×add-sqr-sqrt
671×*-un-lft-identity add-cube-cbrt
570×cbrt-prod
153×distribute-lft-neg-in distribute-rgt-neg-in
76×div-inv
75×associate-/l*
51×neg-mul-1
37×add-exp-log
21×add-cbrt-cube
18×div-exp
14×associate-/r*
11×pow1
9×cbrt-undiv
5×prod-exp
4×insert-posit16 add-log-exp
3×rec-exp 1-exp swap-sqr associate-*r* associate-*l* cbrt-unprod
2×cbrt-div clear-num frac-2neg associate-/l/
1×pow2 pow-plus pow1/3 pow-prod-down associate-/r/ pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 773
Calls
4 calls:
Slowest
21.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
12.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
10.0ms
(* (acos a) (acos a))
10.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
53.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
38.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
19.0ms
(* (acos a) (acos a))

simplify1.2m

Counts
1394 → 785
Calls
1394 calls:
Slowest
604.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) 1)
532.0ms
(* (* (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
294.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
291.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
283.0ms
(/ (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))

prune4.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample860.0ms

Algorithm
intervals
Results
411.0ms8000×body80valid
291.0ms7694×body80nan