Details

Time bar (total: 3.2m)

sample35.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
10.0ms251×body80nan

simplify6.0ms

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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
Counts
1 → 58
Calls
1 calls:
Slowest
10.0ms
(/ a (- (acos a)))

series33.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
33.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
230.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
69.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
58.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
39.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))
38.0ms
(* -1 (/ a (acos a)))

prune425.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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
Counts
2 → 223
Calls
2 calls:
Slowest
16.0ms
(/ (- (acos a)) a)
11.0ms
(/ 1 (/ (- (acos a)) a))

series111.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(/ (- (acos a)) a)
48.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.7s

Counts
326 → 229
Calls
326 calls:
Slowest
466.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
454.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
401.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
375.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
358.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite70.0ms

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×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 586
Calls
2 calls:
Slowest
23.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
44.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.5m

Counts
1031 → 592
Calls
1031 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
702.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (* (cbrt (/ 1 a)) (cbrt (/ 1 a))))
607.0ms
(/ (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
587.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))
584.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune4.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize28.0ms

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))

rewrite121.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 781
Calls
4 calls:
Slowest
32.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
15.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
12.0ms
(* (acos a) (acos a))
6.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
62.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
57.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
15.0ms
(* (acos a) (acos a))

simplify1.2m

Counts
1311 → 793
Calls
1311 calls:
Slowest
512.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (acos a))) 1)
291.0ms
(/ (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))
257.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
246.0ms
(/ (* (cbrt (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))) (cbrt (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
246.0ms
(cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a)))

prune5.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample931.0ms

Algorithm
intervals
Results
455.0ms8000×body80valid
294.0ms7971×body80nan