Details

Time bar (total: 25.2s)

sample50.0ms

Algorithm
intervals
Results
21.0ms293×body80nan
18.0ms256×body80valid

simplify4.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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

series46.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
46.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 59
Calls
77 calls:
Slowest
210.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
86.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
48.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
38.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
38.0ms
(* -1 (/ a (acos a)))

prune445.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite32.0ms

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

series90.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
50.0ms
(/ (- (acos a)) a)
40.0ms
(/ 1 (/ (- (acos a)) a))

simplify15.1s

Counts
326 → 225
Calls
326 calls:
Slowest
522.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
473.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
406.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
353.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
351.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ 1 (* (- (acos a)) (/ 1 a)))
0.3b
(* (- (acos a)) (/ 1 a))

rewrite25.0ms

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
13.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
10.0ms
(* (- (acos a)) (/ 1 a))

series93.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(* (- (acos a)) (/ 1 a))
44.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify3.0s

Counts
64 → 92
Calls
64 calls:
Slowest
455.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
209.0ms
(- 0 (log (* (- (acos a)) (/ 1 a))))
203.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a))))
191.0ms
(- (log 1) (log (* (- (acos a)) (/ 1 a))))
155.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))))

prune571.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.9b
(sqrt (acos a))
0.9b
(sqrt (acos a))
0.6b
(cbrt a)
0.6b
(cbrt a)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 52
Calls
4 calls:
Slowest
2.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))
1.0ms
(cbrt a)
1.0ms
(cbrt a)

series692.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
337.0ms
(cbrt a)
321.0ms
(cbrt a)
17.0ms
(sqrt (acos a))
17.0ms
(sqrt (acos a))

simplify427.0ms

Counts
28 → 64
Calls
28 calls:
Slowest
150.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
127.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
31.0ms
(pow (/ 1 a) -1/3)
24.0ms
(pow (/ 1 a) -1/3)
8.0ms
(sqrt 1)

prune602.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes114.0ms

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
579.0ms8000×body80valid
444.0ms8001×body80nan