Details

Time bar (total: 1.1m)

sample53.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
17.0ms284×body80nan

simplify6.0ms

Counts
1 → 1
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

localize15.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 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
10.0ms
(/ a (- (acos a)))

series63.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
63.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 59
Calls
77 calls:
Slowest
232.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
85.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
54.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
36.0ms
(* -1 (/ a (acos a)))
31.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune368.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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
13.0ms
(/ 1 (/ (- (acos a)) a))
6.0ms
(/ (- (acos a)) a)

series88.0ms

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

simplify14.1s

Counts
326 → 225
Calls
326 calls:
Slowest
479.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
458.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
374.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
352.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
314.0ms
(/ (* (* 1 1) 1) (* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a)))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
101×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×div-inv
8×add-exp-log
6×add-cbrt-cube associate-/l*
4×neg-mul-1
3×pow1 div-exp
2×cbrt-undiv clear-num frac-2neg insert-posit16 add-log-exp
1×acos-asin rec-exp 1-exp div-sub associate-/r/ pow-flip distribute-neg-frac inv-pow
Counts
2 → 170
Calls
2 calls:
Slowest
7.0ms
(/ 1 (- (/ (acos a) a)))
6.0ms
(/ (acos a) a)

series76.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
41.0ms
(/ 1 (- (/ (acos a) a)))
35.0ms
(/ (acos a) a)

simplify8.9s

Counts
247 → 176
Calls
247 calls:
Slowest
422.0ms
(/ (* (* (acos a) (acos a)) (acos a)) (* (* a a) a))
264.0ms
(/ (sqrt 1) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
263.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
252.0ms
(/ (* (* 1 1) 1) (* (* (- (/ (acos a) a)) (- (/ (acos a) a))) (- (/ (acos a) a))))
248.0ms
(/ 1 (- (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a)))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
206×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×div-inv
28×add-exp-log
18×div-exp
16×associate-/r* add-cbrt-cube associate-/l*
9×cbrt-undiv
3×pow1 rec-exp 1-exp
2×clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 252
Calls
2 calls:
Slowest
10.0ms
(/ (/ 1 (acos a)) (/ -1 a))
4.0ms
(/ 1 (acos a))

series50.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
44.0ms
(/ (/ 1 (acos a)) (/ -1 a))
5.0ms
(/ 1 (acos a))

simplify34.7s

Counts
407 → 258
Calls
407 calls:
Slowest
941.0ms
(/ (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (* (cbrt a) (cbrt a))))
650.0ms
(/ (/ (* (* 1 1) 1) (* (* (acos a) (acos a)) (acos a))) (* (* (/ -1 a) (/ -1 a)) (/ -1 a)))
592.0ms
(/ (/ (sqrt 1) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt -1) (cbrt -1)) 1))
558.0ms
(/ (/ (sqrt 1) 1) (/ (* (cbrt -1) (cbrt -1)) (* (cbrt a) (cbrt a))))
540.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) 1) (/ (* (cbrt -1) (cbrt -1)) (* (cbrt a) (cbrt a))))

prune1.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
600.0ms8000×body80valid
367.0ms8133×body80nan