Details

Time bar (total: 2.0m)

sample47.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
15.0ms257×body80nan

simplify4.0ms

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

prune5.0ms

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)))

series54.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
54.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 59
Calls
77 calls:
Slowest
190.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
97.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
54.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
50.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
35.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune443.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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
12.0ms
(/ 1 (/ (- (acos a)) a))
11.0ms
(/ (- (acos a)) a)

series114.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(/ (- (acos a)) a)
37.0ms
(/ 1 (/ (- (acos a)) a))

simplify15.0s

Counts
326 → 225
Calls
326 calls:
Slowest
474.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
461.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
441.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
371.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
361.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
1177×times-frac
526×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
126×distribute-lft-neg-in distribute-rgt-neg-in
50×div-inv
42×neg-mul-1
41×add-exp-log
34×associate-/l*
32×div-exp
13×associate-/r* add-cbrt-cube
8×cbrt-undiv rec-exp 1-exp
1×pow1 clear-num frac-2neg associate-/r/ insert-posit16 add-log-exp associate-/l/
Counts
1 → 522
Calls
1 calls:
Slowest
15.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series54.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
54.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify1.5m

Counts
952 → 525
Calls
952 calls:
Slowest
1.1s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
640.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
616.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
582.0ms
(/ (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))
573.0ms
(/ (/ 1 (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune3.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1 a))
0.5b
(cbrt (/ 1 a))
0.5b
(cbrt (/ 1 a))
0.5b
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
119×cbrt-prod
97×add-sqr-sqrt
79×times-frac
67×*-un-lft-identity
57×add-cube-cbrt
18×swap-sqr
16×associate-*r* associate-*l* unswap-sqr
11×pow1
9×pow1/3 div-inv
7×cbrt-div
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
2.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
284.0ms
(cbrt (/ 1 a))
242.0ms
(cbrt (/ 1 a))
217.0ms
(cbrt (/ 1 a))

simplify3.0s

Counts
170 → 169
Calls
170 calls:
Slowest
407.0ms
(* (pow (/ 1 (pow a 2)) 1/3) (pow (cbrt -1) 2))
114.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
113.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
102.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
76.0ms
(* (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))) (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))))

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
506.0ms8000×body80valid
333.0ms7749×body80nan