Details

Time bar (total: 2.0m)

sample60.0ms

Algorithm
intervals
Results
23.0ms257×body80nan
23.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
7.0ms
(/ a (- (acos a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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

series40.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
40.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
226.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
58.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
43.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
35.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
35.0ms
(* -1 (/ a (acos a)))

prune465.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

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
9.0ms
(/ 1 (/ (- (acos a)) a))
6.0ms
(/ (- (acos a)) a)

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
53.0ms
(/ (- (acos a)) a)
44.0ms
(/ 1 (/ (- (acos a)) a))

simplify15.2s

Counts
326 → 229
Calls
326 calls:
Slowest
508.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
475.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
354.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
346.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
327.0ms
(/ 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

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite55.0ms

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×expm1-log1p-u pow1 clear-num frac-2neg associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
Counts
1 → 524
Calls
1 calls:
Slowest
16.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series39.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
39.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify1.5m

Counts
952 → 527
Calls
952 calls:
Slowest
1.4s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
805.0ms
(/ (/ 1 (- (sqrt (acos a)))) (/ 1 (* (cbrt a) (cbrt a))))
763.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
676.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))
658.0ms
(/ (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (* (cbrt a) (cbrt a))))

prune3.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize41.0ms

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)))

rewrite37.0ms

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×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u 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 → 165
Calls
4 calls:
Slowest
24.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
4.0ms
(cbrt (/ 1 a))
3.0ms
(cbrt (/ 1 a))
3.0ms
(cbrt (/ 1 a))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(cbrt (/ 1 a))
282.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
261.0ms
(cbrt (/ 1 a))
254.0ms
(cbrt (/ 1 a))

simplify3.3s

Counts
170 → 177
Calls
170 calls:
Slowest
449.0ms
(* (pow (/ 1 (pow a 2)) 1/3) (pow (cbrt -1) 2))
143.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
130.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
128.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
86.0ms
(* (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))) (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))))

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
633.0ms8000×body80valid
418.0ms7749×body80nan