Details

Time bar (total: 11.3s)

sample22.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
4.0ms226×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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 div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
11.0ms
(/ a (- (acos a)))

series29.0ms

Counts
1 → 3
Calls
1 calls:
29.0ms
(/ a (- (acos a)))

simplify991.0ms

Counts
58 → 58
Iterations
IterNodes
done5001
32040
2462
1171
094

prune211.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite36.0ms

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 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 217
Calls
2 calls:
13.0ms
(/ 1 (/ (- (acos a)) a))
7.0ms
(/ (- (acos a)) a)

series74.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ 1 (/ (- (acos a)) a))
47.0ms
(/ (- (acos a)) a)

simplify1.7s

Counts
223 → 223
Iterations
IterNodes
done5000
24452
1785
0288

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (* (- (acos a)) (/ 1 a)))
0.4b
(* (- (acos a)) (/ 1 a))

rewrite54.0ms

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 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 → 84
Calls
2 calls:
31.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
20.0ms
(* (- (acos a)) (/ 1 a))

series79.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
43.0ms
(* (- (acos a)) (/ 1 a))

simplify1.7s

Counts
90 → 90
Iterations
IterNodes
done5001
22278
1378
0125

prune204.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
262×cbrt-prod
228×times-frac
176×add-sqr-sqrt
164×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
43×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×add-cbrt-cube 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 → 276
Calls
4 calls:
81.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
6.0ms
(cbrt (/ (- (acos a)) a))
5.0ms
(cbrt (/ (- (acos a)) a))
4.0ms
(cbrt (/ (- (acos a)) a))

series1.2s

Counts
4 → 12
Calls
4 calls:
262.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
205.0ms
(cbrt (/ (- (acos a)) a))
229.0ms
(cbrt (/ (- (acos a)) a))
516.0ms
(cbrt (/ (- (acos a)) a))

simplify1.2s

Counts
288 → 288
Iterations
IterNodes
done5001
21996
1519
0296

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done4
04

end0.0ms

sample1.1s

Algorithm
intervals
Results
467.0ms8000×body80valid
218.0ms7970×body80nan