Details

Time bar (total: 10.4s)

sample39.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
7.0ms248×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune5.0ms

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)))

rewrite323.0ms

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)))

series41.0ms

Counts
1 → 3
Calls
1 calls:
41.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
58 → 58
Iterations

Useful iterations: 3 (305.0ms)

IterNodesCost
094601
1171569
2462553
32040551
done5001551

prune213.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- (acos a)) a)
0.5b
(/ 1 (/ (- (acos a)) a))

rewrite44.0ms

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:
11.0ms
(/ (- (acos a)) a)
14.0ms
(/ 1 (/ (- (acos a)) a))

series73.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(/ (- (acos a)) a)
30.0ms
(/ 1 (/ (- (acos a)) a))

simplify1.4s

Counts
223 → 223
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02883166
17852618
238762554
done50002550

prune582.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

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 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))

series591.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(cbrt a)
269.0ms
(cbrt a)
14.0ms
(sqrt (acos a))
20.0ms
(sqrt (acos a))

simplify2.0s

Counts
60 → 60
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
040284
162254
2136238
3372232
4982232
53389232
done5001232

prune279.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 50
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))

series381.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(cbrt a)
18.0ms
(sqrt (acos a))
18.0ms
(sqrt (acos a))
14.0ms
(sqrt (acos a))

simplify1.9s

Counts
62 → 62
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
040296
162257
2136247
3372244
4982244
53389244
done5001244

prune254.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes121.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify0.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample974.0ms

Algorithm
intervals
Results
332.0ms8000×body80valid
258.0ms7876×body80nan