Details

Time bar (total: 10.8s)

sample30.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
6.0ms248×body80nan

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

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 log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
6.0ms
(/ a (- (acos a)))

series40.0ms

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

simplify1.1s

Counts
60 → 60
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
096613
1173581
2466563
32093563
done5000563

prune245.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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 log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 221
Calls
2 calls:
6.0ms
(/ (- (acos a)) a)
13.0ms
(/ 1 (/ (- (acos a)) a))

series83.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (- (acos a)) a)
46.0ms
(/ 1 (/ (- (acos a)) a))

simplify1.6s

Counts
227 → 227
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02923194
17902646
239772582
done50012578

prune619.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

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))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))

series609.0ms

Counts
4 → 12
Calls
4 calls:
303.0ms
(cbrt a)
275.0ms
(cbrt a)
14.0ms
(sqrt (acos a))
17.0ms
(sqrt (acos a))

simplify2.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
044312
166282
2137266
3363260
4960260
53446260
done5000260

prune374.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize46.0ms

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))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 58
Calls
4 calls:
1.0ms
(cbrt a)
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))

series327.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(cbrt a)
12.0ms
(sqrt (acos a))
11.0ms
(sqrt (acos a))
15.0ms
(sqrt (acos a))

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
044326
166287
2137277
3363274
4960274
53446274
done5000274

prune307.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample969.0ms

Algorithm
intervals
Results
368.0ms8000×body80valid
243.0ms7876×body80nan