Details

Time bar (total: 11.0s)

sample17.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms234×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
4.0ms
(/ a (- (acos a)))

series29.0ms

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

simplify1.7s

Counts
58 → 58
Iterations

Useful iterations: 5 (931.0ms)

IterNodesCost
094601
1164569
2328551
3713551
41237551
52179546
done5001546

prune110.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
101×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×div-inv
8×add-exp-log
6×add-cbrt-cube associate-/l*
4×neg-mul-1
3×pow1 div-exp
2×cbrt-undiv frac-2neg clear-num add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 168
Calls
2 calls:
2.0ms
(/ (acos a) a)
10.0ms
(/ 1 (- (/ (acos a) a)))

series53.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (acos a) a)
26.0ms
(/ 1 (- (/ (acos a) a)))

simplify2.3s

Counts
174 → 174
Iterations

Useful iterations: 3 (501.0ms)

IterNodesCost
02612383
14831978
27851835
317081689
434521689
done50001689

prune206.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
29×times-frac
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
15×add-exp-log
13×associate-*r*
9×add-cbrt-cube
6×associate-/r*
5×pow1
4×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in div-exp prod-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp associate-*r/ associate-/r/ un-div-inv cbrt-unprod div-inv distribute-neg-frac add-log-exp
1×pow-flip frac-2neg pow-prod-down clear-num *-commutative inv-pow
Counts
2 → 81
Calls
2 calls:
3.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
10.0ms
(* (acos a) (/ 1 a))

series53.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
28.0ms
(* (acos a) (/ 1 a))

simplify2.1s

Counts
87 → 87
Iterations

Useful iterations: 3 (616.0ms)

IterNodesCost
0134955
1293674
2658593
32316559
done5000559

prune123.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt a)
0.7b
(cbrt a)
1.0b
(sqrt (acos a))
1.0b
(sqrt (acos a))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 48
Calls
4 calls:
0.0ms
(cbrt a)
0.0ms
(cbrt a)
1.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))

series381.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt a)
179.0ms
(cbrt a)
10.0ms
(sqrt (acos a))
10.0ms
(sqrt (acos a))

simplify3.3s

Counts
60 → 60
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
040284
160252
2103238
3185232
4388232
51076232
64197232
done5001232

prune137.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample439.0ms

Algorithm
intervals
Results
162.0ms8000×body80valid
109.0ms8035×body80nan