Details

Time bar (total: 20.9s)

sample34.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
8.0ms251×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
8.0ms
(/ a (- (acos a)))

series34.0ms

Counts
1 → 3
Calls
1 calls:
34.0ms
(/ a (- (acos a)))

simplify4.7s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.7s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune187.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

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
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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 172
Calls
2 calls:
20.0ms
(/ 1 (- (/ (acos a) a)))
6.0ms
(/ (acos a) a)

series102.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ 1 (- (/ (acos a) a)))
53.0ms
(/ (acos a) a)

simplify6.1s

Counts
178 → 178
Iterations

Useful iterations: 3 (693.0ms)

IterNodesCost
02652409
14722004
27821861
315341711
427841711
done50001711

prune279.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (/ PI 2) a) (/ (asin a) a))
0.0b
(/ (asin a) a)
0.2b
(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
0.3b
(/ (/ PI 2) a)

rewrite688.0ms

Algorithm
rewrite-expression-head
Rules
1626×times-frac
1097×add-sqr-sqrt
980×*-un-lft-identity
908×add-cube-cbrt
559×prod-diff
124×div-inv
56×distribute-lft-neg-in distribute-rgt-neg-in
54×difference-of-squares
43×fma-neg
38×associate-/r*
36×distribute-lft-out--
19×associate-/l*
15×add-exp-log
13×add-cbrt-cube
9×distribute-rgt-out--
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u neg-mul-1 associate-/r/ log1p-expm1-u distribute-neg-frac
3×frac-2neg clear-num
2×asin-acos flip3-- div-sub frac-sub flip-- sub-div
1×sub-neg rec-exp pow-flip diff-log 1-exp associate-/l/ inv-pow associate--r-
Counts
4 → 885
Calls
4 calls:
90.0ms
(- (/ (/ PI 2) a) (/ (asin a) a))
6.0ms
(/ (asin a) a)
185.0ms
(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
17.0ms
(/ (/ PI 2) a)

series318.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (/ (/ PI 2) a) (/ (asin a) a))
38.0ms
(/ (asin a) a)
143.0ms
(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))
47.0ms
(/ (/ PI 2) a)

simplify2.0s

Counts
897 → 897
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0107036729
1216032089
2418824236
done500024233

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (asin a))
0.7b
(pow (cbrt (asin a)) 3)
0.7b
(pow (cbrt (asin a)) 3)
0.7b
(pow (cbrt (asin a)) 3)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×unpow-prod-down cube-prod
9×pow-unpow
7×pow1 add-exp-log
6×pow-pow
4×expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×cube-mult pow-to-exp unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 109
Calls
4 calls:
1.0ms
(cbrt (asin a))
4.0ms
(pow (cbrt (asin a)) 3)
4.0ms
(pow (cbrt (asin a)) 3)
4.0ms
(pow (cbrt (asin a)) 3)

series623.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (asin a))
163.0ms
(pow (cbrt (asin a)) 3)
161.0ms
(pow (cbrt (asin a)) 3)
174.0ms
(pow (cbrt (asin a)) 3)

simplify2.9s

Counts
121 → 121
Iterations

Useful iterations: 3 (837.0ms)

IterNodesCost
049961
1113612
2324530
33136518
done5000518

prune288.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample673.0ms

Algorithm
intervals
Results
306.0ms8000×body80valid
162.0ms7851×body80nan