Details

Time bar (total: 22.7s)

sample35.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms218×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

localize10.0ms

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)))

series35.0ms

Counts
1 → 3
Calls
1 calls:
35.0ms
(/ a (- (acos a)))

simplify4.8s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.8s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune204.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

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:
6.0ms
(/ (acos a) a)
20.0ms
(/ 1 (- (/ (acos a) a)))

series71.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (acos a) a)
31.0ms
(/ 1 (- (/ (acos a) a)))

simplify6.9s

Counts
178 → 178
Iterations

Useful iterations: 3 (653.0ms)

IterNodesCost
02652409
14722004
27741861
315101711
427551711
done50001711

prune413.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite548.0ms

Algorithm
rewrite-expression-head
Rules
1617×times-frac
1088×add-sqr-sqrt
971×*-un-lft-identity
899×add-cube-cbrt
559×prod-diff
123×div-inv
56×distribute-lft-neg-in distribute-rgt-neg-in
54×difference-of-squares
43×fma-neg
36×distribute-lft-out--
35×associate-/r*
16×associate-/l*
12×add-exp-log
10×add-cbrt-cube
9×distribute-rgt-out--
5×div-exp add-log-exp
4×pow1 cbrt-undiv neg-mul-1 associate-/r/ distribute-neg-frac
3×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg clear-num frac-sub flip-- sub-div
1×sub-neg rec-exp asin-acos pow-flip diff-log 1-exp div-sub associate-/l/ inv-pow associate--r-
Counts
3 → 855
Calls
3 calls:
110.0ms
(- (/ (/ PI 2) a) (/ (asin a) a))
20.0ms
(/ (/ PI 2) a)
274.0ms
(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))

series348.0ms

Counts
3 → 9
Calls
3 calls:
109.0ms
(- (/ (/ PI 2) a) (/ (asin a) a))
58.0ms
(/ (/ PI 2) a)
180.0ms
(/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))

simplify3.0s

Counts
864 → 864
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0105336471
1213331850
2414924003
done500023996

prune2.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (acos a))
0.4b
(/ (/ 1 (acos a)) (- (/ 1 a)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
930×times-frac
437×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
182×distribute-lft-neg-in distribute-rgt-neg-in
61×div-inv
33×associate-/r*
16×associate-/l*
15×add-exp-log
14×neg-mul-1
9×add-cbrt-cube
8×div-exp
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ associate-/l/ distribute-neg-frac inv-pow
Counts
2 → 486
Calls
2 calls:
6.0ms
(/ 1 (acos a))
45.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

series55.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (acos a))
47.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

simplify2.0s

Counts
492 → 492
Iterations

Useful iterations: done (2.0s)

IterNodesCost
071310319
117377603
226406678
done50006309

prune488.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes65.0ms

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

sample1.0s

Algorithm
intervals
Results
340.0ms8000×body80valid
223.0ms8039×body80nan