Details

Time bar (total: 16.1s)

sample28.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
5.0ms250×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

localize5.0ms

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)))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(/ a (- (acos a)))

simplify1.3s

Counts
60 → 60
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
096613
1173581
2463563
32074563
done5000563

prune160.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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 frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 221
Calls
2 calls:
11.0ms
(/ (- (acos a)) a)
26.0ms
(/ 1 (/ (- (acos a)) a))

series72.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(/ (- (acos a)) a)
28.0ms
(/ 1 (/ (- (acos a)) a))

simplify2.2s

Counts
227 → 227
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02923194
17902648
239972582
done50002578

prune490.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×add-exp-log neg-mul-1
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ associate-/l/ inv-pow
Counts
2 → 584
Calls
2 calls:
18.0ms
(/ 1 (- (acos a)))
45.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series55.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(/ 1 (- (acos a)))
42.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.7s

Counts
590 → 590
Iterations

Useful iterations: done (2.7s)

IterNodesCost
081112543
129509132
done50018296

prune530.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
111×add-exp-log
71×div-exp
42×times-frac
33×add-sqr-sqrt 1-exp
32×prod-exp
28×add-cbrt-cube
27×*-un-lft-identity
26×add-cube-cbrt
18×rec-exp
13×associate-*l* associate-/l*
12×cbrt-undiv
10×associate-*r*
6×cbrt-unprod
4×pow1 div-inv
3×distribute-lft-neg-in distribute-rgt-neg-in unswap-sqr
2×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
1×neg-mul-1 frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ *-commutative distribute-rgt-neg-out associate-/l/
Counts
2 → 127
Calls
2 calls:
42.0ms
(/ (/ 1 1) (* (/ 1 a) (- (acos a))))
43.0ms
(* (/ 1 a) (- (acos a)))

series112.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ (/ 1 1) (* (/ 1 a) (- (acos a))))
71.0ms
(* (/ 1 a) (- (acos a)))

simplify6.7s

Counts
133 → 133
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
02081738
17431083
24619835
done5000835

prune270.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes110.0ms

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

sample956.0ms

Algorithm
intervals
Results
310.0ms8000×body80valid
264.0ms7919×body80nan