Details

Time bar (total: 13.9s)

sample18.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
4.0ms282×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: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ 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)))

series25.0ms

Counts
1 → 3
Calls
1 calls:
25.0ms
(/ a (- (acos a)))

simplify3.2s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.3s)

IterNodesCost
094601
1164571
2328553
3713553
41238553
52173548
done5001548

prune101.0ms

Pruning

10 alts after pruning (9 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)))

rewrite24.0ms

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)
13.0ms
(/ 1 (- (/ (acos a) a)))

series52.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(/ (acos a) a)
24.0ms
(/ 1 (- (/ (acos a) a)))

simplify3.6s

Counts
174 → 174
Iterations

Useful iterations: 3 (878.0ms)

IterNodesCost
02612383
14832068
29581838
320441689
441511689
done50001689

prune195.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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))))
8.0ms
(* (acos a) (/ 1 a))

series56.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
32.0ms
(* (acos a) (/ 1 a))

simplify3.6s

Counts
87 → 87
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0134955
1293718
2746593
32390559
done5001559

prune130.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
206×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
30×div-inv
26×add-exp-log
17×div-exp
16×associate-/r* add-cbrt-cube associate-/l*
9×cbrt-undiv
2×pow1 rec-exp frac-2neg 1-exp clear-num add-log-exp
1×associate-/r/ associate-/l/
Counts
2 → 246
Calls
2 calls:
2.0ms
(/ -1 (acos a))
14.0ms
(/ (/ -1 (acos a)) (/ 1 a))

series30.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ -1 (acos a))
25.0ms
(/ (/ -1 (acos a)) (/ 1 a))

simplify2.1s

Counts
252 → 252
Iterations

Useful iterations: done (2.1s)

IterNodesCost
04144738
112054099
233963374
done50013371

prune279.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes61.0ms

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

sample449.0ms

Algorithm
intervals
Results
164.0ms8000×body80valid
108.0ms8246×body80nan