Details

Time bar (total: 3.3s)

sample22.0ms

Algorithm
intervals
Results
6.0ms290×body80nan
5.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043
143
done43

prune1.0ms

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)))

rewrite9.0ms

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:
7.0ms
(/ a (- (acos a)))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(/ a (- (acos a)))

simplify89.0ms

Counts
58 → 58
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
0164376
1491364
21440359
33702358
45001358
done5001358

prune99.0ms

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

rewrite33.0ms

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×rec-exp frac-2neg 1-exp clear-num add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 217
Calls
2 calls:
7.0ms
(/ (- (acos a)) a)
14.0ms
(/ 1 (/ (- (acos a)) a))

series58.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(/ (- (acos a)) a)
28.0ms
(/ 1 (/ (- (acos a)) a))

simplify65.0ms

Counts
223 → 223
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06591916
130601699
250011507
done50011507

prune239.0ms

Pruning

10 alts after pruning (8 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))

rewrite82.0ms

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×frac-2neg clear-num add-log-exp
1×pow-flip associate-/r/ associate-/l/ inv-pow
Counts
2 → 580
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
28.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series30.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
23.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify104.0ms

Counts
586 → 586
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
025177392
150026273
done50026273

prune569.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
1355×times-frac
635×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
544×exp-prod
525×log-pow
156×distribute-lft-neg-in distribute-rgt-neg-in
57×div-inv
52×neg-mul-1
41×associate-/l*
23×associate-/r*
20×pow1
17×add-exp-log
11×add-cbrt-cube
8×div-exp
5×add-log-exp
4×cbrt-undiv
3×log-prod
2×rec-exp frac-2neg 1-exp clear-num
1×pow-flip rem-log-exp associate-/r/ rem-exp-log inv-pow
Counts
4 → 709
Calls
4 calls:
9.0ms
(/ 1 (- (acos a)))
13.0ms
(exp (/ 1 (- (acos a))))
15.0ms
(log (exp (/ 1 (- (acos a)))))
66.0ms
(/ (log (exp (/ 1 (- (acos a))))) (/ 1 a))

series70.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1 (- (acos a)))
33.0ms
(exp (/ 1 (- (acos a))))
7.0ms
(log (exp (/ 1 (- (acos a)))))
23.0ms
(/ (log (exp (/ 1 (- (acos a))))) (/ 1 a))

simplify110.0ms

Counts
721 → 721
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
023358717
150017628
done50017628

prune922.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes39.0ms

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
043
143
done43

end0.0ms

sample492.0ms

Algorithm
intervals
Results
162.0ms8000×body80valid
98.0ms7965×body80nan