Details

Time bar (total: 16.9s)

sample23.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
5.0ms278×body80nan

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04171
done4171

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

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 *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×pow1 cbrt-undiv clear-num frac-2neg div-exp div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
7.0ms
(/ a (- (acos a)))

series49.0ms

Counts
1 → 3
Calls
1 calls:
49.0ms
(/ a (- (acos a)))

simplify1.8s

Counts
58 → 58
Iterations

Useful iterations: 3 (384.0ms)

IterNodesCost
09419112
117118312
244818272
3130818232
done500018232

prune224.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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 clear-num frac-2neg 1-exp add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 217
Calls
2 calls:
13.0ms
(/ 1 (/ (- (acos a)) a))
9.0ms
(/ (- (acos a)) a)

series81.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ 1 (/ (- (acos a)) a))
39.0ms
(/ (- (acos a)) a)

simplify3.8s

Counts
223 → 223
Iterations

Useful iterations: 3 (2.3s)

IterNodesCost
028897190
176780637
2154980099
3373374888
done515974888

prune688.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×add-cbrt-cube prod-exp
15×*-un-lft-identity
14×times-frac add-cube-cbrt
13×associate-*r*
10×associate-*l*
9×rec-exp 1-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l* unswap-sqr
2×pow-prod-down associate-*r/ associate-/r/ un-div-inv div-inv pow-flip add-log-exp
1×distribute-lft-neg-out clear-num associate-/r* neg-mul-1 frac-2neg *-commutative inv-pow
Counts
2 → 84
Calls
2 calls:
31.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
16.0ms
(* (- (acos a)) (/ 1 a))

series90.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
42.0ms
(* (- (acos a)) (/ 1 a))

simplify3.2s

Counts
90 → 90
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
012526997
134621345
288920364
3254418954
done506618954

prune354.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×neg-mul-1 add-exp-log
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×clear-num frac-2neg add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 580
Calls
2 calls:
11.0ms
(/ 1 (- (acos a)))
49.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series56.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(/ 1 (- (acos a)))
43.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify4.5s

Counts
586 → 586
Iterations

Useful iterations: 2 (3.2s)

IterNodesCost
0807365174
12680270001
24850250395
done5002250395

prune797.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes146.0ms

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
04171
done4171

end0.0ms

sample782.0ms

Algorithm
intervals
Results
336.0ms8000×body80valid
200.0ms8008×body80nan