Details

Time bar (total: 19.1s)

sample37.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
8.0ms278×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04171
done4171

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
11.0ms
(/ a (- (acos a)))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(/ a (- (acos a)))

simplify1.9s

Counts
60 → 60
Iterations

Useful iterations: 3 (429.0ms)

IterNodesCost
09619614
117318814
243718774
3126318734
done500318734

prune249.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 221
Calls
2 calls:
17.0ms
(/ 1 (/ (- (acos a)) a))
9.0ms
(/ (- (acos a)) a)

series89.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ 1 (/ (- (acos a)) a))
46.0ms
(/ (- (acos a)) a)

simplify4.7s

Counts
227 → 227
Iterations

Useful iterations: 3 (2.7s)

IterNodesCost
029298276
177481723
2201680896
3474174953
done502074953

prune737.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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×expm1-log1p-u pow-prod-down associate-*r/ associate-/r/ un-div-inv log1p-expm1-u 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 → 88
Calls
2 calls:
16.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
16.0ms
(* (- (acos a)) (/ 1 a))

series79.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
51.0ms
(* (- (acos a)) (/ 1 a))

simplify3.2s

Counts
94 → 94
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
012928245
135622389
286421450
3245819958
done503419958

prune382.0ms

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))

rewrite95.0ms

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×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 584
Calls
2 calls:
12.0ms
(/ 1 (- (acos a)))
30.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series60.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(/ 1 (- (acos a)))
46.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify5.3s

Counts
590 → 590
Iterations

Useful iterations: 2 (3.8s)

IterNodesCost
0811366342
12690271014
24924253586
done5009253586

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes102.0ms

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

sample878.0ms

Algorithm
intervals
Results
322.0ms8000×body80valid
281.0ms8008×body80nan