Details

Time bar (total: 13.5s)

sample19.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
3.0ms228×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

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
7.0ms
(/ a (- (acos a)))

series28.0ms

Counts
1 → 3
Calls
1 calls:
28.0ms
(/ a (- (acos a)))

simplify3.1s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.3s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune125.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 172
Calls
2 calls:
18.0ms
(/ 1 (- (/ (acos a) a)))
6.0ms
(/ (acos a) a)

series60.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ 1 (- (/ (acos a) a)))
29.0ms
(/ (acos a) a)

simplify4.2s

Counts
178 → 178
Iterations

Useful iterations: 3 (630.0ms)

IterNodesCost
02652409
14722004
27821861
315341711
427841711
done50001711

prune229.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (- (* (acos a) (/ 1 a))))
0.4b
(* (acos a) (/ 1 a))

rewrite28.0ms

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 expm1-log1p-u rec-exp 1-exp associate-*r/ associate-/r/ un-div-inv cbrt-unprod log1p-expm1-u div-inv distribute-neg-frac add-log-exp
1×pow-flip frac-2neg pow-prod-down clear-num *-commutative inv-pow
Counts
2 → 85
Calls
2 calls:
11.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
15.0ms
(* (acos a) (/ 1 a))

series51.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
27.0ms
(* (acos a) (/ 1 a))

simplify2.5s

Counts
91 → 91
Iterations

Useful iterations: 3 (726.0ms)

IterNodesCost
0138989
1288700
2660619
32163581
done5000581

prune146.0ms

Pruning

13 alts after pruning (10 fresh and 3 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))

rewrite87.0ms

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:
7.0ms
(/ 1 (- (acos a)))
31.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series32.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ 1 (- (acos a)))
24.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify1.8s

Counts
590 → 590
Iterations

Useful iterations: done (1.8s)

IterNodesCost
081112543
123508820
232627448
done50007226

prune331.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes65.0ms

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

sample511.0ms

Algorithm
intervals
Results
170.0ms8000×body80valid
110.0ms7863×body80nan