Details

Time bar (total: 3.8s)

sample19.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
4.0ms290×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043
143
done43

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)))

series32.0ms

Counts
1 → 3
Calls
1 calls:
32.0ms
(/ a (- (acos a)))

simplify102.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0166384
1493372
21442367
33704366
45002366
done5002366

prune120.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 221
Calls
2 calls:
8.0ms
(/ (- (acos a)) a)
16.0ms
(/ 1 (/ (- (acos a)) a))

series68.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ (- (acos a)) a)
27.0ms
(/ 1 (/ (- (acos a)) a))

simplify77.0ms

Counts
227 → 227
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06631934
130641717
250011525
done50011525

prune293.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite90.0ms

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:
8.0ms
(/ 1 (- (acos a)))
34.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series35.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
28.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify123.0ms

Counts
590 → 590
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
025217412
150026293
done50026293

prune697.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize11.0ms

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))

rewrite179.0ms

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 expm1-log1p-u log1p-expm1-u
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 → 717
Calls
4 calls:
8.0ms
(/ 1 (- (acos a)))
17.0ms
(exp (/ 1 (- (acos a))))
16.0ms
(log (exp (/ 1 (- (acos a)))))
70.0ms
(/ (log (exp (/ 1 (- (acos a))))) (/ 1 a))

series89.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1 (- (acos a)))
40.0ms
(exp (/ 1 (- (acos a))))
7.0ms
(log (exp (/ 1 (- (acos a)))))
28.0ms
(/ (log (exp (/ 1 (- (acos a))))) (/ 1 a))

simplify119.0ms

Counts
729 → 729
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
023438759
150017670
done50017670

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes40.0ms

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

sample497.0ms

Algorithm
intervals
Results
163.0ms8000×body80valid
107.0ms7965×body80nan