Details

Time bar (total: 24.2s)

sample35.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
8.0ms288×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: 0.3b

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ a (- (acos a)))

rewrite10.0ms

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

series49.0ms

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

simplify5.1s

Counts
60 → 60
Iterations

Useful iterations: 5 (2.0s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune213.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

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:
33.0ms
(/ 1 (- (/ (acos a) a)))
13.0ms
(/ (acos a) a)

series92.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ 1 (- (/ (acos a) a)))
61.0ms
(/ (acos a) a)

simplify6.0s

Counts
178 → 178
Iterations

Useful iterations: 3 (725.0ms)

IterNodesCost
02652409
14722004
27821861
315341711
427841711
done50001711

prune335.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- (/ (acos a) a)))
0.5b
(cbrt (- (/ (acos a) a)))
0.5b
(cbrt (- (/ (acos a) a)))
0.6b
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
218×cbrt-prod
126×times-frac
121×add-sqr-sqrt
117×*-un-lft-identity
113×add-cube-cbrt
93×distribute-rgt-neg-in
91×distribute-lft-neg-in
35×swap-sqr
33×associate-*r* associate-*l*
14×div-inv
11×pow1
9×pow1/3
7×neg-mul-1 cbrt-div distribute-neg-frac
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 251
Calls
4 calls:
10.0ms
(cbrt (- (/ (acos a) a)))
5.0ms
(cbrt (- (/ (acos a) a)))
5.0ms
(cbrt (- (/ (acos a) a)))
81.0ms
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))

series1.1s

Counts
4 → 12
Calls
4 calls:
234.0ms
(cbrt (- (/ (acos a) a)))
248.0ms
(cbrt (- (/ (acos a) a)))
277.0ms
(cbrt (- (/ (acos a) a)))
295.0ms
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))

simplify4.4s

Counts
263 → 263
Iterations

Useful iterations: done (4.3s)

IterNodesCost
02694084
14273854
211313762
319643614
446243382
done50013239

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- (/ (acos a) a)))
0.6b
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))
0.6b
(cbrt a)
1.0b
(cbrt (- (acos a)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
171×cbrt-prod
95×add-sqr-sqrt
91×*-un-lft-identity
90×times-frac
87×add-cube-cbrt
70×distribute-rgt-neg-in
68×distribute-lft-neg-in
35×swap-sqr
33×associate-*r* associate-*l*
11×pow1
10×div-inv
9×pow1/3
6×add-exp-log neg-mul-1
5×cbrt-div distribute-neg-frac
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 202
Calls
4 calls:
14.0ms
(cbrt (- (/ (acos a) a)))
109.0ms
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))
2.0ms
(cbrt a)
2.0ms
(cbrt (- (acos a)))

series1.1s

Counts
4 → 12
Calls
4 calls:
236.0ms
(cbrt (- (/ (acos a) a)))
335.0ms
(* (cbrt (- (/ (acos a) a))) (cbrt (- (/ (acos a) a))))
314.0ms
(cbrt a)
261.0ms
(cbrt (- (acos a)))

simplify2.5s

Counts
214 → 214
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03073218
14853022
213022809
327812674
done50002595

prune953.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes96.0ms

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

sample783.0ms

Algorithm
intervals
Results
354.0ms8000×body80valid
198.0ms8037×body80nan