Details

Time bar (total: 3.5s)

sample19.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
3.0ms258×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: 0.3b

localize4.0ms

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

series27.0ms

Counts
1 → 3
Calls
1 calls:
27.0ms
(/ a (- (acos a)))

simplify110.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0166384
1493372
21442367
33704366
45002366
done5002366

prune116.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

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)
20.0ms
(/ 1 (/ (- (acos a)) a))

series69.0ms

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

simplify75.0ms

Counts
227 → 227
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06631934
130641717
250011525
done50011525

prune304.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (* (- (acos a)) (/ 1 a)))
0.4b
(* (- (acos a)) (/ 1 a))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×prod-exp add-cbrt-cube
15×*-un-lft-identity
14×add-cube-cbrt times-frac
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-flip associate-*r/ pow-prod-down associate-/r/ un-div-inv log1p-expm1-u div-inv add-log-exp
1×distribute-lft-neg-out neg-mul-1 frac-2neg clear-num associate-/r* *-commutative inv-pow
Counts
2 → 88
Calls
2 calls:
21.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
24.0ms
(* (- (acos a)) (/ 1 a))

series67.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
35.0ms
(* (- (acos a)) (/ 1 a))

simplify45.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0355529
11644425
25001401
done5001401

prune148.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
262×cbrt-prod
228×times-frac
176×add-sqr-sqrt
164×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
43×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
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 → 284
Calls
4 calls:
66.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
4.0ms
(cbrt (/ (- (acos a)) a))
4.0ms
(cbrt (/ (- (acos a)) a))
5.0ms
(cbrt (/ (- (acos a)) a))

series797.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
187.0ms
(cbrt (/ (- (acos a)) a))
186.0ms
(cbrt (/ (- (acos a)) a))
181.0ms
(cbrt (/ (- (acos a)) a))

simplify76.0ms

Counts
296 → 296
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04823424
116453354
250013217
done50013217

prune876.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0b

regimes93.0ms

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
160.0ms8000×body80valid
103.0ms8048×body80nan