Details

Time bar (total: 17.9s)

sample62.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
23.0ms286×body80nan

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
14
04

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
1 → 56
Calls
1 calls:
5.0ms
(/ a (- (acos a)))

series27.0ms

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

simplify725.0ms

Counts
59 → 59
Iterations
IterNodes
42160
3767
2342
1167
095

prune394.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 219
Calls
2 calls:
7.0ms
(/ 1 (/ (- (acos a)) a))
5.0ms
(/ (- (acos a)) a)

series77.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ 1 (/ (- (acos a)) a))
37.0ms
(/ (- (acos a)) a)

simplify2.9s

Counts
225 → 225
Iterations
IterNodes
34026
21685
1756
0290

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite63.0ms

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×clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 582
Calls
2 calls:
10.0ms
(/ 1 (- (acos a)))
16.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series56.0ms

Counts
2 → 6
Calls
2 calls:
10.0ms
(/ 1 (- (acos a)))
45.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify1.4s

Counts
588 → 588
Iterations
IterNodes
12655
0809

prune4.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (acos a) (acos a))
0.4b
(/ (cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a))))) (/ 1 a))
1.0b
(* (* (acos a) (acos a)) (- (acos a)))
1.0b
(cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a)))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
135×add-sqr-sqrt
132×*-un-lft-identity add-cube-cbrt
105×cbrt-prod
27×div-inv
20×add-exp-log
16×pow1
14×add-cbrt-cube
13×associate-/r* associate-*r*
10×associate-/l*
6×div-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 add-log-exp
3×distribute-lft-neg-in cbrt-undiv distribute-rgt-neg-in swap-sqr
2×cbrt-div *-commutative unswap-sqr
1×pow2 rec-exp clear-num neg-mul-1 frac-2neg pow-plus pow1/3 1-exp associate-/r/ pow-sqr pow-prod-up distribute-rgt-neg-out associate-/l/
Counts
4 → 243
Calls
4 calls:
11.0ms
(* (acos a) (acos a))
31.0ms
(/ (cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a))))) (/ 1 a))
37.0ms
(* (* (acos a) (acos a)) (- (acos a)))
32.0ms
(cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a)))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (acos a) (acos a))
88.0ms
(/ (cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a))))) (/ 1 a))
44.0ms
(* (* (acos a) (acos a)) (- (acos a)))
49.0ms
(cbrt (/ 1 (* (* (acos a) (acos a)) (- (acos a)))))

simplify2.4s

Counts
255 → 255
Iterations
IterNodes
35162
21768
1891
0348

prune1.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
14
04

end0.0ms

sample1.5s

Algorithm
intervals
Results
936.0ms8000×body80valid
375.0ms7862×body80nan