Details

Time bar (total: 10.0s)

sample30.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
9.0ms228×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:
6.0ms
(/ a (- (acos a)))

series28.0ms

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

simplify689.0ms

Counts
59 → 59
Iterations
IterNodes
done2002
31333
2452
1172
095

prune223.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:
13.0ms
(/ (- (acos a)) a)
15.0ms
(/ 1 (/ (- (acos a)) a))

series91.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ (- (acos a)) a)
53.0ms
(/ 1 (/ (- (acos a)) a))

simplify770.0ms

Counts
225 → 225
Iterations
IterNodes
done2014
21568
1770
0290

prune662.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (- (acos a)))
0.5b
(/ (/ 1 (- (acos a))) (/ 1 a))

rewrite70.0ms

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)))
27.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series59.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(/ 1 (- (acos a)))
47.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify759.0ms

Counts
588 → 588
Iterations
IterNodes
done2000
0809

prune2.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
1.0b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
1.0b
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
1.0b
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
302×add-exp-log
273×times-frac
185×add-sqr-sqrt
178×*-un-lft-identity
157×add-cube-cbrt
148×prod-exp
120×div-exp
68×associate-*r*
60×add-cbrt-cube
59×pow1
58×rec-exp 1-exp
51×distribute-rgt-neg-in
45×distribute-lft-neg-in
42×swap-sqr
35×associate-*l*
31×pow-prod-up
29×pow-flip inv-pow
22×cbrt-unprod
20×cbrt-undiv cbrt-div
19×frac-times associate-*l/
15×cbrt-prod neg-mul-1
13×associate-/r* div-inv
12×unswap-sqr
10×pow-prod-down associate-*r/ un-div-inv associate-/l/
9×pow-sqr
7×pow-plus
4×insert-posit16 associate-/l* add-log-exp
3×pow2
2×pow3 *-commutative
1×clear-num frac-2neg pow1/3 associate-/r/ rem-cbrt-cube
Counts
4 → 443
Calls
4 calls:
15.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
59.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
43.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
25.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
36.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
52.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
29.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify1.2s

Counts
455 → 455
Iterations
IterNodes
done2003
11562
0535

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes78.0ms

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
done4
04

end0.0ms

sample1.3s

Algorithm
intervals
Results
630.0ms8000×body80valid
472.0ms7785×body80nan