Details

Time bar (total: 8.1s)

sample57.0ms

Algorithm
intervals
Results
26.0ms736×body80nan
11.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
done1613

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
29×add-sqr-sqrt
27×times-frac
23×add-cube-cbrt
20×sqrt-prod
8×log-prod
7×associate-/l*
6×add-exp-log
5×pow1 add-cbrt-cube difference-of-squares
4×sqrt-div distribute-lft-out
3×log-div associate-/r* div-inv add-log-exp
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp rem-log-exp frac-add clear-num log-pow flip-+
Counts
3 → 81
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
29.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series520.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(sqrt (- 1.0 (* x x)))
324.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
131.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify562.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
02151548
14741434
216131343
done50001343

prune290.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
54×times-frac
52×add-sqr-sqrt
48×sqrt-prod
42×add-cube-cbrt
14×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube distribute-lft-out difference-of-squares
6×pow1 associate-/r* div-inv
4×associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square distribute-rgt-out flip3-- frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num flip-- flip-+
Counts
4 → 132
Calls
4 calls:
7.0ms
(/ (sqrt (- 1.0 (* x x))) x)
8.0ms
(/ (sqrt (- 1.0 (* x x))) x)
58.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
70.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series786.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (sqrt (- 1.0 (* x x))) x)
183.0ms
(/ (sqrt (- 1.0 (* x x))) x)
241.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
217.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify568.0ms

Counts
144 → 144
Iterations

Useful iterations: done (562.0ms)

IterNodesCost
02282688
14902434
215942328
done50002326

prune524.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b
(/ 1 (sqrt x))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.4b
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
184×add-sqr-sqrt
161×times-frac
148×sqrt-prod
101×*-un-lft-identity
90×add-cube-cbrt
46×associate-*r*
33×add-exp-log
25×unswap-sqr
22×associate-*l*
20×add-cbrt-cube
13×difference-of-squares
12×associate-/r*
11×div-exp
10×associate-/l*
9×pow1
8×prod-exp
6×cbrt-undiv
5×log-div
4×log-prod cbrt-unprod div-inv add-log-exp
3×rec-exp pow-flip 1-exp frac-add
2×frac-times frac-2neg sqrt-div associate-*r/ associate-*l/ clear-num associate-/l/
1×sqrt-undiv flip3-- sqrt-pow1 flip3-+ pow1/2 rem-log-exp pow-prod-down log-pow *-commutative flip-- flip-+ distribute-lft-out inv-pow
Counts
4 → 250
Calls
4 calls:
7.0ms
(log (+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
3.0ms
(/ 1 (sqrt x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
41.0ms
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

series535.0ms

Counts
4 → 12
Calls
4 calls:
318.0ms
(log (+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
27.0ms
(/ 1 (sqrt x))
71.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
118.0ms
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

simplify1.8s

Counts
262 → 262
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03825005
110084426
239943797
done50013790

prune526.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01129
11229
done1229

end0.0ms

sample1.5s

Algorithm
intervals
Results
779.0ms23884×body80nan
320.0ms8000×body80valid