Details

Time bar (total: 7.5s)

sample50.0ms

Algorithm
intervals
Results
23.0ms736×body80nan
13.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)

rewrite35.0ms

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×expm1-log1p-u log-div associate-/r* log1p-expm1-u 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 → 87
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series494.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(sqrt (- 1.0 (* x x)))
300.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
135.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify578.0ms

Counts
96 → 96
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
02211608
14921480
214661389
done50001384

prune252.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
68×times-frac
58×*-un-lft-identity
52×sqrt-prod
42×add-cube-cbrt
14×associate-/l*
12×hypot-def
10×sqrt-div
8×add-exp-log add-cbrt-cube distribute-lft-out difference-of-squares
6×pow1 associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u 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 → 152
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
50.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
51.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series862.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (sqrt (- 1.0 (* x x))) x)
131.0ms
(/ (sqrt (- 1.0 (* x x))) x)
393.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
211.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify666.0ms

Counts
164 → 164
Iterations

Useful iterations: done (657.0ms)

IterNodesCost
02322780
15132506
214432404
done50012372

prune576.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.1b
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
0.1b
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
0.4b
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
292×sqrt-prod
208×add-sqr-sqrt
179×times-frac
112×add-cube-cbrt *-un-lft-identity
36×swap-sqr
28×associate-*r* associate-*l*
22×difference-of-squares
21×pow1
16×unswap-sqr
10×sqrt-pow1 pow1/2
8×add-exp-log sqrt-div add-cbrt-cube
7×div-inv associate-/l*
6×rem-sqrt-square
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down associate-/r* pow-sqr
2×associate-/l/
1×cbrt-undiv pow2 frac-times flip3-- frac-2neg pow-plus sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 265
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
46.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (sqrt (- 1.0 (* x x))) x)
208.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
207.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
255.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

simplify733.0ms

Counts
277 → 277
Iterations

Useful iterations: done (724.0ms)

IterNodesCost
03336462
16274800
220974542
done50014531

prune737.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

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

sample1.4s

Algorithm
intervals
Results
759.0ms23884×body80nan
314.0ms8000×body80valid