Details

Time bar (total: 9.3s)

sample47.0ms

Algorithm
intervals
Results
22.0ms736×body80nan
10.0ms256×body80valid

simplify8.0ms

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

localize12.0ms

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)

rewrite38.0ms

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:
4.0ms
(sqrt (- 1.0 (* x x)))
25.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series825.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(sqrt (- 1.0 (* x x)))
604.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
153.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify625.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
02211608
14951482
217221389
done50011389

prune286.0ms

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)))

rewrite160.0ms

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:
8.0ms
(/ (sqrt (- 1.0 (* x x))) x)
7.0ms
(/ (sqrt (- 1.0 (* x x))) x)
64.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
74.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series728.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (sqrt (- 1.0 (* x x))) x)
155.0ms
(/ (sqrt (- 1.0 (* x x))) x)
229.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
209.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify656.0ms

Counts
164 → 164
Iterations

Useful iterations: done (650.0ms)

IterNodesCost
02322780
15162506
217712404
done50002394

prune678.0ms

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

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
614×times-frac
512×sqrt-prod
370×add-sqr-sqrt
325×*-un-lft-identity
319×add-cube-cbrt
53×associate-/l*
50×difference-of-squares
12×add-exp-log associate-/r*
11×add-cbrt-cube
9×div-inv
6×pow1
5×log-prod
4×cbrt-undiv expm1-log1p-u sqrt-div div-exp log1p-expm1-u add-log-exp
3×log-div sqrt-undiv associate-/l/
2×flip3-- frac-2neg clear-num flip-- distribute-lft-out
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp frac-add log-pow flip-+
Counts
4 → 455
Calls
4 calls:
185.0ms
(log (+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))))
3.0ms
(sqrt (- 1.0 (* x x)))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
23.0ms
(/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))

series676.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(log (+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))))
65.0ms
(sqrt (- 1.0 (* x x)))
74.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
207.0ms
(/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))

simplify2.1s

Counts
467 → 467
Iterations

Useful iterations: 2 (540.0ms)

IterNodesCost
056911600
1133310242
245649510
done50009510

prune784.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

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
740.0ms23884×body80nan
315.0ms8000×body80valid