Details

Time bar (total: 8.7s)

sample56.0ms

Algorithm
intervals
Results
14.0ms283×body160nan
13.0ms578×body80nan
8.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1119
2129
done129

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
29.1b
(sqrt (- (* x x) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-cube-cbrt log-prod sqrt-prod
3×add-exp-log
2×expm1-log1p-u log-div sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 rem-log-exp log-pow flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
10.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
7.0ms
(sqrt (- (* x x) 1.0))

series252.0ms

Counts
2 → 6
Calls
2 calls:
197.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms
(sqrt (- (* x x) 1.0))

simplify1.9s

Counts
41 → 41
Iterations

Useful iterations: 3 (399.0ms)

IterNodesCost
0129590
1288532
2918485
34389442
done5000442

prune131.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
0.3b
(/ 0.09375 (pow x 4))
0.8b
(/ 0.25 (* x x))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
106×*-un-lft-identity
53×add-sqr-sqrt
48×prod-diff
43×add-cube-cbrt
34×distribute-lft-out--
33×pow1
30×log-pow
24×times-frac
19×associate--r+
16×distribute-lft-out
13×add-exp-log
12×unpow-prod-down
10×add-cbrt-cube
8×associate-/r*
7×add-log-exp
6×associate-/l*
5×diff-log div-exp difference-of-squares
4×fma-neg associate--l+ sqr-pow
3×cbrt-undiv expm1-log1p-u log-prod log1p-expm1-u
2×sub-neg frac-2neg clear-num div-inv
1×pow-to-exp flip3-- pow-exp prod-exp sum-log flip-- cbrt-unprod associate--r-
Counts
3 → 156
Calls
3 calls:
357.0ms
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
4.0ms
(/ 0.09375 (pow x 4))
4.0ms
(/ 0.25 (* x x))

series184.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
51.0ms
(/ 0.09375 (pow x 4))
33.0ms
(/ 0.25 (* x x))

simplify961.0ms

Counts
165 → 165
Iterations

Useful iterations: 2 (209.0ms)

IterNodesCost
02544666
15513880
219273136
done50003136

prune377.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x))
0.2b
(log (/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x)))
0.3b
(/ 0.09375 (pow x 4))
0.8b
(/ 0.25 (* x x))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
112×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
53×log-prod
24×associate-/r*
23×add-exp-log
21×exp-sum
16×add-cbrt-cube
12×unpow-prod-down
11×div-exp div-inv
9×associate-/l*
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg rem-log-exp clear-num
2×associate-/r/
1×pow-to-exp log-div pow-exp prod-exp log-pow cbrt-unprod
Counts
4 → 221
Calls
4 calls:
114.0ms
(/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x))
85.0ms
(log (/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x)))
4.0ms
(/ 0.09375 (pow x 4))
3.0ms
(/ 0.25 (* x x))

series404.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x))
213.0ms
(log (/ 2 (/ (exp (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))) x)))
37.0ms
(/ 0.09375 (pow x 4))
32.0ms
(/ 0.25 (* x x))

simplify1.5s

Counts
233 → 233
Iterations

Useful iterations: done (1.5s)

IterNodesCost
04315394
19485171
238554925
done50004924

prune873.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
11517
done1517

end0.0ms

sample1.4s

Algorithm
intervals
Results
387.0ms7682×body160nan
364.0ms16083×body80nan
247.0ms8000×body80valid