Details

Time bar (total: 9.0s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
4.0ms93×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 52
Calls
2 calls:
17.0ms
(+ 1.0 (sqrt (+ x 1.0)))
79.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series288.0ms

Counts
2 → 6
Calls
2 calls:
71.0ms
(+ 1.0 (sqrt (+ x 1.0)))
216.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts
58 → 58
Iterations

Useful iterations: 3 (977.0ms)

IterNodesCost
0121771
1289722
2872665
33751657
done5000657

prune205.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
96×*-un-lft-identity
62×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
17×distribute-lft-out
16×add-exp-log
10×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
5×add-log-exp
4×pow1 cbrt-undiv
3×expm1-log1p-u fma-def log1p-expm1-u
2×rec-exp frac-2neg flip3-+ 1-exp clear-num flip-+ associate-/l/
1×+-commutative pow-flip sum-log associate-/r/ inv-pow
Counts
3 → 142
Calls
3 calls:
18.0ms
(+ 1.0 (sqrt (+ x 1.0)))
76.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
51.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series385.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ 1.0 (sqrt (+ x 1.0)))
123.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
208.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify999.0ms

Counts
151 → 151
Iterations

Useful iterations: done (991.0ms)

IterNodesCost
02352543
15582217
214171979
done50011947

prune314.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
0.2b
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
2.1b
(- (* 1.0 1.0) (+ x 1.0))
2.1b
(- 1.0 (sqrt (+ x 1.0)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
226×add-sqr-sqrt
210×times-frac
158×*-un-lft-identity
106×add-cube-cbrt
76×difference-of-squares
36×associate-/r*
34×sqrt-prod
25×prod-diff
22×distribute-lft-out--
11×add-exp-log associate-/r/ add-cbrt-cube add-log-exp
8×flip3-- flip--
7×associate-/l*
6×div-inv
4×pow1 cbrt-undiv expm1-log1p-u fma-neg div-exp log1p-expm1-u distribute-lft-out
3×diff-log
2×sub-neg frac-2neg clear-num associate-/l/
1×div-sub sum-log associate--r+
Counts
4 → 256
Calls
4 calls:
117.0ms
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
118.0ms
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
37.0ms
(- (* 1.0 1.0) (+ x 1.0))
26.0ms
(- 1.0 (sqrt (+ x 1.0)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
231.0ms
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
17.0ms
(- (* 1.0 1.0) (+ x 1.0))
76.0ms
(- 1.0 (sqrt (+ x 1.0)))

simplify2.1s

Counts
268 → 268
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03947117
19326372
236475453
done50025422

prune745.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample668.0ms

Algorithm
intervals
Results
396.0ms7998×body80valid
82.0ms2742×body80nan
0.0ms2×body1280valid