Details

Time bar (total: 16.8s)

sample19.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms82×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

localize12.0ms

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))))

rewrite74.0ms

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:
24.0ms
(+ 1.0 (sqrt (+ x 1.0)))
49.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series265.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(+ 1.0 (sqrt (+ x 1.0)))
209.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts
58 → 58
Iterations

Useful iterations: 3 (906.0ms)

IterNodesCost
0121771
1289722
2872665
33751657
done5000657

prune198.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (expm1 (log1p (+ 1.0 (sqrt (+ x 1.0))))))
0.6b
(log1p (+ 1.0 (sqrt (+ x 1.0))))
1.7b
(expm1 (log1p (+ 1.0 (sqrt (+ x 1.0)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×add-exp-log add-cbrt-cube add-log-exp
5×expm1-log1p-u
4×pow1 log1p-expm1-u
3×fma-def associate-/r* associate-/l*
1×cbrt-undiv +-commutative log1p-udef expm1-log1p frac-2neg flip3-+ log1p-expm1 div-exp clear-num sum-log flip-+ div-inv distribute-lft-out expm1-udef
Counts
4 → 68
Calls
4 calls:
24.0ms
(+ 1.0 (sqrt (+ x 1.0)))
10.0ms
(/ x (expm1 (log1p (+ 1.0 (sqrt (+ x 1.0))))))
1.0ms
(log1p (+ 1.0 (sqrt (+ x 1.0))))
1.0ms
(expm1 (log1p (+ 1.0 (sqrt (+ x 1.0)))))

series945.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ 1.0 (sqrt (+ x 1.0)))
501.0ms
(/ x (expm1 (log1p (+ 1.0 (sqrt (+ x 1.0))))))
172.0ms
(log1p (+ 1.0 (sqrt (+ x 1.0))))
223.0ms
(expm1 (log1p (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.0s

Counts
80 → 80
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01571152
1372996
21116891
34815874
done5000874

prune224.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))
0.0b
(fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0))))
7.2b
(fma (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2 (fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
3 → 30
Calls
3 calls:
0.0ms
(fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))
1.0ms
(fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0))))
1.0ms
(fma (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2 (fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))))

series2.1s

Counts
3 → 9
Calls
3 calls:
554.0ms
(fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))
910.0ms
(fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0))))
631.0ms
(fma (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2 (fma (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3)) 1/4 (fma (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2)) (pow (/ x (sqrt 1.0)) 3) (/ x (+ (sqrt 1.0) 1.0)))))

simplify2.4s

Counts
39 → 39
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0671694
11371670
25441455
335421434
done50001431

prune366.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
0.2b
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
4.5b
(- (* 1.0 1.0) (+ x 1.0))
4.5b
(- 1.0 (sqrt (+ x 1.0)))

rewrite356.0ms

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:
116.0ms
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
140.0ms
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
39.0ms
(- (* 1.0 1.0) (+ x 1.0))
41.0ms
(- 1.0 (sqrt (+ x 1.0)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0))))
97.0ms
(/ x (/ (- (* 1.0 1.0) (+ x 1.0)) (- 1.0 (sqrt (+ x 1.0)))))
21.0ms
(- (* 1.0 1.0) (+ x 1.0))
81.0ms
(- 1.0 (sqrt (+ x 1.0)))

simplify2.4s

Counts
268 → 268
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03947117
19326372
236525453
done50005422

prune759.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample724.0ms

Algorithm
intervals
Results
360.0ms8000×body80valid
120.0ms2751×body80nan