Details

Time bar (total: 20.5s)

sample24.0ms

Algorithm
intervals
Results
12.0ms255×body80valid
2.0ms85×body80nan
0.0ms1×body1280valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
11.0ms
(sqrt (+ x 1.0))
17.0ms
(+ 1.0 (sqrt (+ x 1.0)))
33.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series328.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(sqrt (+ x 1.0))
77.0ms
(+ 1.0 (sqrt (+ x 1.0)))
216.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0140917
1316848
2899783
33660775
done5001773

prune232.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.7b
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite414.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
106×times-frac
101×*-un-lft-identity
71×sqrt-prod
65×add-cube-cbrt
32×add-exp-log
27×associate-*r* associate-*l*
20×add-cbrt-cube
15×distribute-lft-out unswap-sqr
14×associate-/r*
11×div-exp
10×sqrt-div
9×pow1
8×prod-exp associate-/r/
6×cbrt-undiv associate-/l*
5×flip3-+ flip-+
4×cbrt-unprod div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×frac-times rem-sqrt-square associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 205
Calls
4 calls:
55.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
264.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
40.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
38.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
212.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
219.0ms
(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
666.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
305.0ms
(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.7s

Counts
217 → 217
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03024664
17714108
223593495
done50003449

prune659.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize74.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))) (/ x (+ (sqrt 1.0) 1.0)))
0.0b
(+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2)))
8.6b
(+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))

rewrite3.2s

Algorithm
rewrite-expression-head
Rules
36×frac-add
19×add-log-exp
13×associate-*r/ associate-*l/
12×cube-div
10×flip3-+ sum-log flip-+
6×frac-times
5×*-un-lft-identity
3×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt add-cbrt-cube
1×associate-+l+ associate-+r+ distribute-lft-out
Counts
3 → 60
Calls
3 calls:
2.7s
(+ (+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))) (/ x (+ (sqrt 1.0) 1.0)))
337.0ms
(+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2)))
128.0ms
(+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))

series2.8s

Counts
3 → 9
Calls
3 calls:
732.0ms
(+ (+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))) (/ x (+ (sqrt 1.0) 1.0)))
1.4s
(+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2)))
686.0ms
(+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))

simplify3.0s

Counts
69 → 69
Iterations

Useful iterations: 2 (974.0ms)

IterNodesCost
01937112
17956504
241836040
done50006040

prune543.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
16.0ms
(sqrt (+ x 1.0))
68.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
32.0ms
(+ 1.0 (sqrt (+ x 1.0)))
138.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ x 1.0))
479.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
69.0ms
(+ 1.0 (sqrt (+ x 1.0)))
218.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.2s

Counts
144 → 144
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02162303
15202031
217081857
done50001834

prune356.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes46.0ms

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

sample771.0ms

Algorithm
intervals
Results
415.0ms7997×body80valid
84.0ms2731×body80nan
1.0ms3×body1280valid