Details

Time bar (total: 15.3s)

sample31.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms90×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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))))

rewrite112.0ms

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:
15.0ms
(sqrt (+ x 1.0))
32.0ms
(+ 1.0 (sqrt (+ x 1.0)))
62.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series346.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(sqrt (+ x 1.0))
79.0ms
(+ 1.0 (sqrt (+ x 1.0)))
223.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0140917
1316848
2899783
33660775
done5001773

prune222.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
0.1b
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
0.2b
(pow (sqrt (+ x 1.0)) 3)
4.0b
(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
23×add-sqr-sqrt add-cube-cbrt
20×cbrt-prod
16×sqrt-prod
14×unpow-prod-down cube-prod
12×times-frac
9×distribute-lft-out
7×add-exp-log add-cbrt-cube
6×pow1 add-log-exp
4×cube-div flip3-+ sqrt-div associate-/r* flip-+
3×pow-unpow pow-pow associate-/l*
2×cube-mult cbrt-div unpow3 associate-/r/ sqr-pow
1×cbrt-undiv +-commutative pow-to-exp frac-2neg sqrt-pow1 pow1/2 pow1/3 div-exp pow-exp clear-num sum-log sqrt-pow2 rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 112
Calls
4 calls:
61.0ms
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
99.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
20.0ms
(pow (sqrt (+ x 1.0)) 3)
18.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

series422.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
220.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
91.0ms
(pow (sqrt (+ x 1.0)) 3)
40.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify1.1s

Counts
124 → 124
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01991877
14591315
213311234
done50001232

prune340.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
0.0b
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
0.0b
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
6.0b
(- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

rewrite879.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
22×prod-exp
20×add-log-exp
13×frac-add add-cbrt-cube
12×div-exp associate-*r*
10×add-sqr-sqrt *-un-lft-identity
9×associate-*r/
8×add-cube-cbrt times-frac
7×pow-to-exp pow-exp sum-log
6×pow1
5×flip3-+ flip-+
4×flip3-- frac-sub flip-- cbrt-unprod
3×unpow-prod-down diff-log associate-*l*
2×cbrt-undiv +-commutative sub-neg associate-+r+
1×associate-+r- associate-+l+ pow-prod-down *-commutative div-inv distribute-lft-out unpow2 unswap-sqr sqr-pow
Counts
4 → 95
Calls
4 calls:
104.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
538.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
112.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
116.0ms
(- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
259.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
734.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
735.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
700.0ms
(- (/ (* 1/4 (pow x 3)) (* (pow (+ (sqrt 1.0) 1.0) 3) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

simplify2.2s

Counts
107 → 107
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02295905
17225378
234664947
done50014946

prune701.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

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:
44.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(sqrt (+ x 1.0))
33.0ms
(+ 1.0 (sqrt (+ x 1.0)))
165.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series831.0ms

Counts
4 → 12
Calls
4 calls:
454.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
63.0ms
(sqrt (+ x 1.0))
74.0ms
(+ 1.0 (sqrt (+ x 1.0)))
240.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.3s

Counts
144 → 144
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02162303
15202031
217081857
done50001834

prune396.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes86.0ms

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

sample1.2s

Algorithm
intervals
Results
848.0ms7998×body80valid
83.0ms2659×body80nan
0.0ms2×body1280valid