Details

Time bar (total: 5.6s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms76×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

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))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
20.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series192.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(+ 1.0 (sqrt (+ x 1.0)))
143.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify379.0ms

Counts
51 → 51
Iterations

Useful iterations: done (377.0ms)

IterNodesCost
0117739
1283693
21060636
done5000630

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
15.0ms
(+ (sqrt (+ x 1.0)) 1.0)
23.0ms
(/ x (+ (sqrt (+ x 1.0)) 1.0))

series188.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(+ (sqrt (+ x 1.0)) 1.0)
140.0ms
(/ x (+ (sqrt (+ x 1.0)) 1.0))

simplify362.0ms

Counts
51 → 51
Iterations

Useful iterations: done (360.0ms)

IterNodesCost
0117739
1283691
21061634
done5000630

prune98.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
3.2b
(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
7.3b
(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
43×add-sqr-sqrt
34×sqrt-prod
31×add-cube-cbrt
28×distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
14×sqrt-div
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×flip3-+ flip-+
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×frac-times sum-cubes unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus sqrt-unprod diff-log unpow3 div-exp pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 164
Calls
4 calls:
22.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
3.0ms
(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
65.0ms
(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms
(pow (sqrt (+ x 1.0)) 3)
72.0ms
(- (* 1.0 1.0) (* (sqrt (+ x 1.0)) 1.0))
195.0ms
(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

simplify1.6s

Counts
176 → 176
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02532705
15962016
228851873
done50001867

prune361.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
53×add-sqr-sqrt
52×times-frac
37×add-cube-cbrt
35×sqrt-prod
30×associate-*r*
14×distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-*l* associate-/l* unswap-sqr
5×pow1 add-log-exp
4×associate-/r* associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 116
Calls
3 calls:
15.0ms
(+ (sqrt (+ x 1.0)) 1.0)
24.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
53.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series479.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (sqrt (+ x 1.0)) 1.0)
293.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
138.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify655.0ms

Counts
125 → 125
Iterations

Useful iterations: done (652.0ms)

IterNodesCost
01932125
14951882
219741708
done50001701

prune206.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes17.0ms

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

sample312.0ms

Algorithm
intervals
Results
158.0ms7998×body80valid
39.0ms2640×body80nan
0.0ms2×body1280valid