Details

Time bar (total: 3.6s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms98×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184
done84

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))))

rewrite51.0ms

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:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
33.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series178.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
138.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0290412
11095368
25001361
done5001361

prune117.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

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)
2.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
38.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
12.0ms
(pow (sqrt (+ x 1.0)) 3)
28.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
86.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms
(pow (sqrt (+ x 1.0)) 3)
59.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify134.0ms

Counts
206 → 206
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08251791
141301518
250011510
done50011510

prune448.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
0.2b
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
5.2b
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×cbrt-prod
51×times-frac
45×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down cube-prod
17×associate-/r*
13×distribute-lft-out
7×add-exp-log
6×cube-div cube-mult unpow3 add-cbrt-cube add-log-exp sqr-pow
5×pow1
4×expm1-log1p-u cbrt-div flip3-+ flip-+ log1p-expm1-u
3×pow-unpow fma-def associate-/l*
2×associate-/r/
1×cbrt-undiv +-commutative pow-to-exp pow-pow frac-2neg pow1/3 div-exp pow-exp clear-num sum-log rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 160
Calls
4 calls:
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
63.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
29.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
32.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series333.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
140.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
109.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
43.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify64.0ms

Counts
172 → 172
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05191477
122351340
250011310
done50011310

prune276.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
54×add-sqr-sqrt
52×times-frac
38×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×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
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 → 125
Calls
3 calls:
33.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
81.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series456.0ms

Counts
3 → 9
Calls
3 calls:
285.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
39.0ms
(+ 1.0 (sqrt (+ x 1.0)))
132.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify59.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05111228
121961085
250011054
done50011054

prune236.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes38.0ms

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
084
184
done84

end0.0ms

sample349.0ms

Algorithm
intervals
Results
159.0ms7996×body80valid
40.0ms2715×body80nan
0.0ms4×body1280valid