Details

Time bar (total: 3.4s)

sample15.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms98×body80nan

simplify4.0ms

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

localize8.0ms

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))))

rewrite46.0ms

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
(+ 1.0 (sqrt (+ x 1.0)))
30.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series176.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
136.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0278393
11058351
25002347
done5002347

prune100.0ms

Pruning

4 alts after pruning (3 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)
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)))

rewrite170.0ms

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×sum-cubes 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 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 → 184
Calls
4 calls:
39.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms
(pow (sqrt (+ x 1.0)) 3)
27.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
85.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
65.0ms
(pow (sqrt (+ x 1.0)) 3)
62.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
182.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify131.0ms

Counts
196 → 196
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
07711703
138731474
250021459
done50021459

prune395.0ms

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))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
70×cbrt-prod *-un-lft-identity
51×times-frac
44×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×cbrt-div flip3-+ flip-+
3×pow-unpow 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 → 149
Calls
4 calls:
14.0ms
(+ 1.0 (sqrt (+ x 1.0)))
62.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
28.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
30.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series326.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
135.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
107.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
44.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify62.0ms

Counts
161 → 161
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04981438
121741302
250021278
done50021278

prune230.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize9.0ms

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)))))

rewrite128.0ms

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:
33.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
76.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series441.0ms

Counts
3 → 9
Calls
3 calls:
273.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
124.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify59.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04911191
121421050
250021025
done50021025

prune214.0ms

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

sample346.0ms

Algorithm
intervals
Results
155.0ms7996×body80valid
39.0ms2715×body80nan
0.0ms4×body1280valid