Details

Time bar (total: 7.5s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms82×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

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

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:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
20.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series218.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
36.0ms
(sqrt (+ x 1.0))
140.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts
70 → 70
Iterations

Useful iterations: 3 (640.0ms)

IterNodesCost
0140917
1316848
2954783
34782775
done5000775

prune142.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

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)
2.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite114.0ms

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:
24.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms
(pow (sqrt (+ x 1.0)) 3)
14.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
61.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms
(pow (sqrt (+ x 1.0)) 3)
66.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
193.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.1s

Counts
196 → 196
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03134015
17362931
228542700
done50012696

prune452.0ms

Pruning

4 alts after pruning (2 fresh and 2 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
(/ x (+ 1.0 (sqrt (+ x 1.0))))
2.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
2.7b
(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-div
43×*-un-lft-identity
35×flip3-+ flip-+
33×add-sqr-sqrt
32×associate-*r/
26×sqrt-prod
21×add-cube-cbrt
20×frac-sub
19×pow1
12×frac-times times-frac
11×swap-sqr add-log-exp
10×distribute-lft-out
8×add-exp-log sqrt-pow1 pow1/2 associate-*l/ add-cbrt-cube
7×associate-*r* associate-*l*
5×pow-prod-up
4×associate-/r* sub-div unswap-sqr
3×diff-log pow-prod-down pow-sqr associate-/l*
2×sub-neg flip3-- associate-/r/ flip--
1×cbrt-undiv pow2 distribute-rgt-out-- frac-2neg pow-plus sqrt-unprod div-exp prod-exp associate--l+ clear-num sum-log rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 146
Calls
4 calls:
22.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
20.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
20.0ms
(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
141.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
66.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
67.0ms
(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

simplify730.0ms

Counts
158 → 158
Iterations

Useful iterations: done (725.0ms)

IterNodesCost
02993473
16852599
221752349
done50012347

prune410.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:
9.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
19.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
51.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(sqrt (+ x 1.0))
297.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
137.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify638.0ms

Counts
144 → 144
Iterations

Useful iterations: done (634.0ms)

IterNodesCost
02162303
15292031
217631857
done50011848

prune265.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01846
12646
done2646

end0.0ms

sample320.0ms

Algorithm
intervals
Results
159.0ms7997×body80valid
44.0ms2656×body80nan
0.0ms3×body1280valid