Details

Time bar (total: 10.5s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
2.0ms69×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: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×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×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u 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 hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
19.0ms
(+ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series302.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(sqrt (+ x 1.0))
55.0ms
(+ 1.0 (sqrt (+ x 1.0)))
209.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify867.0ms

Counts
80 → 80
Iterations

Useful iterations: done (864.0ms)

IterNodesCost
0146959
1343886
21581822
done5001815

prune187.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

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)
4.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite240.0ms

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:
55.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms
(pow (sqrt (+ x 1.0)) 3)
44.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
118.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
81.0ms
(pow (sqrt (+ x 1.0)) 3)
91.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
269.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify650.0ms

Counts
206 → 206
Iterations

Useful iterations: done (638.0ms)

IterNodesCost
03264145
19523032
done50012795

prune602.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
0.1b
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
288×*-un-lft-identity
190×sqrt-prod
189×add-sqr-sqrt
186×add-cube-cbrt
51×distribute-lft-out
34×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/l*
9×div-inv
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def flip3-+ flip-+
2×frac-2neg sqrt-div clear-num associate-/l/
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def
Counts
4 → 305
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
19.0ms
(+ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
54.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
48.0ms
(+ 1.0 (sqrt (+ x 1.0)))
177.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
140.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify701.0ms

Counts
317 → 317
Iterations

Useful iterations: done (687.0ms)

IterNodesCost
03846996
110216387
done50006149

prune700.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
32.8b
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity
60×times-frac
48×add-sqr-sqrt add-cube-cbrt
42×cbrt-prod
36×unpow-prod-down cube-prod
17×distribute-lft-out
10×associate-/r/
9×add-exp-log add-cbrt-cube
6×flip3-+ flip-+ add-log-exp
5×pow1 div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×pow-unpow fma-def associate-/l*
2×cbrt-undiv cube-div cube-mult unpow3 div-exp pow-exp rem-cube-cbrt sqr-pow
1×+-commutative pow-to-exp cbrt-div pow-pow frac-2neg pow1/3 clear-num sum-log rem-cbrt-cube
Counts
4 → 164
Calls
4 calls:
17.0ms
(+ 1.0 (sqrt (+ x 1.0)))
35.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
36.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
41.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

series916.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ 1.0 (sqrt (+ x 1.0)))
227.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
410.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
204.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

simplify2.7s

Counts
176 → 176
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02483277
18002741
246562517
done50002506

prune432.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes85.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.5b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02356
12956
done2956

end0.0ms

sample786.0ms

Algorithm
intervals
Results
421.0ms7998×body80valid
115.0ms2664×body80nan
0.0ms2×body1280valid