Details

Time bar (total: 13.6s)

sample20.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
2.0ms69×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

rewrite75.0ms

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
(sqrt (+ x 1.0))
21.0ms
(+ 1.0 (sqrt (+ x 1.0)))
43.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series273.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(sqrt (+ x 1.0))
44.0ms
(+ 1.0 (sqrt (+ x 1.0)))
175.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify905.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (288.0ms)

IterNodesCost
0140917
1326848
21523785
done5000785

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 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)
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)))

rewrite237.0ms

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:
73.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
11.0ms
(pow (sqrt (+ x 1.0)) 3)
30.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
108.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
114.0ms
(pow (sqrt (+ x 1.0)) 3)
73.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
234.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify599.0ms

Counts
196 → 196
Iterations

Useful iterations: done (590.0ms)

IterNodesCost
03134015
18952975
done50002738

prune684.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite201.0ms

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:
8.0ms
(sqrt (+ x 1.0))
41.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(+ 1.0 (sqrt (+ x 1.0)))
128.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
411.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
58.0ms
(+ 1.0 (sqrt (+ x 1.0)))
225.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.6s

Counts
144 → 144
Iterations

Useful iterations: done (3.6s)

IterNodesCost
02162303
15572115
239781873
done50011847

prune411.0ms

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))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
60×times-frac
47×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×associate-/r*
3×pow-unpow 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 → 153
Calls
4 calls:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
56.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
42.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

series883.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ 1.0 (sqrt (+ x 1.0)))
216.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
396.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
212.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

simplify2.7s

Counts
165 → 165
Iterations

Useful iterations: 2 (934.0ms)

IterNodesCost
02403199
17782679
246382455
done50012455

prune528.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes98.0ms

Accuracy

99.8% (0.0b remaining)

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

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02356
13056
done3056

end0.0ms

sample807.0ms

Algorithm
intervals
Results
443.0ms7998×body80valid
92.0ms2664×body80nan
0.0ms2×body1280valid