Details

Time bar (total: 7.7s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms80×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

localize5.0ms

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))))

rewrite33.0ms

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:
7.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series213.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
139.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify380.0ms

Counts
70 → 70
Iterations

Useful iterations: done (378.0ms)

IterNodesCost
0140917
1324848
21160783
done5001775

prune130.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
13.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
8.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
87.0ms
(cbrt (+ x 1.0))
90.0ms
(cbrt (+ x 1.0))
211.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify844.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (212.0ms)

IterNodesCost
02722241
16902085
229061964
done50001964

prune287.0ms

Pruning

5 alts after pruning (3 fresh and 2 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)
5.0b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite108.0ms

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:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms
(pow (sqrt (+ x 1.0)) 3)
13.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
57.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
63.0ms
(pow (sqrt (+ x 1.0)) 3)
66.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
197.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.0s

Counts
196 → 196
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03134015
17742947
235622700
done50002696

prune421.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))
34.3b
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite72.0ms

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:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
19.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
22.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

series614.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ 1.0 (sqrt (+ x 1.0)))
271.0ms
(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
140.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
154.0ms
(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

simplify1.1s

Counts
165 → 165
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02403199
16592663
228292420
done50002412

prune269.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes42.0ms

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
068
188
done88

end0.0ms

sample319.0ms

Algorithm
intervals
Results
157.0ms7993×body80valid
45.0ms2733×body80nan
1.0ms7×body1280valid