Details

Time bar (total: 13.1s)

sample23.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
2.0ms97×body80nan

simplify3.0ms

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

rewrite73.0ms

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:
21.0ms
(+ 1.0 (sqrt (+ x 1.0)))
15.0ms
(sqrt (+ x 1.0))
35.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series251.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ 1.0 (sqrt (+ x 1.0)))
44.0ms
(sqrt (+ x 1.0))
149.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0140917
1316848
2899783
33661775
done5000773

prune262.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

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:
61.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
20.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
8.0ms
(cbrt (+ x 1.0))
8.0ms
(cbrt (+ x 1.0))

series706.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
280.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
135.0ms
(cbrt (+ x 1.0))
142.0ms
(cbrt (+ x 1.0))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02722241
16812077
223731964
done50001889

prune498.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize33.0ms

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)
3.3b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.5b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite255.0ms

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:
62.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
11.0ms
(pow (sqrt (+ x 1.0)) 3)
41.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
123.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
77.0ms
(pow (sqrt (+ x 1.0)) 3)
85.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
263.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.2s

Counts
196 → 196
Iterations

Useful iterations: 2 (732.0ms)

IterNodesCost
03134015
17462931
227432700
done50002700

prune679.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

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)))))

rewrite225.0ms

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))
53.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
29.0ms
(+ 1.0 (sqrt (+ x 1.0)))
129.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
476.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
68.0ms
(+ 1.0 (sqrt (+ x 1.0)))
238.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.3s

Counts
144 → 144
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02162303
15202031
217081857
done50001834

prune364.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
11215
done1215

end0.0ms

sample695.0ms

Algorithm
intervals
Results
356.0ms7999×body80valid
105.0ms2697×body80nan
0.0ms1×body1280valid