Details

Time bar (total: 1.9m)

sample67.0ms

Algorithm
intervals
Results
17.0ms72×body640valid
10.0ms198×body80nan
9.0ms32×body1280valid
7.0ms121×body80valid
4.0ms21×body320valid
1.0ms10×body160valid

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11111
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.5b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
14.0ms
(sqrt (+ x 1.0))
30.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
129.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (+ x 1.0))
95.0ms
(/ 1.0 (sqrt (+ x 1.0)))
49.0ms
(/ 1.0 (sqrt x))
200.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.6s

Counts
770 → 770
Iterations

Useful iterations: done (2.6s)

IterNodesCost
070140764
1153135216
2301226244
done500120672

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 18.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
2.5b
(- (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))))

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
39191×times-frac
21393×*-un-lft-identity
19708×add-sqr-sqrt
19588×add-cube-cbrt
12323×sqrt-prod
10864×prod-diff
6607×cbrt-prod
876×distribute-lft-out
847×div-inv
582×cbrt-div sqrt-div associate-/r/
291×flip3-+ flip-+
97×fma-neg
31×associate-/l*
25×difference-of-squares
15×distribute-lft-out--
9×add-exp-log add-cbrt-cube
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp associate-/r*
2×pow1/3
1×sub-neg flip3-- frac-2neg diff-log clear-num frac-sub flip-- associate-/l/
Counts
4 → 11186
Calls
4 calls:
19.0ms
(/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))
2.0ms
(cbrt x)
2.0ms
(cbrt x)
991.0ms
(- (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))))

series943.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))
210.0ms
(cbrt x)
204.0ms
(cbrt x)
228.0ms
(- (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))))

simplify5.4s

Counts
11198 → 11198
Iterations

Useful iterations: 0 (2.2s)

IterNodesCost
092341376707
done92341376707

prune1.3m

Pruning

50 alts after pruning (50 fresh and 0 done)

Merged error: 18.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
2.5b
(- (* (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))) (* (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod frac-sub
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×frac-times associate-*r/ associate-*l/ add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 65
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
38.0ms
(- (* (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))) (* (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0))))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt x)
188.0ms
(cbrt x)
194.0ms
(cbrt x)
212.0ms
(- (* (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x)))) (* (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0))))))

simplify647.0ms

Counts
77 → 77
Iterations

Useful iterations: done (645.0ms)

IterNodesCost
01772205
15012093
216071762
done50011692

prune802.0ms

Pruning

50 alts after pruning (49 fresh and 1 done)

Merged error: 18.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
17.4b
(- (/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

rewrite767.0ms

Algorithm
rewrite-expression-head
Rules
8339×times-frac
5437×*-un-lft-identity
4779×add-sqr-sqrt
4696×add-cube-cbrt
3743×sqrt-prod
3267×prod-diff
1146×cbrt-prod
412×div-inv
364×distribute-lft-out
242×sqrt-div associate-/r/
121×flip3-+ fma-neg flip-+
21×difference-of-squares
13×associate-/l*
9×add-exp-log associate-/r* add-cbrt-cube
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×cbrt-undiv div-exp
2×pow1/3
1×sub-neg flip3-- frac-2neg diff-log clear-num frac-sub flip-- associate-/l/
Counts
4 → 3610
Calls
4 calls:
14.0ms
(/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x)))
2.0ms
(cbrt x)
1.0ms
(cbrt x)
289.0ms
(- (/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

series799.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x)))
189.0ms
(cbrt x)
193.0ms
(cbrt x)
136.0ms
(- (/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts
3622 → 3622
Iterations

Useful iterations: done (769.0ms)

IterNodesCost
02755255917
done5000255547

prune13.9s

Pruning

51 alts after pruning (50 fresh and 1 done)

Merged error: 18.7b

regimes550.0ms

Accuracy

0% (1.0b remaining)

Error of 20.5b against oracle of 19.5b and baseline of 20.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02595
13295
done3295

end0.0ms

sample1.6s

Algorithm
intervals
Results
532.0ms1857×body640valid
312.0ms8006×body80nan
227.0ms1173×body1280valid
156.0ms3994×body80valid
56.0ms659×body320valid
18.0ms317×body160valid