Details

Time bar (total: 14.7s)

sample121.0ms

Algorithm
intervals
Results
65.0ms78×body1280valid
18.0ms43×body640valid
13.0ms27×body2560valid
6.0ms27×body320valid
4.0ms65×body80valid
2.0ms16×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
35.0ms
(+ x (sqrt (+ (* x x) 1.0)))
34.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
12.0ms
(sqrt (+ (* x x) 1.0))

series393.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(+ x (sqrt (+ (* x x) 1.0)))
247.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify799.0ms

Counts
51 → 51
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
0133761
1319691
21350618
done5002606

prune261.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
154.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series244.0ms

Counts
1 → 3
Calls
1 calls:
244.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify646.0ms

Counts
273 → 273
Iterations

Useful iterations: done (636.0ms)

IterNodesCost
02933830
18542926
done50012645

prune549.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.4b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
17.1b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite904.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
68×*-un-lft-identity
66×add-sqr-sqrt
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
12×cube-prod
10×log-prod distribute-lft-out-- sqr-pow
9×add-log-exp
8×frac-sub add-cbrt-cube difference-of-squares
6×div-exp associate-/l*
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num div-inv
1×associate--l- rem-log-exp log-pow
Counts
4 → 160
Calls
4 calls:
15.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (pow x 3))
255.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
607.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ 0.0625 (pow x 5))
57.0ms
(/ 0.125 (pow x 3))
285.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
76.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.8s

Counts
172 → 172
Iterations

Useful iterations: 2 (660.0ms)

IterNodesCost
03202874
17022609
231272481
done50022481

prune632.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.3b
(/ 0.125 (pow x 3))
10.7b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
54×*-un-lft-identity
51×times-frac
30×add-cube-cbrt
15×add-log-exp
14×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log distribute-lft-out difference-of-squares
6×log-prod add-cbrt-cube sqr-pow
5×pow1 sum-log
4×cube-mult unpow3 distribute-lft-out--
3×div-exp associate-/l*
2×associate-+r- log-div flip3-+ diff-log flip-+
1×cbrt-undiv +-commutative pow-to-exp sub-neg associate-+r+ flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow frac-sub flip-- div-inv
Counts
4 → 125
Calls
4 calls:
87.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
584.0ms
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
17.0ms
(/ 0.125 (pow x 3))
497.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
48.0ms
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
77.0ms
(/ 0.125 (pow x 3))
230.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify1.6s

Counts
137 → 137
Iterations

Useful iterations: 2 (573.0ms)

IterNodesCost
02252109
15261903
224931771
done50021771

prune315.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch110.0ms

Steps
ItersRangePoint
8
0.01136632641909174
309.51167567074003
0.8828713596856151
10
-1950712569354.648
-0.00015980627971116164
-1.0227411808047386

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13857
done3857

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.6s2328×body1280valid
649.0ms1549×body640valid
582.0ms797×body320valid
396.0ms819×body2560valid
155.0ms2085×body80valid
99.0ms422×body160valid