Details

Time bar (total: 14.7s)

sample108.0ms

Algorithm
intervals
Results
54.0ms72×body1280valid
21.0ms54×body640valid
9.0ms19×body2560valid
7.0ms26×body320valid
4.0ms73×body80valid
2.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07232
19232
done9232

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 42
Calls
3 calls:
45.0ms
(+ x (sqrt (+ (* x x) 1.0)))
25.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
14.0ms
(sqrt (+ (* x x) 1.0))

series421.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(+ x (sqrt (+ (* x x) 1.0)))
290.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
57.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
51 → 51
Iterations

Useful iterations: done (1.0s)

IterNodesCost
013418845
132014789
2137714143
done500113983

prune303.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
0.1b
(* 1/6 (* x (* x x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
16×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
6×associate-*l*
5×add-sqr-sqrt pow-prod-up
4×*-un-lft-identity add-cube-cbrt
2×associate-*r* *-commutative add-log-exp
1×pow2 pow-plus cube-unmult pow-sqr unswap-sqr
Counts
2 → 45
Calls
2 calls:
13.0ms
(* x (* x x))
50.0ms
(* 1/6 (* x (* x x)))

series92.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(* x (* x x))
46.0ms
(* 1/6 (* x (* x x)))

simplify1.0s

Counts
51 → 51
Iterations

Useful iterations: 2 (209.0ms)

IterNodesCost
0598200
11546462
28596025
done50006025

prune160.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.1b
(* (* x x) x)
0.3b
(/ 0.125 (* (* x x) x))
9.0b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* (* x x) x)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
19×*-un-lft-identity add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod add-log-exp
5×distribute-lft-out
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+ distribute-lft-out--
1×+-commutative clear-num associate-/r* sum-log frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
15.0ms
(+ x (/ 0.5 x))
18.0ms
(* (* x x) x)
20.0ms
(/ 0.125 (* (* x x) x))
168.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* (* x x) x)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ x (/ 0.5 x))
52.0ms
(* (* x x) x)
61.0ms
(/ 0.125 (* (* x x) x))
206.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* (* x x) x)))))

simplify2.2s

Counts
92 → 92
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
015723652
140419384
2269218382
done500018382

prune297.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (* (* x x) x))
11.2b
(log (- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.7b
(- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
27×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
19×add-exp-log
15×add-cbrt-cube
12×unpow-prod-down
9×add-log-exp
8×associate-/r*
6×log-prod div-exp frac-sub associate-/l*
5×pow1 log-div
4×cbrt-undiv distribute-lft-out-- sqr-pow
3×prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ div-inv flip-- distribute-lft-out difference-of-squares
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+
Counts
4 → 108
Calls
4 calls:
11.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (* (* x x) x))
146.0ms
(log (- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
142.0ms
(- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ 0.0625 (pow x 5))
54.0ms
(/ 0.125 (* (* x x) x))
305.0ms
(log (- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
100.0ms
(- (/ 0.125 (* (* x x) x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify3.2s

Counts
120 → 120
Iterations

Useful iterations: done (3.2s)

IterNodesCost
026566005
167659632
2386448026
done500147987

prune468.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch126.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
160.65039477392645
0.8907247814494134
10
-83422883652835.42
-0.9341403346610884
-1.02659151339998

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0351409
1411409
2431409
3451409
done451409

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.5s2395×body1280valid
572.0ms796×body320valid
509.0ms1540×body640valid
389.0ms772×body2560valid
107.0ms2087×body80valid
47.0ms410×body160valid