Details

Time bar (total: 15.5s)

sample132.0ms

Algorithm
intervals
Results
61.0ms72×body1280valid
26.0ms54×body640valid
11.0ms19×body2560valid
8.0ms26×body320valid
5.0ms73×body80valid
2.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.6b

localize33.0ms

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))

rewrite57.0ms

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:
28.0ms
(+ x (sqrt (+ (* x x) 1.0)))
19.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series468.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(+ x (sqrt (+ (* x x) 1.0)))
286.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
80.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
51 → 51
Iterations
IterNodes
done5001
21377
1320
0134

prune297.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 2 expressions with local error:

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

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
18×pow1
17×prod-exp cbrt-unprod
16×times-frac
14×associate-*r*
13×*-un-lft-identity associate-*l* add-cube-cbrt
10×cbrt-undiv div-exp
5×pow-prod-up
4×pow-prod-down
3×sqrt-prod unswap-sqr
2×*-commutative div-inv add-log-exp
1×pow2 frac-times pow-plus cube-unmult associate-*l/ associate-*r/ pow-sqr
Counts
2 → 77
Calls
2 calls:
31.0ms
(* x (* x x))
70.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

series211.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(* x (* x x))
150.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

simplify2.2s

Counts
83 → 83
Iterations
IterNodes
done5001
23548
1453
0141

prune332.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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))))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 *-un-lft-identity add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod prod-exp cbrt-unprod add-log-exp
5×pow-prod-up distribute-lft-out
3×cbrt-undiv times-frac div-exp associate-*l* pow-prod-down associate-/l*
2×log-div flip3-+ flip-+ distribute-lft-out--
1×pow2 +-commutative clear-num associate-/r* sum-log frac-2neg pow-plus cube-unmult rem-log-exp associate-*r* pow-sqr log-pow *-commutative div-inv unswap-sqr
Counts
4 → 76
Calls
4 calls:
9.0ms
(+ x (/ 0.5 x))
14.0ms
(* x (* x x))
14.0ms
(/ 0.125 (* x (* x x)))
147.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ x (/ 0.5 x))
44.0ms
(* x (* x x))
40.0ms
(/ 0.125 (* x (* x x)))
173.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

simplify1.3s

Counts
88 → 88
Iterations
IterNodes
done5000
22549
1414
0158

prune335.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

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))))

rewrite339.0ms

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:
12.0ms
(/ 0.0625 (pow x 5))
26.0ms
(/ 0.125 (* x (* x x)))
129.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
165.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 0.0625 (pow x 5))
51.0ms
(/ 0.125 (* x (* x x)))
263.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
76.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.8s

Counts
120 → 120
Iterations
IterNodes
done5002
23908
1691
0268

prune659.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes308.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch112.0ms

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

simplify26.0ms

Iterations
IterNodes
done40
140
034

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.6s2395×body1280valid
736.0ms772×body2560valid
615.0ms1540×body640valid
254.0ms796×body320valid
110.0ms2087×body80valid
53.0ms410×body160valid