Details

Time bar (total: 15.4s)

sample101.0ms

Algorithm
intervals
Results
48.0ms83×body1280valid
20.0ms46×body640valid
10.0ms26×body2560valid
5.0ms26×body320valid
3.0ms61×body80valid
2.0ms14×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.0b
(sqrt (+ (* x x) 1.0))

rewrite66.0ms

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:
43.0ms
(+ x (sqrt (+ (* x x) 1.0)))
14.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series388.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(+ x (sqrt (+ (* x x) 1.0)))
242.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
60.0ms
(sqrt (+ (* x x) 1.0))

simplify1.1s

Counts
51 → 51
Iterations
IterNodes
done5001
21377
1320
0134

prune280.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
0.3b
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

rewrite120.0ms

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:
24.0ms
(* x (* x x))
91.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

series143.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(* x (* x x))
103.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

simplify2.1s

Counts
83 → 83
Iterations
IterNodes
done5001
23548
1453
0141

prune342.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 0.0625 (pow x 5))
0.6b
(/ 0.125 (* x (* x x)))
15.3b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.6b
(- (/ 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:
6.0ms
(/ 0.0625 (pow x 5))
15.0ms
(/ 0.125 (* x (* x x)))
149.0ms
(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))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ 0.0625 (pow x 5))
69.0ms
(/ 0.125 (* x (* x x)))
231.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
80.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify3.1s

Counts
120 → 120
Iterations
IterNodes
done5002
23908
1691
0268

prune570.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))
0.1b
(* x (* x x))
0.6b
(/ 0.125 (* x (* x x)))
12.9b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
19×pow1 add-exp-log
18×add-cbrt-cube
13×add-log-exp
9×add-sqr-sqrt
8×add-cube-cbrt distribute-lft-out
6×log-prod prod-exp cbrt-unprod
5×pow-prod-up
4×sum-log distribute-lft-out--
3×cbrt-undiv associate-+r+ times-frac div-exp associate-*l* pow-prod-down associate-/l*
2×log-div flip3-+ diff-log flip-+
1×pow2 +-commutative clear-num associate-+r- associate-/r* sub-neg frac-2neg pow-plus cube-unmult rem-log-exp associate-*r* associate--l+ pow-sqr log-pow *-commutative div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
145.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))
13.0ms
(* x (* x x))
13.0ms
(/ 0.125 (* x (* x x)))
123.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))
54.0ms
(* x (* x x))
55.0ms
(/ 0.125 (* x (* x x)))
181.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (* x (* x x))))))

simplify1.7s

Counts
96 → 96
Iterations
IterNodes
done5000
22690
1407
0159

prune345.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.6b

bsearch122.0ms

Steps
ItersRangePoint
11
3.4817375791661903e-26
573579.0075499975
0.8840407169458702
10
-84463.33967257517
-3.2432757514909933e-09
-0.9983730585657322

simplify7.0ms

Iterations
IterNodes
done40
140
034

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s2331×body1280valid
647.0ms1609×body640valid
326.0ms807×body2560valid
168.0ms2084×body80valid
158.0ms784×body320valid
89.0ms385×body160valid