Details

Time bar (total: 16.6s)

sample80.0ms

Algorithm
intervals
Results
38.0ms76×body1280valid
13.0ms45×body640valid
10.0ms31×body2560valid
3.0ms70×body80valid
2.0ms17×body320valid
2.0ms17×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: 52.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b
(sqrt (+ (* x x) 1.0))

rewrite60.0ms

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:
37.0ms
(+ x (sqrt (+ (* x x) 1.0)))
14.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series436.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(+ x (sqrt (+ (* x x) 1.0)))
268.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
66.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
51 → 51
Iterations
IterNodes
done5001
21377
1320
0134

prune267.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0)))
0.1b
(* x (* x x))
0.1b
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
40×add-cbrt-cube add-exp-log
20×add-sqr-sqrt
19×pow1
17×prod-exp cbrt-unprod
16×times-frac
14×*-un-lft-identity associate-*r* add-cube-cbrt
13×associate-*l*
10×cbrt-undiv div-exp
7×add-log-exp
6×frac-sub
5×pow-prod-up
4×pow-prod-down
3×frac-times flip3-+ associate-*l/ associate-*r/ sqrt-prod flip-+ unswap-sqr
2×diff-log *-commutative div-inv
1×pow2 sum-log sub-neg pow-plus flip3-- cube-unmult associate--l+ pow-sqr flip--
Counts
3 → 97
Calls
3 calls:
237.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0)))
16.0ms
(* x (* x x))
59.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

series345.0ms

Counts
3 → 9
Calls
3 calls:
181.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0)))
48.0ms
(* x (* x x))
116.0ms
(* (/ (* x (* x x)) (sqrt 1.0)) (/ 1/6 1.0))

simplify2.3s

Counts
106 → 106
Iterations
IterNodes
done5000
24729
1641
0203

prune412.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (* x (* x x)))
12.2b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.0b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite305.0ms

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:
9.0ms
(/ 0.0625 (pow x 5))
22.0ms
(/ 0.125 (* x (* x x)))
118.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
151.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ 0.0625 (pow x 5))
40.0ms
(/ 0.125 (* x (* x x)))
290.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
85.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.9s

Counts
120 → 120
Iterations
IterNodes
done5002
23908
1691
0268

prune702.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

10.0b
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
10.0b
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
19.0b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
19.0b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite586.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
18×log-prod
16×add-sqr-sqrt
14×add-log-exp
12×frac-sub sqrt-prod
10×log-div sqrt-div
8×pow1 add-cube-cbrt distribute-lft-out--
6×add-exp-log log-pow
4×flip3-+ flip3-- add-cbrt-cube diff-log frac-add flip-+ flip-- distribute-lft-out difference-of-squares
2×sum-log sub-neg sqrt-pow1 pow1/2 rem-log-exp associate--r+
Counts
4 → 90
Calls
4 calls:
115.0ms
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
131.0ms
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
192.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
145.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
114.0ms
(log (sqrt (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
78.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
98.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.4s

Counts
102 → 102
Iterations
IterNodes
done5000
21779
1376
0149

prune725.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes190.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.2b

bsearch94.0ms

Steps
ItersRangePoint
10
2.777137017098532e-16
1126.7541422477805
0.9010700472866574
9
-291337.82152789796
-0.7274215675205146
-1.0196402015835608

simplify7.0ms

Iterations
IterNodes
done40
140
034

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s2341×body1280valid
587.0ms1573×body640valid
353.0ms763×body2560valid
169.0ms806×body320valid
157.0ms2086×body80valid
52.0ms431×body160valid