Details

Time bar (total: 14.1s)

sample128.0ms

Algorithm
intervals
Results
52.0ms75×body1280valid
25.0ms30×body2560valid
20.0ms43×body640valid
9.0ms31×body320valid
4.0ms61×body80valid
3.0ms16×body160valid

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
3.4b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.6b
(sqrt (+ (* x x) 1.0))

rewrite47.0ms

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:
14.0ms
(+ x (sqrt (+ (* x x) 1.0)))
20.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
12.0ms
(sqrt (+ (* x x) 1.0))

series444.0ms

Counts
3 → 9
Calls
3 calls:
109.0ms
(+ x (sqrt (+ (* x x) 1.0)))
272.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
63.0ms
(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts
51 → 51
Iterations
IterNodes
done5001
21377
1320
0134

prune295.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
0.1b
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
106×times-frac
76×associate-*l*
52×*-un-lft-identity add-cube-cbrt
44×sqrt-prod
26×add-exp-log
22×unpow-prod-down cube-prod
18×unswap-sqr
14×add-cbrt-cube
13×associate-*r*
10×div-exp sqr-pow
8×prod-exp
6×cube-mult unpow3 frac-sub add-log-exp
4×pow1 cbrt-undiv cbrt-unprod
3×frac-times flip3-+ associate-*l/ associate-*r/ flip-+
2×pow-to-exp diff-log pow-exp div-inv
1×sum-log sub-neg flip3-- pow-prod-down associate--l+ *-commutative flip--
Counts
2 → 151
Calls
2 calls:
150.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
80.0ms
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

series290.0ms

Counts
2 → 6
Calls
2 calls:
184.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
106.0ms
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

simplify1.6s

Counts
157 → 157
Iterations
IterNodes
done5000
23791
1733
0236

prune676.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.1b
(/ 0.125 (pow x 3))
10.7b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
15.6b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×pow-to-exp cbrt-undiv clear-num frac-2neg flip3-+ flip3-- diff-log frac-add pow-exp flip-+ div-inv flip--
1×sum-log sub-neg rem-log-exp log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
10.0ms
(/ 0.0625 (pow x 5))
13.0ms
(/ 0.125 (pow x 3))
136.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
180.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series497.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ 0.0625 (pow x 5))
55.0ms
(/ 0.125 (pow x 3))
279.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
102.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.5s

Counts
172 → 172
Iterations
IterNodes
done5000
23244
1721
0316

prune781.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.1b
(/ 0.125 (pow x 3))
8.3b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×associate-/r* unpow-prod-down cube-prod
9×add-exp-log
6×log-prod
5×add-cbrt-cube distribute-lft-out add-log-exp
4×cube-mult pow1 unpow3 sqr-pow
3×div-exp associate-/l*
2×log-div flip3-+ flip-+ distribute-lft-out--
1×pow-to-exp cbrt-undiv +-commutative clear-num sum-log frac-2neg rem-log-exp pow-exp log-pow div-inv
Counts
3 → 94
Calls
3 calls:
12.0ms
(+ x (/ 0.5 x))
7.0ms
(/ 0.125 (pow x 3))
219.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series338.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(+ x (/ 0.5 x))
51.0ms
(/ 0.125 (pow x 3))
213.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify1.1s

Counts
103 → 103
Iterations
IterNodes
done5001
21987
1418
0184

prune351.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch127.0ms

Steps
ItersRangePoint
8
0.00104763160503943
5.1212688054922095
0.8884086436842497
9
-205.8624528279525
-0.0007095347148853646
-1.0022756540898416

simplify8.0ms

Iterations
IterNodes
done39
139
034

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.0s2252×body1280valid
680.0ms1576×body640valid
339.0ms762×body2560valid
221.0ms836×body320valid
114.0ms2144×body80valid
57.0ms430×body160valid