Details

Time bar (total: 17.1s)

sample90.0ms

Algorithm
intervals
Results
37.0ms69×body1280valid
18.0ms51×body640valid
8.0ms20×body2560valid
7.0ms33×body320valid
3.0ms71×body80valid
1.0ms12×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize17.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
3.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.2b
(sqrt (+ (* x x) 1.0))

rewrite74.0ms

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:
30.0ms
(+ x (sqrt (+ (* x x) 1.0)))
35.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series410.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(+ x (sqrt (+ (* x x) 1.0)))
241.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
79.0ms
(sqrt (+ (* x x) 1.0))

simplify2.0s

Counts
51 → 51
Iterations
IterNodes
done5015
33474
2937
1312
0134

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b
(* x (* x x))
0.2b
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
0.2b
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
191×add-sqr-sqrt
190×*-un-lft-identity add-cube-cbrt
108×sqrt-prod
54×associate-/r*
42×add-cbrt-cube add-exp-log
37×div-inv
19×cbrt-undiv div-exp
17×pow1
9×prod-exp cbrt-unprod associate-/l*
6×associate-/r/
5×pow-prod-up
3×associate-*l* pow-prod-down add-log-exp
2×clear-num frac-2neg
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative unswap-sqr
Counts
3 → 310
Calls
3 calls:
13.0ms
(* x (* x x))
23.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
16.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

series266.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* x (* x x))
111.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
113.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

simplify3.1s

Counts
319 → 319
Iterations
IterNodes
done5000
24791
11286
0447

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 0.125 x) (* x x))
9.5b
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
26×*-un-lft-identity
17×add-sqr-sqrt add-cube-cbrt
15×add-exp-log
14×add-cbrt-cube
13×associate-/l*
6×cbrt-undiv log-prod div-exp
5×distribute-lft-out
3×pow1 div-inv
2×log-div prod-exp cbrt-unprod add-log-exp
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp log-pow flip-+ distribute-lft-out-- associate-/l/
Counts
2 → 63
Calls
2 calls:
14.0ms
(/ (/ 0.125 x) (* x x))
246.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

series265.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ (/ 0.125 x) (* x x))
195.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

simplify1.5s

Counts
69 → 69
Iterations
IterNodes
done5000
21294
1410
0171

prune277.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 0.125 x) (* x x))
0.3b
(/ 0.0625 (pow x 5))
11.7b
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.1b
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
58×times-frac
49×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
22×add-exp-log
18×add-cbrt-cube
16×associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×div-inv distribute-lft-out-- sqr-pow
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add prod-exp cbrt-unprod flip-+ flip-- distribute-lft-out
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+ associate-/l/
Counts
4 → 135
Calls
4 calls:
11.0ms
(/ (/ 0.125 x) (* x x))
6.0ms
(/ 0.0625 (pow x 5))
115.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
158.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series811.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (/ 0.125 x) (* x x))
93.0ms
(/ 0.0625 (pow x 5))
574.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
74.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.7s

Counts
147 → 147
Iterations
IterNodes
done5097
22797
1774
0318

prune704.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

100% (0.0b remaining)

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

bsearch134.0ms

Steps
ItersRangePoint
11
1.9534460235190362e-22
53640.016154094046
0.8987700841367662
10
-17239113253358.373
-4.96108325192681e-05
-1.0098163723001696

simplify10.0ms

Iterations
IterNodes
done40
140
035

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s2408×body1280valid
639.0ms1473×body640valid
363.0ms786×body2560valid
285.0ms808×body320valid
135.0ms2122×body80valid
47.0ms403×body160valid