Details

Time bar (total: 24.7s)

sample94.0ms

Algorithm
intervals
Results
40.0ms73×body1280valid
17.0ms24×body2560valid
16.0ms45×body640valid
7.0ms34×body320valid
4.0ms69×body80valid
1.0ms11×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
29
19
07

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1)))
2.9b
(log (+ x (sqrt (+ (* x x) 1))))
15.2b
(sqrt (+ (* x x) 1))

rewrite40.0ms

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-+ insert-posit16
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 → 45
Calls
3 calls:
21.0ms
(+ x (sqrt (+ (* x x) 1)))
12.0ms
(log (+ x (sqrt (+ (* x x) 1))))
7.0ms
(sqrt (+ (* x x) 1))

series231.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ x (sqrt (+ (* x x) 1)))
125.0ms
(log (+ x (sqrt (+ (* x x) 1))))
37.0ms
(sqrt (+ (* x x) 1))

simplify1.6s

Counts
54 → 54
Iterations
IterNodes
43922
31654
2660
1271
0121

prune405.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* (* x x) x)
0.1b
(* -1/6 (* (* x x) x))
19.3b
(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
51×pow1
23×add-cbrt-cube add-exp-log
12×pow-plus pow-prod-down prod-exp pow-prod-up cbrt-unprod
9×add-sqr-sqrt
7×*-un-lft-identity associate-*r* add-cube-cbrt
6×add-log-exp
5×associate-*l*
4×pow2 pow-sqr insert-posit16
3×*-commutative
2×pow3 unswap-sqr
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 92
Calls
4 calls:
14.0ms
(* (* x x) x)
16.0ms
(* (* x x) x)
35.0ms
(* -1/6 (* (* x x) x))
41.0ms
(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* x x) x)
45.0ms
(* (* x x) x)
55.0ms
(* -1/6 (* (* x x) x))
189.0ms
(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify2.8s

Counts
104 → 104
Iterations
IterNodes
35081
2907
1256
088

prune618.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1/8 x) (* x x))
0.2b
(/ -1/16 (* (* x x) (* (* x x) x)))
10.2b
(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
18.8b
(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
45×add-cbrt-cube
34×times-frac
31×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
17×prod-exp cbrt-unprod
16×associate-/l*
13×cbrt-undiv div-exp
9×add-log-exp
6×frac-add
5×pow1 log-div log-prod
4×insert-posit16 div-inv distribute-lft-out
2×associate-+l+ clear-num associate-/r* sum-log frac-2neg flip3-+ flip3-- frac-sub flip-+ flip-- distribute-lft-out--
1×+-commutative sub-neg diff-log rem-log-exp log-pow associate-+l- associate-/l/
Counts
4 → 120
Calls
4 calls:
16.0ms
(/ (/ 1/8 x) (* x x))
67.0ms
(/ -1/16 (* (* x x) (* (* x x) x)))
137.0ms
(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
142.0ms
(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (/ 1/8 x) (* x x))
72.0ms
(/ -1/16 (* (* x x) (* (* x x) x)))
140.0ms
(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
77.0ms
(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify913.0ms

Counts
132 → 132
Iterations
IterNodes
22651
1733
0277

prune833.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (/ 1/8 x) (* x x)) (+ x x))
0.0b
(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
0.1b
(/ (/ 1/8 x) (* x x))
8.5b
(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
36×add-sqr-sqrt times-frac
19×add-cube-cbrt
18×add-log-exp
17×add-exp-log
16×add-cbrt-cube
14×frac-sub
13×associate-/l*
12×distribute-lft-out--
8×log-prod
7×diff-log difference-of-squares
6×cbrt-undiv log-div div-exp
5×pow1 flip3-- flip--
4×insert-posit16
3×sub-neg flip3-+ flip-+ div-inv distribute-lft-out associate--r+
2×sum-log prod-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg rem-log-exp log-pow associate--r- associate-/l/
Counts
4 → 120
Calls
4 calls:
51.0ms
(- (/ (/ 1/8 x) (* x x)) (+ x x))
63.0ms
(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
10.0ms
(/ (/ 1/8 x) (* x x))
77.0ms
(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (/ (/ 1/8 x) (* x x)) (+ x x))
60.0ms
(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
62.0ms
(/ (/ 1/8 x) (* x x))
98.0ms
(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

simplify10.1s

Counts
132 → 132
Iterations
IterNodes
38868
21891
1660
0263

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.9b

bsearch93.0ms

Steps
ItersRangePoint
9
5.277777168093308e-05
15.597049771107491
0.955290469990551
10
-1231591086050.0088
-0.0006858147917088189
-1.0776022250282242

simplify14.0ms

Iterations
IterNodes
237
137
030

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.6s2298×body1280valid
719.0ms1629×body640valid
547.0ms801×body2560valid
502.0ms800×body320valid
194.0ms2076×body80valid
63.0ms396×body160valid