Details

Time bar (total: 19.9s)

sample179.0ms

Algorithm
intervals
Results
88.0ms69×body1280valid
37.0ms54×body640valid
18.0ms23×body2560valid
11.0ms28×body320valid
7.0ms73×body80valid
2.0ms9×body160valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
211
111
07

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize25.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1)))
2.5b
(log (+ x (sqrt (+ (* x x) 1))))
13.7b
(sqrt (+ (* x x) 1))

rewrite59.0ms

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:
24.0ms
(+ x (sqrt (+ (* x x) 1)))
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))
14.0ms
(sqrt (+ (* x x) 1))

series243.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ x (sqrt (+ (* x x) 1)))
140.0ms
(log (+ x (sqrt (+ (* x x) 1))))
45.0ms
(sqrt (+ (* x x) 1))

simplify1.6s

Counts
54 → 54
Iterations
IterNodes
43878
31588
2647
1272
0121

prune468.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* (* x x) (* (* x x) x))
0.1b
(* (* (* x x) x) 1/6)
17.8b
(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
154×pow1
75×pow-prod-up
39×pow-plus add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
19×pow2 pow-sqr
9×add-log-exp
7×add-sqr-sqrt associate-*r*
6×*-un-lft-identity add-cube-cbrt
5×pow3
4×insert-posit16
3×diff-log associate-*l* *-commutative
2×sub-neg associate--r+
1×flip3-- flip-- associate--r- unswap-sqr
Counts
4 → 133
Calls
4 calls:
27.0ms
(* (* x x) x)
53.0ms
(* (* x x) (* (* x x) x))
54.0ms
(* (* (* x x) x) 1/6)
244.0ms
(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

series250.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* x x) x)
61.0ms
(* (* x x) (* (* x x) x))
48.0ms
(* (* (* x x) x) 1/6)
82.0ms
(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

simplify2.6s

Counts
145 → 145
Iterations
IterNodes
34849
21058
1351
0128

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
0.1b
(* (* x x) x)
0.1b
(/ -1/8 (* (* x x) x))
11.9b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
24×pow1
19×add-exp-log
18×add-cbrt-cube
13×add-log-exp
12×distribute-lft-out
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod sum-log pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+
1×+-commutative associate-+r+ clear-num associate-/r* frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Counts
4 → 89
Calls
4 calls:
625.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
28.0ms
(* (* x x) x)
27.0ms
(/ -1/8 (* (* x x) x))
386.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
38.0ms
(* (* x x) x)
40.0ms
(/ -1/8 (* (* x x) x))
116.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))

simplify3.7s

Counts
101 → 101
Iterations
IterNodes
36923
21246
1371
0155

prune689.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* (* x x) x))
0.1b
(/ 1/8 (* (* x x) x))
13.9b
(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
20.6b
(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite544.0ms

Algorithm
rewrite-expression-head
Rules
127×pow1
69×pow-prod-up
35×add-exp-log
34×add-cbrt-cube
33×pow-plus
18×prod-exp cbrt-unprod
17×pow2 *-un-lft-identity pow-sqr
15×pow-prod-down
9×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
6×frac-add
5×log-div log-prod
4×pow3 insert-posit16 distribute-lft-out
3×cbrt-undiv times-frac div-exp associate-/l*
2×associate-+l+ sum-log flip3-+ flip3-- frac-sub flip-+ flip-- distribute-lft-out--
1×+-commutative clear-num associate-/r* sub-neg frac-2neg diff-log rem-log-exp associate-*r* associate-*l* log-pow *-commutative associate-+l- div-inv
Counts
4 → 130
Calls
4 calls:
78.0ms
(* (* x x) (* (* x x) x))
13.0ms
(/ 1/8 (* (* x x) x))
183.0ms
(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
264.0ms
(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* x x) (* (* x x) x))
55.0ms
(/ 1/8 (* (* x x) x))
161.0ms
(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
87.0ms
(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify751.0ms

Counts
142 → 142
Iterations
IterNodes
22086
1579
0211

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.7b

bsearch168.0ms

Steps
ItersRangePoint
10
3.724243043503383e-05
335086.0623706297
0.9626554548619399
9
-1352.1675980196485
-0.00125944232679287
-1.0507751989105836

simplify12.0ms

Iterations
IterNodes
239
139
031

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.3s2389×body1280valid
801.0ms1509×body640valid
493.0ms823×body2560valid
265.0ms804×body320valid
196.0ms2089×body80valid
119.0ms386×body160valid