Details

Time bar (total: 39.9s)

sample212.0ms

Algorithm
intervals
Results
57.0ms292×body80valid
44.0ms52×body1280valid
35.0ms45×body10240exit
17.0ms31×body640valid
10.0ms25×body320valid
3.0ms14×body160valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5000
41391
3370
2124
147
019

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
3.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
29×flip3-- flip--
27×flip3-+ flip-+
18×un-div-inv
12×add-sqr-sqrt exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
5×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 163
Calls
4 calls:
53.0ms
(* (- 1.0 eps) x)
10.0ms
(exp (- (* (+ 1.0 eps) x)))
19.0ms
(exp (- (* (- 1.0 eps) x)))
108.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (- 1.0 eps) x)
72.0ms
(exp (- (* (+ 1.0 eps) x)))
57.0ms
(exp (- (* (- 1.0 eps) x)))
377.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify6.3s

Counts
175 → 175
Iterations
IterNodes
done5000
23823
11234
0393

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
6.4b
(fma (* x (* x x)) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
7×add-cbrt-cube add-exp-log
5×pow-prod-up
4×add-sqr-sqrt
3×*-un-lft-identity associate-*l* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative fma-udef unswap-sqr
Counts
2 → 38
Calls
2 calls:
34.0ms
(* x (* x x))
1.0ms
(fma (* x (* x x)) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

series136.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(* x (* x x))
74.0ms
(fma (* x (* x x)) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

simplify3.2s

Counts
44 → 44
Iterations
IterNodes
done5003
31222
2305
1113
060

prune460.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 0.6666666666666667 x) 1.0)
0.0b
(+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0)))
0.0b
(* (* x x) (- (* 0.6666666666666667 x) 1.0))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
15×prod-diff
11×add-sqr-sqrt
10×distribute-rgt-in associate-+r+ *-un-lft-identity distribute-lft-in add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
7×add-log-exp
5×sub-neg
3×expm1-log1p-u fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×flip3-- associate-*r/ flip--
1×+-commutative sum-log flip3-+ fma-neg diff-log associate-*l* *-commutative flip-+ unswap-sqr
Counts
3 → 80
Calls
3 calls:
11.0ms
(- (* 0.6666666666666667 x) 1.0)
13.0ms
(+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0)))
90.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))

series317.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(- (* 0.6666666666666667 x) 1.0)
85.0ms
(+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0)))
150.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))

simplify3.1s

Counts
89 → 89
Iterations
IterNodes
done5001
21275
1389
0133

prune854.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize88.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 2.0 (* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))))
0.0b
(- (* 0.6666666666666667 x) 1.0)
0.0b
(* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0))))
15.0b
(posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* prod-diff pow-prod-down prod-exp cbrt-unprod
1×+-commutative sum-log sub-neg flip3-+ flip3-- fma-neg diff-log associate-*l* *-commutative flip-+ remove-posit16 flip-- unswap-sqr
Counts
4 → 69
Calls
4 calls:
17.0ms
(+ 2.0 (* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))))
22.0ms
(- (* 0.6666666666666667 x) 1.0)
48.0ms
(* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0))))
2.0ms
(posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ 2.0 (* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))))
71.0ms
(- (* 0.6666666666666667 x) 1.0)
143.0ms
(* (* x x) (posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0))))
80.0ms
(posit16->real (real->posit16 (- (* 0.6666666666666667 x) 1.0)))

simplify8.0s

Counts
81 → 81
Iterations
IterNodes
done5000
34501
21016
1314
0118

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes414.0ms

Accuracy

94.4% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 17.3b

bsearch257.0ms

Steps
ItersRangePoint
8
4.1750260115318935e-11
1.508099977930646e-06
1.4798868095701662e-06

simplify34.0ms

Iterations
IterNodes
done61
261
153
036

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.0s1971×body10240exit
2.2s10203×body80valid
1.5s1717×body1280valid
686.0ms1176×body640valid
339.0ms656×body320valid
56.0ms277×body160valid