Details

Time bar (total: 25.2s)

sample209.0ms

Algorithm
intervals
Results
62.0ms56×body10240exit
49.0ms56×body1280valid
42.0ms335×body80valid
13.0ms25×body640valid
7.0ms19×body320valid
3.0ms13×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5005
41357
3352
2122
146
019

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cbrt-cube add-cube-cbrt
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 173
Calls
4 calls:
35.0ms
(* (- 1.0 eps) x)
86.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
88.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
79.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (- 1.0 eps) x)
87.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
87.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
282.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.0s

Counts
185 → 185
Iterations
IterNodes
done5001
24373
11224
0399

prune976.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* 0.6666666666666667 x) (* x x))
8.8b
(+ (- 2.0 (* (* x x) 1.0)) (* (* 0.6666666666666667 x) (* x x)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-cbrt-cube add-exp-log
8×pow-prod-down prod-exp cbrt-unprod
7×add-log-exp
2×add-sqr-sqrt associate-+l+ sum-log *-un-lft-identity add-cube-cbrt
1×+-commutative sub-neg flip3-+ diff-log associate-*r* associate-*l* *-commutative associate-+l- flip-+
Counts
2 → 37
Calls
2 calls:
42.0ms
(* (* 0.6666666666666667 x) (* x x))
46.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* (* 0.6666666666666667 x) (* x x)))

series88.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(* (* 0.6666666666666667 x) (* x x))
47.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* (* 0.6666666666666667 x) (* x x)))

simplify1.7s

Counts
43 → 43
Iterations
IterNodes
done5000
2795
1210
075

prune196.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg *-un-lft-identity distribute-lft-in associate-*r/ add-cube-cbrt
1×flip3-- associate-*l* *-commutative flip-- add-log-exp unswap-sqr
Counts
1 → 25
Calls
1 calls:
60.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))

series139.0ms

Counts
1 → 3
Calls
1 calls:
138.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))

simplify2.6s

Counts
28 → 28
Iterations
IterNodes
done5001
32799
2629
1172
057

prune112.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- eps 1.0))
0.0b
(/ (exp (* x (- eps 1.0))) eps)
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
4.4b
(- (* 1.0 (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×associate-*r/
24×*-un-lft-identity
22×times-frac
20×add-cube-cbrt
18×frac-sub
16×exp-sum
12×exp-neg frac-times
11×distribute-rgt-in sub-neg distribute-lft-in flip3-- flip--
10×add-cbrt-cube
9×neg-sub0 flip3-+ exp-diff associate-*l* flip-+
8×pow1 associate-*r* add-exp-log
7×associate-/l*
6×associate-*l/ add-log-exp
3×associate-/r* un-div-inv difference-of-squares
2×pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv clear-num frac-2neg diff-log div-exp div-inv
Counts
4 → 131
Calls
4 calls:
17.0ms
(* x (- eps 1.0))
21.0ms
(/ (exp (* x (- eps 1.0))) eps)
83.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
66.0ms
(- (* 1.0 (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* x (- eps 1.0))
38.0ms
(/ (exp (* x (- eps 1.0))) eps)
77.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
234.0ms
(- (* 1.0 (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.0s

Counts
143 → 143
Iterations
IterNodes
done5006
23110
1820
0308

prune947.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes89.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch264.0ms

Steps
ItersRangePoint
11
2.0412262699081644e-18
848.2985553752982
121.48694228142615

simplify9.0ms

Iterations
IterNodes
done48
248
142
029

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.4s1887×body10240exit
2.1s1792×body1280valid
1.5s10003×body80valid
738.0ms1206×body640valid
264.0ms622×body320valid
71.0ms338×body160valid