Details

Time bar (total: 26.6s)

sample178.0ms

Algorithm
intervals
Results
44.0ms335×body80valid
43.0ms56×body10240exit
42.0ms56×body1280valid
11.0ms25×body640valid
6.0ms19×body320valid
3.0ms13×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize61.0ms

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)))))

rewrite276.0ms

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:
34.0ms
(* (- 1.0 eps) x)
51.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
108.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
65.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (- 1.0 eps) x)
72.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
55.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
296.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.7s

Counts
185 → 185
Iterations
IterNodes
done5000
11274
0399

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
17×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
6×add-sqr-sqrt pow-plus pow-prod-up
5×*-un-lft-identity add-cube-cbrt
4×associate-*r* associate-*l*
2×pow2 associate-+r+ sum-log pow-sqr *-commutative
1×+-commutative associate-+r- sub-neg flip3-+ diff-log pow3 flip-+ unswap-sqr
Counts
3 → 64
Calls
3 calls:
43.0ms
(* 0.6666666666666667 (* (* x x) x))
25.0ms
(* (* x x) x)
60.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* (* 1.0 x) x)))

series181.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(* 0.6666666666666667 (* (* x x) x))
47.0ms
(* (* x x) x)
73.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* (* 1.0 x) x)))

simplify1.4s

Counts
73 → 73
Iterations
IterNodes
done5000
21672
1262
090

prune280.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

4.0b
(cbrt (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))))))
8.8b
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
8.8b
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
8.8b
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times
26×cbrt-div
19×add-log-exp
14×associate-*r/
8×associate-*l/
6×diff-log
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log sub-neg associate--l+
1×cbrt-prod pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 78
Calls
4 calls:
2.0s
(cbrt (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))))))
343.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
411.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
352.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(cbrt (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (* (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))) (- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x))))))
60.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
53.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))
51.0ms
(- (+ (* 0.6666666666666667 (* x (* x x))) 2.0) (* 1.0 (* x x)))

simplify2.3s

Counts
90 → 90
Iterations
IterNodes
done5001
21929
1339
0140

prune668.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize51.0ms

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)))))

rewrite262.0ms

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:
21.0ms
(* x (- eps 1.0))
13.0ms
(/ (exp (* x (- eps 1.0))) eps)
110.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
107.0ms
(- (* 1.0 (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series436.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* x (- eps 1.0))
34.0ms
(/ (exp (* x (- eps 1.0))) eps)
96.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
268.0ms
(- (* 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
done5000
24250
1828
0308

prune957.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes168.0ms

Accuracy

96.1% (0.6b remaining)

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

bsearch340.0ms

Steps
ItersRangePoint
11
2.0412262699081644e-18
848.2985553752982
121.48694228142615

simplify12.0ms

Iterations
IterNodes
done52
252
146
031

end0.0ms

sample7.5s

Algorithm
intervals
Results
2.4s1887×body10240exit
1.8s10003×body80valid
1.5s1792×body1280valid
1.2s1206×body640valid
239.0ms622×body320valid
64.0ms338×body160valid