Details

Time bar (total: 15.3s)

sample106.0ms

Algorithm
intervals
Results
31.0ms63×body10240exit
21.0ms47×body1280valid
20.0ms338×body80valid
11.0ms39×body640valid
3.0ms16×body320valid
1.0ms12×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
01929
14629
212229
330527
4102227
5421727
done500027

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- 1.0 eps) x)
2.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
73×exp-neg
72×frac-times
55×neg-sub0 exp-diff
40×associate-*l/
36×associate-*r/
29×flip3-- flip--
28×flip3-+ flip-+
18×un-div-inv
15×add-sqr-sqrt
13×*-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
3.0ms
(exp (- (* (+ 1.0 eps) x)))
11.0ms
(* (+ 1.0 eps) x)
9.0ms
(* (- 1.0 eps) x)
25.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (- (* (+ 1.0 eps) x)))
31.0ms
(* (+ 1.0 eps) x)
29.0ms
(* (- 1.0 eps) x)
200.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.2s

Counts
165 → 165
Iterations

Useful iterations: 2 (435.0ms)

IterNodesCost
03777441
111996791
238366308
done50016308

prune391.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
6.8b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
7.0ms
(* 0.6666666666666667 (pow x 3))
25.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(* 0.6666666666666667 (pow x 3))
43.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify2.2s

Counts
51 → 51
Iterations

Useful iterations: 3 (905.0ms)

IterNodesCost
084590
1210548
2693498
34114462
done5000462

prune302.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* (* 0.6666666666666667 x) x) x)
0.1b
(* (* 0.6666666666666667 x) x)
6.8b
(- (+ (* (* (* 0.6666666666666667 x) x) x) 2.0) (* 1.0 (pow x 2)))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-exp-log add-cbrt-cube
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
6×associate-*r*
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
2×diff-log associate-*l* *-commutative
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 53
Calls
3 calls:
20.0ms
(* (* (* 0.6666666666666667 x) x) x)
6.0ms
(* (* 0.6666666666666667 x) x)
182.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) x) 2.0) (* 1.0 (pow x 2)))

series105.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* (* (* 0.6666666666666667 x) x) x)
29.0ms
(* (* 0.6666666666666667 x) x)
40.0ms
(- (+ (* (* (* 0.6666666666666667 x) x) x) 2.0) (* 1.0 (pow x 2)))

simplify2.7s

Counts
62 → 62
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
088766
1246726
21021556
34946550
done5000550

prune138.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(pow (* 1.0 (pow x 2)) 3)
10.8b
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
12.6b
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (+ 2.0 (* 1.0 (pow x 2))) (* 0.6666666666666667 (pow x 3))) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
40×difference-of-squares
39×times-frac
37×*-un-lft-identity
33×sqr-pow
27×add-cube-cbrt
17×add-exp-log
15×unpow-prod-down cube-prod
13×associate-/l*
12×associate-*r*
11×add-cbrt-cube
6×pow-exp prod-exp add-log-exp
5×pow1 difference-cubes distribute-lft-out--
4×unswap-sqr
3×pow-to-exp pow-unpow associate-*l* associate-/r*
2×cube-mult flip3-- unpow3 associate-/r/ flip-- cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-undiv sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp clear-num *-commutative flip-+ div-inv
Counts
4 → 148
Calls
4 calls:
7.0ms
(* 0.6666666666666667 (pow x 3))
3.0ms
(pow (* 1.0 (pow x 2)) 3)
58.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
126.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (+ 2.0 (* 1.0 (pow x 2))) (* 0.6666666666666667 (pow x 3))) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* 0.6666666666666667 (pow x 3))
50.0ms
(pow (* 1.0 (pow x 2)) 3)
96.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
148.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (+ 2.0 (* 1.0 (pow x 2))) (* 0.6666666666666667 (pow x 3))) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

simplify810.0ms

Counts
160 → 160
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
02597131
16426836
222126582
done50006582

prune624.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes155.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 16.7b

bsearch158.0ms

Steps
ItersRangePoint
10
1.1679697638036715e-17
38.74833267440093
33.94148395765872

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
14550
24750
done4750

end0.0ms

sample3.0s

Algorithm
intervals
Results
821.0ms1900×body10240exit
780.0ms1697×body1280valid
599.0ms10134×body80valid
347.0ms1259×body640valid
116.0ms650×body320valid
38.0ms327×body160valid