Details

Time bar (total: 18.1s)

sample208.0ms

Algorithm
intervals
Results
84.0ms72×body10240exit
37.0ms52×body1280valid
33.0ms312×body80valid
13.0ms30×body640valid
5.0ms17×body320valid
4.0ms19×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
01929
14629
212229
337727
4226727
done500027

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(exp (* (- 1.0 eps) x))
0.0b
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
2.9b
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
56×add-sqr-sqrt
46×times-frac
24×add-cube-cbrt
12×difference-of-squares
11×distribute-lft-out--
10×associate-/l* add-log-exp
8×add-cbrt-cube
6×add-exp-log associate-/r* distribute-lft-out
4×pow1 associate-/l/
2×cbrt-undiv flip3-- exp-to-pow frac-2neg diff-log div-sub div-exp clear-num flip-- div-inv
1×sub-neg exp-prod flip3-+ frac-sub flip-+ rem-exp-log associate--r-
Counts
4 → 109
Calls
4 calls:
76.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
16.0ms
(exp (* (- 1.0 eps) x))
90.0ms
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
326.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series403.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
35.0ms
(exp (* (- 1.0 eps) x))
57.0ms
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
232.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.3s

Counts
121 → 121
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02172790
15352663
222602529
done50012524

prune431.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.2b
(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 2.0)
6.4b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×associate-*r*
10×add-exp-log
9×times-frac
8×add-log-exp
7×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 associate-*l* prod-exp associate-/r* associate-/l*
2×flip3-- diff-log flip-- associate-/l/ sqr-pow
1×cbrt-undiv cube-mult pow-to-exp sub-neg frac-2neg unpow3 div-sub div-exp pow-exp associate--l+ clear-num sum-log *-commutative cbrt-unprod div-inv
Counts
3 → 75
Calls
3 calls:
18.0ms
(* 0.6666666666666667 (pow x 3))
137.0ms
(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 2.0)
75.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* 0.6666666666666667 (pow x 3))
70.0ms
(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 2.0)
45.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify998.0ms

Counts
84 → 84
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
01341370
13391313
214001205
done50021203

prune279.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.2b
(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))) 2.0)
6.4b
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×associate-*r*
10×add-exp-log
9×times-frac
8×add-log-exp
7×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 associate-*l* prod-exp associate-/r* associate-/l*
2×associate-+r- associate-+r+ flip3-+ sum-log flip-+ associate-/l/ sqr-pow
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num *-commutative cbrt-unprod div-inv
Counts
3 → 76
Calls
3 calls:
28.0ms
(* 0.6666666666666667 (pow x 3))
76.0ms
(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))) 2.0)
18.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series214.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(* 0.6666666666666667 (pow x 3))
77.0ms
(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))) 2.0)
72.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify776.0ms

Counts
85 → 85
Iterations

Useful iterations: done (773.0ms)

IterNodesCost
01331372
13201293
212861195
done50011193

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

6.4b
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
6.4b
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
8.0b
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))
8.0b
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log associate-+r+ flip3-+ sqrt-div sum-log add-cbrt-cube flip-+
2×+-commutative associate-+r- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 60
Calls
4 calls:
26.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
34.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
35.0ms
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))
33.0ms
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
73.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
87.0ms
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))
79.0ms
(sqrt (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))

simplify654.0ms

Counts
72 → 72
Iterations

Useful iterations: done (650.0ms)

IterNodesCost
0721446
11811332
27291216
done50001100

prune462.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes147.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.2b against oracle of 0.5b and baseline of 17.1b

bsearch238.0ms

Steps
ItersRangePoint
9
6.998697613329711e-05
1051.5641664341613
48.83361325535265

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03375
14175
done4175

end0.0ms

sample8.8s

Algorithm
intervals
Results
2.7s1923×body10240exit
2.1s1680×body1280valid
1.9s9821×body80valid
780.0ms1253×body640valid
678.0ms637×body320valid
71.0ms328×body160valid