Details

Time bar (total: 14.7s)

sample100.0ms

Algorithm
intervals
Results
26.0ms61×body10240exit
23.0ms57×body1280valid
16.0ms306×body80valid
11.0ms41×body640valid
3.0ms16×body320valid
1.0ms12×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
01929
14629
212229
333527
493327
5408427
done500027

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize18.0ms

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

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac diff-log distribute-lft-out--
Counts
4 → 172
Calls
4 calls:
20.0ms
(* (+ 1.0 eps) x)
51.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
67.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (+ 1.0 eps) x)
49.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
55.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
203.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.8s

Counts
184 → 184
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03948261
110197509
239186957
done50006943

prune434.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
6.0b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite72.0ms

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:
13.0ms
(* 0.6666666666666667 (pow x 3))
58.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify2.2s

Counts
51 → 51
Iterations

Useful iterations: 3 (580.0ms)

IterNodesCost
084590
1206548
2676498
33807462
done5000462

prune110.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (* x x) (- (* 0.6666666666666667 x) 1.0))
0.0b
(pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3)
3.1b
(cbrt (pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×cube-div
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×distribute-rgt-in cube-mult sub-neg cbrt-div distribute-lft-in flip3-+ unpow3 associate-*r/ flip-+ sqr-pow
1×pow-to-exp flip3-- pow-pow pow1/3 associate-*l* pow-exp *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
3 → 73
Calls
3 calls:
40.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))
10.0ms
(pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3)
7.0ms
(cbrt (pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3))

series192.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(* (* x x) (- (* 0.6666666666666667 x) 1.0))
64.0ms
(pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3)
45.0ms
(cbrt (pow (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))) 3))

simplify678.0ms

Counts
82 → 82
Iterations

Useful iterations: done (672.0ms)

IterNodesCost
01391629
13631397
212461231
done50011229

prune156.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* x x) (- (* x 8.0) 12.0))
9.3b
(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
5×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity
3×cbrt-prod associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg cbrt-div distribute-lft-in associate-*r/ add-log-exp
1×flip3-- flip3-+ pow1/3 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
2 → 38
Calls
2 calls:
40.0ms
(* (* x x) (- (* x 8.0) 12.0))
3.0ms
(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

series231.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(* (* x x) (- (* x 8.0) 12.0))
150.0ms
(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

simplify2.7s

Counts
44 → 44
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0134833
1335774
21141713
34631666
done5001642

prune91.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes54.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.6b

bsearch141.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
178.4372176880553

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03151
14451
25051
done5051

end0.0ms

sample2.9s

Algorithm
intervals
Results
774.0ms1953×body10240exit
711.0ms1697×body1280valid
536.0ms9940×body80valid
308.0ms1285×body640valid
102.0ms646×body320valid
34.0ms333×body160valid