Details

Time bar (total: 8.3s)

sample99.0ms

Algorithm
intervals
Results
29.0ms63×body10240exit
25.0ms61×body1280valid
16.0ms287×body80valid
9.0ms37×body640valid
3.0ms18×body320valid
2.0ms15×body160valid

simplify537.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
01929
14629
212229
331127
4117227
done500027

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.6b
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
60×add-sqr-sqrt
46×times-frac
26×add-cube-cbrt
12×difference-of-squares
11×distribute-lft-out--
10×add-cbrt-cube associate-/l*
8×add-exp-log
7×distribute-lft-out
6×pow1 associate-/r* add-log-exp
4×associate-*l* associate-/l/
3×associate-*r*
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp associate-*l/ clear-num flip-- flip-+ div-inv
1×sub-neg diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod associate--r- unswap-sqr
Counts
4 → 119
Calls
4 calls:
9.0ms
(* (+ 1.0 eps) x)
26.0ms
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
27.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
115.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ 1.0 eps) x)
40.0ms
(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
47.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
175.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify584.0ms

Counts
131 → 131
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
02452879
15822745
217732586
done50002586

prune381.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite38.0ms

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:
6.0ms
(* 0.6666666666666667 (pow x 3))
30.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 0.6666666666666667 (pow x 3))
38.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify387.0ms

Counts
51 → 51
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
084590
1215548
2843498
done5000498

prune110.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
7.6b
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite15.0ms

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 associate-+r+ sum-log sqr-pow
1×+-commutative cube-mult pow-to-exp associate-+r- sub-neg flip3-+ diff-log unpow3 pow-exp *-commutative cbrt-unprod flip-+
Counts
2 → 46
Calls
2 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series78.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify437.0ms

Counts
52 → 52
Iterations

Useful iterations: done (436.0ms)

IterNodesCost
083592
1211534
2809494
done5000464

prune109.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

5.2b
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
5.2b
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite103.0ms

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 flip3-- sqrt-div diff-log add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ sum-log
Counts
4 → 58
Calls
4 calls:
24.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
22.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
26.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
29.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
54.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
37.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify1.3s

Counts
70 → 70
Iterations

Useful iterations: 3 (224.0ms)

IterNodesCost
0721442
11731336
25851236
329651088
done50011088

prune218.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch127.0ms

Steps
ItersRangePoint
9
0.006616288801049052
22276.40736340321
179.02536135484516

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03046
13746
done3746

end0.0ms

sample3.0s

Algorithm
intervals
Results
967.0ms1921×body10240exit
736.0ms1725×body1280valid
539.0ms9975×body80valid
318.0ms1296×body640valid
98.0ms610×body320valid
31.0ms296×body160valid