Details

Time bar (total: 21.6s)

sample246.0ms

Algorithm
intervals
Results
93.0ms63×body10240exit
45.0ms51×body1280valid
40.0ms313×body80valid
25.0ms44×body640valid
10.0ms25×body320valid
2.0ms8×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
019664
146664
2122664
3377584
42266584
done5000584

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
77×exp-neg
76×frac-times
58×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
28×flip3-+ flip-+
19×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 161
Calls
4 calls:
31.0ms
(* (+ 1.0 eps) x)
13.0ms
(exp (- (* (- 1.0 eps) x)))
69.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
49.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ 1.0 eps) x)
43.0ms
(exp (- (* (- 1.0 eps) x)))
74.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
293.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.9s

Counts
173 → 173
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0392163247
11245133427
done5000128176

prune944.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.6666666666666667 (* (* x x) x))
0.1b
(* (* x x) x)
5.4b
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* x x) 1.0))

rewrite535.0ms

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 diff-log pow-sqr *-commutative
1×sum-log sub-neg flip3-- pow3 associate--l+ flip-- unswap-sqr
Counts
3 → 63
Calls
3 calls:
71.0ms
(* 0.6666666666666667 (* (* x x) x))
17.0ms
(* (* x x) x)
444.0ms
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* x x) 1.0))

series159.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* 0.6666666666666667 (* (* x x) x))
41.0ms
(* (* x x) x)
61.0ms
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* x x) 1.0))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: 2 (435.0ms)

IterNodesCost
09115375
127312047
2195511300
done500111300

prune280.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.6666666666666667 (* (* x x) x))
0.1b
(* (* x x) x)
5.4b
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* (* x x) 1.0)))

rewrite169.0ms

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:
76.0ms
(* 0.6666666666666667 (* (* x x) x))
29.0ms
(* (* x x) x)
61.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* (* x x) 1.0)))

series172.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(* 0.6666666666666667 (* (* x x) x))
59.0ms
(* (* x x) x)
53.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* (* x x) 1.0)))

simplify1.5s

Counts
73 → 73
Iterations

Useful iterations: 2 (462.0ms)

IterNodesCost
08915497
126412099
2169811422
done500011422

prune240.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (exp (- (* x eps) (* 1.0 x))) eps)
0.0b
(+ (* x eps) (* 1.0 x))
0.0b
(+ (* x eps) (* 1.0 x))
2.0b
(- (+ (exp (- (* x eps) (* 1.0 x))) (/ (exp (- (* x eps) (* 1.0 x))) eps)) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))

rewrite533.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
16×times-frac
14×add-cube-cbrt
13×add-log-exp
8×exp-sum
6×add-cbrt-cube
5×sub-neg add-exp-log associate-/l*
4×pow1
3×associate-/r* sum-log flip3-+ frac-sub flip-+
2×+-commutative exp-diff diff-log distribute-lft-out-- difference-of-squares
1×cbrt-undiv clear-num frac-2neg flip3-- div-exp frac-add associate--l+ div-inv flip-- distribute-lft-out associate-/l/
Counts
4 → 79
Calls
4 calls:
24.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
6.0ms
(+ (* x eps) (* 1.0 x))
6.0ms
(+ (* x eps) (* 1.0 x))
495.0ms
(- (+ (exp (- (* x eps) (* 1.0 x))) (/ (exp (- (* x eps) (* 1.0 x))) eps)) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))

series276.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
48.0ms
(+ (* x eps) (* 1.0 x))
64.0ms
(+ (* x eps) (* 1.0 x))
125.0ms
(- (+ (exp (- (* x eps) (* 1.0 x))) (/ (exp (- (* x eps) (* 1.0 x))) eps)) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))

simplify1.6s

Counts
91 → 91
Iterations

Useful iterations: done (1.6s)

IterNodesCost
015938178
138635917
2135933210
done500032979

prune541.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes90.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
019664
129664
241664
done41664

end0.0ms

sample8.2s

Algorithm
intervals
Results
2.8s1964×body10240exit
2.2s10200×body80valid
1.6s1723×body1280valid
737.0ms1223×body640valid
243.0ms607×body320valid
110.0ms333×body160valid