Details

Time bar (total: 18.9s)

sample218.0ms

Algorithm
intervals
Results
76.0ms313×body80valid
47.0ms63×body10240exit
42.0ms51×body1280valid
19.0ms44×body640valid
8.0ms25×body320valid
2.0ms8×body160valid

simplify867.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize44.0ms

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:
20.0ms
(* (+ 1.0 eps) x)
7.0ms
(exp (- (* (- 1.0 eps) x)))
71.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
61.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (+ 1.0 eps) x)
37.0ms
(exp (- (* (- 1.0 eps) x)))
73.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
289.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify541.0ms

Counts
173 → 173
Iterations
IterNodes
done5000
11245
0392

prune924.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
5.4b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* (* 1.0 x) x))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×*-un-lft-identity add-cube-cbrt
4×unpow-prod-down add-cbrt-cube cube-prod unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sum-log sub-neg flip3-- unpow3 pow-exp associate--l+ *-commutative cbrt-unprod flip--
Counts
2 → 45
Calls
2 calls:
10.0ms
(* 0.6666666666666667 (pow x 3))
63.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* (* 1.0 x) x))

series143.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(* 0.6666666666666667 (pow x 3))
69.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* (* 1.0 x) x))

simplify610.0ms

Counts
51 → 51
Iterations
IterNodes
done5000
21020
1232
087

prune234.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow x 3) 0.6666666666666667)
0.4b
(exp (log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0)))))
5.4b
(- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))
8.8b
(log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
12×associate-*l*
11×add-cube-cbrt
10×add-exp-log
8×log-prod
6×pow1 add-cbrt-cube add-log-exp
4×log-div exp-prod unpow-prod-down cube-prod exp-sum unswap-sqr
3×associate-*r* prod-exp
2×flip3-+ exp-diff log-pow flip-+ distribute-lft-out sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 rem-log-exp pow-exp *-commutative cbrt-unprod flip-- rem-exp-log
Counts
4 → 76
Calls
4 calls:
10.0ms
(* (pow x 3) 0.6666666666666667)
13.0ms
(exp (log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0)))))
10.0ms
(- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))
30.0ms
(log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))))

series403.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (pow x 3) 0.6666666666666667)
58.0ms
(exp (log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0)))))
175.0ms
(- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))
127.0ms
(log (+ 2.0 (- (* (pow x 3) 0.6666666666666667) (* (* x x) 1.0))))

simplify977.0ms

Counts
88 → 88
Iterations
IterNodes
done5000
21724
1368
0159

prune500.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
26×associate-*l/
23×add-sqr-sqrt
18×frac-sub
16×*-un-lft-identity
13×associate-*l*
12×exp-neg frac-times
11×flip3-- associate-*r* flip--
10×pow1 flip3-+ add-cbrt-cube add-cube-cbrt flip-+
9×neg-sub0 exp-diff add-exp-log
8×associate-*r/
6×add-log-exp
3×sub-neg pow-prod-down prod-exp un-div-inv *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-rgt-in distribute-lft-in distribute-lft-out--
1×times-frac diff-log distribute-lft-out
Counts
4 → 107
Calls
4 calls:
24.0ms
(* x (- eps 1.0))
16.0ms
(* (+ 1.0 eps) x)
102.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
73.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (* x (- eps 1.0)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* x (- eps 1.0))
31.0ms
(* (+ 1.0 eps) x)
87.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
437.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (* x (- eps 1.0)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.9s

Counts
119 → 119
Iterations
IterNodes
done5001
24112
1745
0261

prune702.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes167.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch216.0ms

Steps
ItersRangePoint
8
7.830610238325062
15275.506209221001
83.34029148131637

simplify6.0ms

Iterations
IterNodes
done51
251
145
032

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.1s1964×body10240exit
2.5s10200×body80valid
1.7s1723×body1280valid
724.0ms1223×body640valid
270.0ms607×body320valid
73.0ms333×body160valid