Details

Time bar (total: 16.8s)

sample107.0ms

Algorithm
intervals
Results
28.0ms71×body10240exit
27.0ms54×body1280valid
19.0ms340×body80valid
11.0ms45×body640valid
3.0ms18×body320valid
1.0ms6×body160valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
01929
14629
212229
330527
4102527
5425027
done500027

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
53×*-un-lft-identity
34×times-frac
19×add-cube-cbrt
13×difference-of-squares
12×distribute-lft-out--
10×add-cbrt-cube
9×add-exp-log associate-*l*
8×pow1
6×associate-*r* associate-/l* add-log-exp
4×associate-*l/
3×flip3-- associate-/r* flip-- distribute-lft-out
2×div-sub pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv associate--r-
Counts
4 → 108
Calls
4 calls:
28.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
12.0ms
(* (+ 1.0 eps) x)
11.0ms
(* (- 1.0 eps) x)
119.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
31.0ms
(* (+ 1.0 eps) x)
28.0ms
(* (- 1.0 eps) x)
182.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify956.0ms

Counts
120 → 120
Iterations

Useful iterations: done (952.0ms)

IterNodesCost
02262346
15312253
214732108
done50022077

prune350.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))
0.0b
(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×distribute-rgt-in add-sqr-sqrt sub-neg associate-+r+ distribute-lft-in add-log-exp
3×add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×+-commutative flip3-- flip3-+ associate-*l* sum-log *-commutative flip-- flip-+ unswap-sqr
Counts
2 → 40
Calls
2 calls:
3.0ms
(+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))
17.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

series115.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))
77.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify3.0s

Counts
46 → 46
Iterations

Useful iterations: 2 (132.0ms)

IterNodesCost
081659
1232599
2882535
34628535
done5000535

prune87.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
53×*-un-lft-identity
34×times-frac
19×add-cube-cbrt
13×difference-of-squares
12×distribute-lft-out--
10×add-cbrt-cube
9×add-exp-log associate-*l*
8×pow1
6×associate-*r* associate-/l* add-log-exp
4×associate-*l/
3×flip3-- associate-/r* flip-- distribute-lft-out
2×div-sub pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv associate--r-
Counts
4 → 108
Calls
4 calls:
11.0ms
(* (+ 1.0 eps) x)
29.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms
(* (- 1.0 eps) x)
123.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ 1.0 eps) x)
48.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
29.0ms
(* (- 1.0 eps) x)
180.0ms
(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify778.0ms

Counts
120 → 120
Iterations

Useful iterations: done (773.0ms)

IterNodesCost
02262346
15312253
214732108
done50002077

prune413.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))) (+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))))
6.4b
(+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))
6.4b
(/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))
25.3b
(- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x)))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
175×*-un-lft-identity
109×times-frac
49×distribute-lft-out
41×add-sqr-sqrt
21×add-cube-cbrt
20×difference-of-squares
14×distribute-lft-out--
13×associate-/l/
11×associate-/r* add-cbrt-cube
9×add-exp-log
8×flip3-- flip-- add-log-exp
6×frac-times frac-sub associate-/l*
4×pow1 associate-*r/ associate-*l/
3×cbrt-undiv div-exp associate-/r/
2×frac-2neg flip3-+ div-sub frac-add clear-num flip-+ div-inv
1×+-commutative associate-+r- sub-neg diff-log prod-exp sum-log cbrt-unprod
Counts
4 → 138
Calls
4 calls:
230.0ms
(/ (- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))) (+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))))
101.0ms
(+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))
40.0ms
(/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))
28.0ms
(- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ (- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))) (+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))))
116.0ms
(+ (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))
51.0ms
(/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x))))
373.0ms
(- (* (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))) (/ (* (- (/ 1.0 eps) 1.0) (- (/ 1.0 eps) 1.0)) (exp (* 2 (* (+ 1.0 eps) x)))))

simplify1.7s

Counts
150 → 150
Iterations

Useful iterations: 2 (857.0ms)

IterNodesCost
041312363
1122311806
2478110559
done500010559

prune680.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes75.0ms

Accuracy

96.8% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 17.1b

bsearch161.0ms

Steps
ItersRangePoint
11
1.114667387229191e-09
9.89138814869029e+18
249.63027630533077

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02946
13646
done3646

end0.0ms

sample2.8s

Algorithm
intervals
Results
785.0ms1901×body10240exit
727.0ms1686×body1280valid
555.0ms10100×body80valid
322.0ms1279×body640valid
101.0ms610×body320valid
32.0ms296×body160valid