Details

Time bar (total: 6.7s)

sample96.0ms

Algorithm
intervals
Results
23.0ms52×body1280valid
23.0ms59×body10240exit
17.0ms320×body80valid
11.0ms34×body640valid
3.0ms20×body320valid
1.0ms9×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 26.9b

Counts
2 → 1

localize17.0ms

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 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.1b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
130×associate-/l/
81×frac-sub
40×frac-2neg
38×clear-num
22×div-inv
18×associate-/l*
11×flip3-- flip3-+ flip-- flip-+
3×div-sub
2×associate-*l/ sub-div
1×sub-neg distribute-rgt-out-- *-commutative associate--r-
Counts
4 → 103
Calls
4 calls:
6.0ms
(* (+ 1.0 eps) x)
7.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
5.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
18.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series298.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ 1.0 eps) x)
49.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
40.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
182.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
013592968
150012836

prune421.0ms

Filtered
115 candidates to 85 candidates (73.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1114115
Fresh000
Picked101
Done000
Total1124116

Merged error: 0.4b

Counts
116 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
6.8b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-*r*
2×associate--l+ *-commutative sqr-pow
1×+-commutative sub-neg flip3-- unpow3 flip-- unpow2
Counts
3 → 12
Calls
3 calls:
3.0ms
(* 0.5 (pow x 2))
3.0ms
(* 0.33333333333333337 (pow x 3))
6.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series105.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(* 0.5 (pow x 2))
35.0ms
(* 0.33333333333333337 (pow x 3))
42.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify80.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
09894
134593
2178885
3500185

prune48.0ms

Filtered
21 candidates to 12 candidates (57.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New21021
Fresh033
Picked011
Done000
Total21425

Merged error: 0.4b

Counts
25 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (exp (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
2.1b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
172×associate-/l/
99×frac-sub
55×frac-2neg
53×clear-num
35×div-inv
30×associate-/l*
12×flip3-+ flip-+
2×sub-div
1×sub-neg flip3-- distribute-rgt-out-- flip--
Counts
4 → 121
Calls
4 calls:
4.0ms
(/ 1.0 (exp (* (+ 1.0 eps) x)))
5.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
5.0ms
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
19.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

series205.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (exp (* (+ 1.0 eps) x)))
39.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
37.0ms
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
103.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
014813158
150012993

prune428.0ms

Filtered
133 candidates to 91 candidates (68.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1321133
Fresh112
Picked011
Done011
Total1334137

Merged error: 0.4b

Counts
137 → 4

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 eps) (/ 1.0 eps))
0.3b
(pow (/ 1.0 eps) 3)
3.4b
(/ (- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps)))) (* (* (* 2.0 (exp (* x (- 1.0 eps)))) (+ (* (/ 1.0 eps) (- (/ 1.0 eps) 1.0)) (* 1.0 1.0))) (* 2.0 (- (exp (* (+ 1.0 eps) x))))))
23.6b
(- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
81×associate-*r/
57×associate-*l/
44×frac-sub
39×flip3-+ flip-+
36×distribute-neg-frac
33×frac-times
24×associate-/l/
22×clear-num
21×frac-2neg
19×associate-*l*
15×associate-/r*
11×associate-*r*
8×div-inv
6×*-commutative
4×exp-sum
3×sub-neg
2×distribute-rgt-in flip3-- distribute-lft-in associate-/r/ flip-- distribute-lft-out
1×pow2 pow-to-exp neg-mul-1 unpow-prod-down unpow3 div-sub swap-sqr un-div-inv sqr-pow
Counts
4 → 96
Calls
4 calls:
5.0ms
(* (/ 1.0 eps) (/ 1.0 eps))
2.0ms
(pow (/ 1.0 eps) 3)
53.0ms
(/ (- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps)))) (* (* (* 2.0 (exp (* x (- 1.0 eps)))) (+ (* (/ 1.0 eps) (- (/ 1.0 eps) 1.0)) (* 1.0 1.0))) (* 2.0 (- (exp (* (+ 1.0 eps) x))))))
30.0ms
(- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (/ 1.0 eps) (/ 1.0 eps))
46.0ms
(pow (/ 1.0 eps) 3)
235.0ms
(/ (- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps)))) (* (* (* 2.0 (exp (* x (- 1.0 eps)))) (+ (* (/ 1.0 eps) (- (/ 1.0 eps) 1.0)) (* 1.0 1.0))) (* 2.0 (- (exp (* (+ 1.0 eps) x))))))
99.0ms
(- (* (+ (pow 1.0 3) (pow (/ 1.0 eps) 3)) (* 2.0 (- (exp (* (+ 1.0 eps) x))))) (* (* 2.0 (* (exp (* (- 1.0 eps) x)) (+ (* 1.0 1.0) (- (* (/ 1.0 eps) (/ 1.0 eps)) (* 1.0 (/ 1.0 eps)))))) (- (/ 1.0 eps))))

simplify64.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011303623
150023565

prune945.0ms

Filtered
108 candidates to 89 candidates (82.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1062108
Fresh011
Picked101
Done022
Total1075112

Merged error: 0.4b

Counts
112 → 5

regimes244.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch145.0ms

Steps
ItersRangePoint
10
4.278730963433957e-11
13.656696832425032
1.2530678790452556

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample2.8s

Algorithm
intervals
Results
737.0ms1711×body1280valid
736.0ms1843×body10240exit
552.0ms9938×body80valid
327.0ms1274×body640valid
109.0ms636×body320valid
36.0ms324×body160valid