Details

Time bar (total: 7.5s)

sample107.0ms

Algorithm
intervals
Results
27.0ms60×body10240exit
27.0ms59×body1280valid
17.0ms322×body80valid
10.0ms42×body640valid
3.0ms21×body320valid
1.0ms13×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* (- 1.0 eps) x))
0.3b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.3b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.9b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite396.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
106×times-frac
90×add-sqr-sqrt
34×add-cube-cbrt
26×distribute-lft-out--
17×difference-of-squares
10×distribute-lft-out associate-/l* add-log-exp
8×add-cbrt-cube
6×add-exp-log associate-/r*
4×pow1 div-inv associate-/l/
3×div-sub
2×cbrt-undiv flip3-- exp-to-pow frac-2neg diff-log div-exp clear-num flip--
1×sub-neg exp-prod distribute-rgt-out-- flip3-+ frac-sub flip-+ rem-exp-log sub-div associate--r-
Counts
4 → 127
Calls
4 calls:
8.0ms
(exp (* (- 1.0 eps) x))
39.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
44.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
297.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series315.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(exp (* (- 1.0 eps) x))
44.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
48.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
197.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
06171951
118601845
250011835

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
4.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp unswap-sqr
7×add-cbrt-cube
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×cube-mult sub-neg flip3-- unpow3 associate--l+ sum-log flip--
Counts
3 → 72
Calls
3 calls:
12.0ms
(* 0.5 (pow x 2))
12.0ms
(* 0.33333333333333337 (pow x 3))
56.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(* 0.5 (pow x 2))
42.0ms
(* 0.33333333333333337 (pow x 3))
41.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0281367
11210327
25001314

prune169.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.1b
(pow (* 0.5 (pow x 2)) 3)
8.2b
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
9.0b
(/ (- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

rewrite412.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
40×difference-of-squares
39×times-frac
37×*-un-lft-identity
33×sqr-pow
27×add-cube-cbrt
17×add-exp-log
15×unpow-prod-down cube-prod
13×associate-/l*
12×associate-*r*
11×add-cbrt-cube
6×pow-exp prod-exp add-log-exp
5×pow1 difference-cubes distribute-lft-out--
4×unswap-sqr
3×pow-to-exp pow-unpow associate-*l* associate-/r*
2×cube-mult flip3-- unpow3 associate-/r/ flip-- cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-undiv sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp clear-num *-commutative flip-+ div-inv
Counts
4 → 148
Calls
4 calls:
12.0ms
(* 0.33333333333333337 (pow x 3))
7.0ms
(pow (* 0.5 (pow x 2)) 3)
108.0ms
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
279.0ms
(/ (- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

series351.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* 0.33333333333333337 (pow x 3))
56.0ms
(pow (* 0.5 (pow x 2)) 3)
104.0ms
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
154.0ms
(/ (- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

simplify119.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06323439
129443295
250023293

prune615.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.20833333333333337 (pow x 6))
0.1b
(* 0.33333333333333337 (pow x 3))
0.1b
(* 0.33333333333333337 (pow x 3))
10.0b
(/ (+ (* 0.20833333333333337 (pow x 6)) (+ (* 1.0 (pow x 3)) 1.0)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×associate-*r*
23×add-cube-cbrt *-un-lft-identity
21×add-exp-log
12×unpow-prod-down add-cbrt-cube
11×unswap-sqr
9×times-frac associate-*l* prod-exp
8×cube-prod
6×sqr-pow
4×pow1 add-log-exp
3×pow-to-exp pow-exp associate-/r* *-commutative cbrt-unprod associate-/l*
2×cube-mult flip3-+ unpow3 associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
11.0ms
(* 0.20833333333333337 (pow x 6))
12.0ms
(* 0.33333333333333337 (pow x 3))
12.0ms
(* 0.33333333333333337 (pow x 3))
148.0ms
(/ (+ (* 0.20833333333333337 (pow x 6)) (+ (* 1.0 (pow x 3)) 1.0)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* 0.20833333333333337 (pow x 6))
43.0ms
(* 0.33333333333333337 (pow x 3))
37.0ms
(* 0.33333333333333337 (pow x 3))
140.0ms
(/ (+ (* 0.20833333333333337 (pow x 6)) (+ (* 1.0 (pow x 3)) 1.0)) (+ (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))) (* (pow x 4) (* 0.5 0.5))))

simplify78.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04651377
123701252
250031248

prune604.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes88.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.3b

bsearch150.0ms

Steps
ItersRangePoint
10
3.2716599026957865e-16
2.5556453819330236
2.1946778170758936

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample2.9s

Algorithm
intervals
Results
733.0ms1868×body10240exit
722.0ms1722×body1280valid
536.0ms9981×body80valid
314.0ms1282×body640valid
102.0ms636×body320valid
33.0ms324×body160valid