Details

Time bar (total: 6.1s)

sample98.0ms

Algorithm
intervals
Results
27.0ms61×body10240exit
18.0ms44×body1280valid
17.0ms321×body80valid
14.0ms58×body640valid
4.0ms26×body320valid
1.0ms11×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(exp (* (+ 1.0 eps) x))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.7b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite166.0ms

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 div-exp clear-num flip--
1×sub-neg exp-prod distribute-rgt-out-- flip3-+ diff-log sum-log frac-sub flip-+ rem-exp-log sub-div associate--r-
Counts
4 → 127
Calls
4 calls:
11.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
3.0ms
(exp (* (+ 1.0 eps) x))
10.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
136.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series283.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
18.0ms
(exp (* (+ 1.0 eps) x))
45.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
177.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
06161951
118471845
250011835

prune425.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
6.0ms
(* 0.33333333333333337 (pow x 3))
7.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.33333333333333337 (pow x 3))
42.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune117.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

6.8b
(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
45.6b
(cbrt (* 0.33333333333333337 (pow x 3)))
45.6b
(cbrt (* 0.33333333333333337 (pow x 3)))
45.6b
(cbrt (* 0.33333333333333337 (pow x 3)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cbrt-prod pow1/3
2×diff-log
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
4 → 41
Calls
4 calls:
15.0ms
(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
3.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))
3.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))
3.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))

series183.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
36.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))
41.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))
36.0ms
(cbrt (* 0.33333333333333337 (pow x 3)))

simplify73.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0133470
1483391
22177346
35001327

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

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)
10.2b
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
10.9b
(/ (- (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)))) (* 0.5 (* 0.5 (pow x 4)))))

rewrite64.0ms

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:
6.0ms
(* 0.33333333333333337 (pow x 3))
5.0ms
(pow (* 0.5 (pow x 2)) 3)
13.0ms
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
33.0ms
(/ (- (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)))) (* 0.5 (* 0.5 (pow x 4)))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* 0.33333333333333337 (pow x 3))
53.0ms
(pow (* 0.5 (pow x 2)) 3)
96.0ms
(- (pow (+ (* 0.33333333333333337 (pow x 3)) 1.0) 3) (pow (* 0.5 (pow x 2)) 3))
151.0ms
(/ (- (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)))) (* 0.5 (* 0.5 (pow x 4)))))

simplify118.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06313439
129333295
250013294

prune610.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes118.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.4b

bsearch156.0ms

Steps
ItersRangePoint
9
1.5006309519768893e-05
674.2754902356271
1.2315305524276785

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07068
17268
27268

end0.0ms

sample2.8s

Algorithm
intervals
Results
775.0ms1932×body10240exit
753.0ms1769×body1280valid
531.0ms9961×body80valid
312.0ms1255×body640valid
106.0ms602×body320valid
34.0ms328×body160valid