Details

Time bar (total: 8.1s)

sample154.0ms

Algorithm
intervals
Results
55.0ms328×body80valid
36.0ms51×body1280valid
22.0ms44×body640valid
10.0ms27×body320valid
9.0ms62×body80overflowed
4.0ms14×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(exp (* (+ 1.0 eps) x))
0.0b
(exp (* (- 1.0 eps) x))
2.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
84×times-frac
59×add-sqr-sqrt
23×add-cube-cbrt
22×distribute-lft-out--
14×add-log-exp
10×distribute-lft-out
9×difference-of-squares
6×add-cbrt-cube
5×add-exp-log
4×pow1 exp-to-pow associate-/l*
3×associate-/r* div-inv
2×exp-prod diff-log div-sub rem-exp-log associate-/l/
1×cbrt-undiv sub-neg flip3-- distribute-rgt-out-- frac-2neg flip3-+ div-exp clear-num sum-log frac-sub flip-- flip-+ sub-div associate--r-
Counts
4 → 96
Calls
4 calls:
21.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.0ms
(exp (* (+ 1.0 eps) x))
3.0ms
(exp (* (- 1.0 eps) x))
234.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series262.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
22.0ms
(exp (* (+ 1.0 eps) x))
20.0ms
(exp (* (- 1.0 eps) x))
180.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
04581482
113461407
250011383

prune315.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×associate-*l*
6×add-exp-log
4×add-cube-cbrt unpow-prod-down *-un-lft-identity unswap-sqr
3×associate-*r* prod-exp add-cbrt-cube
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ unpow2 sqr-pow
1×pow1 pow-to-exp flip3-- pow-exp *-commutative flip-- cbrt-unprod add-log-exp
Counts
1 → 33
Calls
1 calls:
14.0ms
(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series80.0ms

Counts
1 → 3
Calls
1 calls:
80.0ms
(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify168.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0158214
1638189
24553189
35001189

prune77.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-- pow1/3 flip--
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
16.0ms
(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

series593.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
139.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
133.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
141.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

simplify51.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04581268
117071161
25001993

prune310.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 4 expressions with local error:

35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
35.0b
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-div associate-*r/
4×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity pow1/3 add-cbrt-cube flip-- add-log-exp
Counts
4 → 44
Calls
4 calls:
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
5.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
136.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
131.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
139.0ms
(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

simplify97.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0239876
1808808
23418664
35002660

prune292.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

regimes89.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.9b

bsearch200.0ms

Steps
ItersRangePoint
9
0.7032085127721847
2014473.2449630217
148.38850205200063

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05060
15060

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.6s9947×body80valid
1.3s1785×body1280valid
627.0ms1233×body640valid
287.0ms1871×body80overflowed
237.0ms631×body320valid
76.0ms293×body160valid