Details

Time bar (total: 7.0s)

sample126.0ms

Algorithm
intervals
Results
36.0ms349×body80valid
28.0ms55×body1280valid
27.0ms46×body10240exit
13.0ms38×body640valid
4.0ms19×body320valid
0.0ms2×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: 26.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 eps) 1.0)
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
1.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
120×*-un-lft-identity
107×times-frac
95×add-sqr-sqrt
34×add-cube-cbrt
27×distribute-lft-out--
19×difference-of-squares
10×distribute-lft-out associate-/l*
8×add-cbrt-cube add-log-exp
6×add-exp-log associate-/r*
4×pow1 div-inv associate-/l/
3×flip3-- div-sub flip--
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num
1×distribute-rgt-out-- flip3-+ frac-sub flip-+ sub-div associate--r-
Counts
4 → 131
Calls
4 calls:
11.0ms
(- (/ 1.0 eps) 1.0)
27.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
22.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
239.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series302.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (/ 1.0 eps) 1.0)
42.0ms
(/ (- (/ 1.0 eps) 1.0) (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))

simplify57.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
06311985
119231876
250011875

prune560.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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)))

rewrite35.0ms

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:
7.0ms
(* 0.33333333333333337 (pow x 3))
27.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series75.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.33333333333333337 (pow x 3))
40.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify36.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0207270
1894242
25002238

prune112.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
4.7b
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.8b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.8b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div diff-log add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ sum-log
Counts
4 → 58
Calls
4 calls:
24.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
23.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
27.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
29.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series183.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
52.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
39.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
37.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify104.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0171688
1611636
23106618
35003616

prune213.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
24×add-log-exp
8×diff-log
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity associate--l+ sum-log add-cbrt-cube flip--
Counts
4 → 56
Calls
4 calls:
29.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
27.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
27.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
30.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
38.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
41.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
39.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify91.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0105620
1424564
22319536
35002536

prune241.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes167.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch174.0ms

Steps
ItersRangePoint
9
0.08251057621007524
71346.30170445908
1.7024416718643414

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04335
14335

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s10117×body80valid
898.0ms1815×body10240exit
875.0ms1738×body1280valid
411.0ms1267×body640valid
152.0ms644×body320valid
53.0ms331×body160valid