Details

Time bar (total: 6.7s)

sample107.0ms

Algorithm
intervals
Results
30.0ms76×body10240exit
27.0ms53×body1280valid
18.0ms324×body80valid
10.0ms41×body640valid
4.0ms23×body320valid
1.0ms9×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
1.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 173
Calls
4 calls:
30.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
44.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms
(* (- 1.0 eps) x)
27.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
55.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
30.0ms
(* (- 1.0 eps) x)
205.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify151.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
012534065
147123787
250013778

prune455.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
7.0b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite38.0ms

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
(* 0.6666666666666667 (pow x 3))
30.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series83.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(* 0.6666666666666667 (pow x 3))
40.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0207270
1894242
25002238

prune115.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
0.1b
(* 0.6666666666666667 (pow x 3))
4.3b
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
7.0b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod associate-*r*
10×add-exp-log unpow-prod-down cube-prod
9×add-log-exp
7×add-cbrt-cube
5×pow1
4×cube-div unswap-sqr sqr-pow
3×cube-mult pow-unpow flip3-- unpow3 associate-*l* prod-exp flip--
2×pow-to-exp cbrt-div diff-log pow-exp
1×sub-neg pow-pow pow1/3 associate--l+ sum-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 93
Calls
4 calls:
28.0ms
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
7.0ms
(* 0.6666666666666667 (pow x 3))
26.0ms
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
27.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
39.0ms
(* 0.6666666666666667 (pow x 3))
41.0ms
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
45.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify54.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0346862
11520806
25001799

prune252.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
388×frac-times
360×sqrt-div
288×exp-neg
261×neg-sub0 exp-diff
234×frac-sub
196×associate-*l/
134×associate-*r/
92×flip3-- flip--
81×flip3-+ flip-+
27×un-div-inv
16×add-sqr-sqrt
14×*-un-lft-identity
13×pow1 add-cbrt-cube
12×add-exp-log associate-*r*
10×add-cube-cbrt associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
3×sqrt-prod *-commutative
2×unswap-sqr
1×sub-neg diff-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 343
Calls
4 calls:
30.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
10.0ms
(* (- 1.0 eps) x)
71.0ms
(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
47.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
31.0ms
(* (- 1.0 eps) x)
58.0ms
(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
210.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

simplify145.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0225812325
1500111927

prune760.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes63.0ms

Accuracy

96.9% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 17.2b

bsearch153.0ms

Steps
ItersRangePoint
10
7.241082556785e-09
30809428.134158503
241.29703678307064

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05332
16132
26132

end0.0ms

sample2.9s

Algorithm
intervals
Results
773.0ms1912×body10240exit
742.0ms1700×body1280valid
561.0ms10216×body80valid
323.0ms1281×body640valid
110.0ms633×body320valid
33.0ms307×body160valid