Details

Time bar (total: 5.8s)

sample96.0ms

Algorithm
intervals
Results
24.0ms61×body10240exit
23.0ms57×body1280valid
17.0ms316×body80valid
11.0ms45×body640valid
4.0ms24×body320valid
1.0ms8×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 31.4b

Counts
2 → 1

localize21.0ms

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 168
Calls
4 calls:
4.0ms
(exp (- (* (- 1.0 eps) x)))
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
14.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
16.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (- (* (- 1.0 eps) x)))
51.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
48.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
201.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify149.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
012054059
144053786
250033771

prune430.0ms

Filtered
180 candidates to 96 candidates (53.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1773180
Fresh000
Picked101
Done000
Total1783181

Merged error: 1.2b

Counts
181 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
5.8b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (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
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series78.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0207273
1894245
25002241

prune109.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh022
Picked101
Done000
Total47754

Merged error: 1.2b

Counts
54 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* 0.6666666666666667 (pow x 3)) 3)
0.1b
(* 0.6666666666666667 (pow x 3))
5.8b
(- (+ (cbrt (pow (* 0.6666666666666667 (pow x 3)) 3)) 2.0) (* 1.0 (pow x 2)))
11.8b
(cbrt (pow (* 0.6666666666666667 (pow x 3)) 3))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-exp-log
12×associate-*r*
10×add-cube-cbrt *-un-lft-identity
9×add-cbrt-cube add-log-exp
8×cbrt-prod
6×unpow-prod-down cube-prod pow-exp prod-exp
5×pow1
4×unswap-sqr sqr-pow
3×cube-mult pow-to-exp pow-unpow unpow3 associate-*l*
2×diff-log cbrt-unprod rem-cube-cbrt
1×sub-neg flip3-- pow-pow pow1/3 associate--l+ sum-log *-commutative flip-- rem-cbrt-cube
Counts
4 → 85
Calls
4 calls:
5.0ms
(pow (* 0.6666666666666667 (pow x 3)) 3)
6.0ms
(* 0.6666666666666667 (pow x 3))
13.0ms
(- (+ (cbrt (pow (* 0.6666666666666667 (pow x 3)) 3)) 2.0) (* 1.0 (pow x 2)))
2.0ms
(cbrt (pow (* 0.6666666666666667 (pow x 3)) 3))

series181.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (* 0.6666666666666667 (pow x 3)) 3)
35.0ms
(* 0.6666666666666667 (pow x 3))
44.0ms
(- (+ (cbrt (pow (* 0.6666666666666667 (pow x 3)) 3)) 2.0) (* 1.0 (pow x 2)))
36.0ms
(cbrt (pow (* 0.6666666666666667 (pow x 3)) 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0278467
11316419
25002412

prune222.0ms

Filtered
97 candidates to 58 candidates (59.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New93497
Fresh336
Picked101
Done000
Total977104

Merged error: 1.2b

Counts
104 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(* 0.6666666666666667 (pow x 3))
9.2b
(+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
10.2b
(/ (+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) (+ 2.0 (* 1.0 (pow x 2))))) (* 1.0 (* 1.0 (pow x 4)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
36×add-sqr-sqrt
24×associate-*r*
22×add-cube-cbrt
16×add-exp-log
15×times-frac
10×add-cbrt-cube distribute-lft-out
8×unpow-prod-down cube-prod add-log-exp unswap-sqr
6×associate-*l* prod-exp
5×distribute-rgt-neg-in associate-/l*
4×pow1 sqr-pow
3×flip3-+ associate-/r* flip-+
2×neg-sub0 cube-mult pow-to-exp associate-+l- unpow3 pow-exp sum-log associate-/r/ *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-sub div-exp neg-log clear-num div-inv
Counts
4 → 117
Calls
4 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
6.0ms
(* 0.6666666666666667 (pow x 3))
17.0ms
(+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
36.0ms
(/ (+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) (+ 2.0 (* 1.0 (pow x 2))))) (* 1.0 (* 1.0 (pow x 4)))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* 0.6666666666666667 (pow x 3))
44.0ms
(* 0.6666666666666667 (pow x 3))
97.0ms
(+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3))
151.0ms
(/ (+ (- (pow (* 1.0 (pow x 2)) 3)) (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) (+ 2.0 (* 1.0 (pow x 2))))) (* 1.0 (* 1.0 (pow x 4)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04291939
120821779
250031773

prune433.0ms

Filtered
129 candidates to 84 candidates (65.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1254129
Fresh336
Picked101
Done000
Total1297136

Merged error: 1.2b

Counts
136 → 7

regimes127.0ms

Accuracy

96.6% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch121.0ms

Steps
ItersRangePoint
7
31.604470015773813
806.1088923385852
70.85452491931149

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06563
17163
27163

end0.0ms

sample2.8s

Algorithm
intervals
Results
754.0ms1741×body1280valid
724.0ms1825×body10240exit
525.0ms9883×body80valid
316.0ms1271×body640valid
107.0ms671×body320valid
32.0ms308×body160valid