Details

Time bar (total: 5.5s)

sample79.0ms

Algorithm
intervals
Results
54.0ms184×body1280valid
6.0ms263×body80valid
6.0ms37×body640valid
2.0ms21×body320valid
1.0ms10×body160valid

simplify215.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0145
1265
2415
3555
4675
51005
61445
72965
813215
950015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (exp x) 2.0)
4.2b
(+ (- (exp x) 2.0) (exp (- x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity add-log-exp
4×add-sqr-sqrt frac-add
3×flip3-- flip--
2×pow1 add-exp-log neg-sub0 exp-neg add-cube-cbrt sub-neg associate-+l+ exp-diff diff-log sum-log add-cbrt-cube distribute-lft-out distribute-lft-out--
1×+-commutative associate-+l- flip3-+ flip-+ difference-of-squares
Counts
2 → 35
Calls
2 calls:
4.0ms
(- (exp x) 2.0)
24.0ms
(+ (- (exp x) 2.0) (exp (- x)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
15.0ms
(- (exp x) 2.0)
54.0ms
(+ (- (exp x) 2.0) (exp (- x)))

simplify90.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0211282
1715269
23477260
35001260

prune88.0ms

Filtered
41 candidates to 29 candidates (70.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b
(* 1/360 (pow x 6))
0.1b
(* 1/12 (pow x 4))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×add-exp-log associate-*r*
12×*-un-lft-identity
11×add-log-exp
10×add-cube-cbrt
8×unpow-prod-down add-cbrt-cube
6×associate-*l* prod-exp unswap-sqr
4×pow1 sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 75
Calls
4 calls:
3.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
11.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms
(* 1/360 (pow x 6))
8.0ms
(* 1/12 (pow x 4))

series262.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
53.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
49.0ms
(* 1/360 (pow x 6))
35.0ms
(* 1/12 (pow x 4))

simplify50.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0329464
11456439
25001423

prune203.0ms

Filtered
87 candidates to 55 candidates (63.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/12 (pow x 4))
0.1b
(* 1/12 (pow x 4))
29.0b
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.0b
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-exp-log associate-*r*
12×add-cube-cbrt
8×unpow-prod-down sqrt-prod add-cbrt-cube
6×pow1 associate-*l* prod-exp unswap-sqr
4×sqrt-div add-log-exp sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 82
Calls
4 calls:
5.0ms
(* 1/12 (pow x 4))
5.0ms
(* 1/12 (pow x 4))
18.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
18.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 1/12 (pow x 4))
35.0ms
(* 1/12 (pow x 4))
96.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
99.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify201.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0259662
11019626
24841616
35001616

prune296.0ms

Filtered
94 candidates to 64 candidates (68.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
30.0b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.0b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.0b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
79.0ms
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
9.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
9.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
9.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series546.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
138.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
129.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
132.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03582077
112361956
250021780

prune351.0ms

Filtered
107 candidates to 75 candidates (70.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01917
11917

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s5639×body1280valid
200.0ms1267×body640valid
180.0ms7784×body80valid
60.0ms599×body320valid
21.0ms328×body160valid