Details

Time bar (total: 3.4s)

sample38.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
12.0ms48×body1280valid
7.0ms40×body640valid
4.0ms129×body80valid
3.0ms24×body320valid
1.0ms15×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.6b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
4.1b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 60
Calls
3 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series17.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms
(+ 1.0 (exp (* -2.0 x)))
9.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0251494
1731465
22771460
35002460

prune139.0ms

Filtered
50 candidates to 69 candidates (-38.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New65469
Fresh000
Picked101
Done000
Total66470

Merged error: 0.0b

Counts
70 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
4.1b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
80×times-frac
62×add-sqr-sqrt
50×add-cube-cbrt
24×swap-sqr distribute-lft-out
18×add-exp-log associate-*r* associate-*l* add-cbrt-cube
11×pow1
10×associate-/r/
8×add-log-exp
6×flip3-+ flip-+ difference-of-squares
5×cbrt-undiv div-exp div-inv
4×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×flip3-- flip-- associate-/l/
1×+-commutative pow2 frac-times sub-neg frac-2neg pow-plus diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num sum-log pow-sqr *-commutative pow-prod-up
Counts
4 → 154
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
19.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
21.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
11.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series53.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(+ 1.0 (exp (* -2.0 x)))
10.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
28.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
13.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify119.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
07222489
137812190
250022172

prune460.0ms

Filtered
110 candidates to 166 candidates (-50.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1651166
Fresh033
Picked101
Done000
Total1664170

Merged error: 0.0b

Counts
170 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(+ 1.0 (exp (* -2.0 x)))
0.3b
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
4.6b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
26×sqrt-prod
20×difference-of-squares
16×*-un-lft-identity times-frac
14×associate-*r*
10×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×flip3-+ flip-+
4×frac-times flip3-- associate-*l* flip--
3×sub-neg distribute-lft-out
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log distribute-lft-out--
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 89
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
50.0ms
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
23.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series51.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ 1.0 (exp (* -2.0 x)))
2.0ms
(+ 1.0 (exp (* -2.0 x)))
32.0ms
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
13.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03971691
117431565
250021552

prune305.0ms

Filtered
64 candidates to 101 candidates (-57.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1010101
Fresh033
Picked011
Done000
Total1014105

Merged error: 0.0b

Counts
105 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b
(* 0.33333333333333337 (pow x 3))
0.2b
(* 5.551115123125783e-17 (pow x 4))
6.2b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sqr-pow
2×pow-to-exp diff-log pow-exp sum-log *-commutative cbrt-unprod
1×+-commutative cube-mult sub-neg flip3-- flip3-+ unpow3 flip-- flip-+ associate--r+
Counts
4 → 81
Calls
4 calls:
5.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
6.0ms
(* 0.33333333333333337 (pow x 3))
5.0ms
(* 5.551115123125783e-17 (pow x 4))
4.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series24.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
4.0ms
(* 0.33333333333333337 (pow x 3))
4.0ms
(* 5.551115123125783e-17 (pow x 4))
10.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify54.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0344493
11475459
25001459

prune129.0ms

Filtered
58 candidates to 93 candidates (-60.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh022
Picked011
Done011
Total93497

Merged error: 0.0b

Counts
97 → 4

regimes506.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04965
14965

end0.0ms

sample1.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
437.0ms1685×body1280valid
222.0ms1258×body640valid
149.0ms4065×body80valid
79.0ms648×body320valid
27.0ms344×body160valid

Profiling

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