Details

Time bar (total: 3.5s)

sample41.0ms

Algorithm
intervals
Results
16.0ms64×body1280valid
7.0ms39×body640valid
4.0ms124×body80valid
2.0ms19×body320valid
1.0ms10×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.6b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.2b
(- (/ 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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify89.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0251494
1731465
22771460
35002460

prune123.0ms

Filtered
69 candidates to 50 candidates (27.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh000
Picked101
Done000
Total67370

Merged error: 0.0b

Counts
70 → 3

localize12.0ms

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))
0.4b
(* 5.551115123125783e-17 (pow x 4))
7.2b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite24.0ms

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:
6.0ms
(- (* 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)))

series22.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(- (* 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))
9.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify53.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0344493
11475459
25001459

prune134.0ms

Filtered
93 candidates to 58 candidates (37.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New93093
Fresh022
Picked011
Done000
Total93396

Merged error: 0.0b

Counts
96 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.3b
(* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
2.2b
(- (* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
120×*-un-lft-identity
98×sqrt-prod
91×add-sqr-sqrt
90×times-frac
62×add-cube-cbrt
29×swap-sqr
26×distribute-lft-out
21×associate-*r* associate-*l*
19×pow1
12×associate-/r/
10×add-exp-log add-cbrt-cube
9×unswap-sqr
8×sqrt-pow1 pow1/2 associate-/r*
6×flip3-+ flip-+ div-inv associate-/l* add-log-exp
5×pow-prod-up
4×sqrt-div
3×pow-prod-down pow-sqr
2×cbrt-undiv frac-2neg div-exp clear-num
1×pow2 frac-times sub-neg flip3-- pow-plus sqrt-unprod diff-log associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 187
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
21.0ms
(* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
15.0ms
(- (* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series35.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms
(* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
11.0ms
(- (* (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify68.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04091824
118301659
250011636

prune383.0ms

Filtered
199 candidates to 121 candidates (39.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1990199
Fresh011
Picked011
Done011
Total1993202

Merged error: 0.0b

Counts
202 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.2b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
304×*-un-lft-identity
229×sqrt-prod
212×add-sqr-sqrt
188×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
20×sqrt-div associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
8×add-log-exp
7×difference-of-squares
4×pow1 cbrt-undiv div-exp
2×frac-2neg clear-num
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 317
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
16.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
65.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series24.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(+ 1.0 (exp (* -2.0 x)))
6.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
8.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
8.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify96.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
07875699
127915067
250024914

prune539.0ms

Filtered
329 candidates to 142 candidates (56.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3290329
Fresh000
Picked011
Done022
Total3293332

Merged error: 0.0b

Counts
332 → 3

regimes404.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 31.7b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03832
13832

end0.0ms

sample1.1s

Algorithm
intervals
Results
434.0ms1692×body1280valid
217.0ms1255×body640valid
141.0ms4065×body80valid
79.0ms658×body320valid
25.0ms330×body160valid

Profiling

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