Details

Time bar (total: 10.1s)

sample331.0ms

Algorithm
intervals
Results
43.0ms226×body10240exit
13.0ms414×body80nan
8.0ms246×body80valid
2.0ms21×body160valid

simplify81.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
750017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b
(- (exp (* 2.0 x)) 1.0)
4.9b
(- (exp x) 1.0)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×sqrt-prod
27×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×associate-/r/
2×sub-neg rem-sqrt-square diff-log div-inv associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 123
Calls
4 calls:
9.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
8.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms
(- (exp (* 2.0 x)) 1.0)
6.0ms
(- (exp x) 1.0)

series203.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
92.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
32.0ms
(- (exp (* 2.0 x)) 1.0)
23.0ms
(- (exp x) 1.0)

simplify124.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
03871380
110541314
242871301
350031293

prune338.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.5b
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
4.9b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.9b
(- (exp x) 1.0)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
591×*-un-lft-identity
554×sqrt-prod
528×times-frac
521×add-sqr-sqrt
184×difference-of-squares
147×add-cube-cbrt
120×distribute-lft-out--
102×distribute-lft-out
13×associate-/r/
9×flip3-- associate-/r* flip--
8×add-log-exp
7×div-inv
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×rem-sqrt-square
2×sub-neg diff-log associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 381
Calls
4 calls:
16.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
38.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
6.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms
(- (exp x) 1.0)

series552.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
340.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
54.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms
(- (exp x) 1.0)

simplify157.0ms

Algorithm
egg-herbie
Counts
393 → 393
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0112610025
147929676
250039484

prune663.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(sqrt (sqrt (exp (* 2.0 x))))
0.5b
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))))))
5.0b
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
5.0b
(- (sqrt (exp x)) (sqrt 1.0))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
2562×sqrt-prod
1717×add-sqr-sqrt
1417×*-un-lft-identity
1383×times-frac
718×difference-of-squares
290×distribute-lft-out--
282×distribute-lft-out
273×add-cube-cbrt
11×associate-/r/
9×sqrt-pow1 add-log-exp
7×pow1 flip3-- flip--
6×div-inv
5×rem-sqrt-square
4×add-exp-log add-cbrt-cube
3×pow1/2
2×sub-neg diff-log
1×exp-prod exp-to-pow sqrt-div
Counts
4 → 786
Calls
4 calls:
3.0ms
(sqrt (sqrt (exp (* 2.0 x))))
91.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))))))
9.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
7.0ms
(- (sqrt (exp x)) (sqrt 1.0))

series2.1s

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (sqrt (exp (* 2.0 x))))
1.8s
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))))))
156.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
37.0ms
(- (sqrt (exp x)) (sqrt 1.0))

simplify236.0ms

Algorithm
egg-herbie
Counts
798 → 798
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0154330146
1500129451

prune916.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.6b
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
5.1b
(- (sqrt (sqrt (exp x))) (sqrt (sqrt 1.0)))
5.1b
(- (sqrt (sqrt (sqrt (exp (* 2.0 x))))) (sqrt (sqrt (sqrt 1.0))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
56×add-sqr-sqrt
28×*-un-lft-identity
25×difference-of-squares
10×cbrt-prod
8×add-log-exp
7×distribute-lft-out--
6×add-cube-cbrt
4×pow1 add-exp-log cbrt-div add-cbrt-cube distribute-lft-out
2×sub-neg flip3-- flip3-+ pow1/3 diff-log flip-- flip-+
Counts
4 → 86
Calls
4 calls:
6.0ms
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
6.0ms
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
9.0ms
(- (sqrt (sqrt (exp x))) (sqrt (sqrt 1.0)))
13.0ms
(- (sqrt (sqrt (sqrt (exp (* 2.0 x))))) (sqrt (sqrt (sqrt 1.0))))

series857.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
225.0ms
(cbrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
119.0ms
(- (sqrt (sqrt (exp x))) (sqrt (sqrt 1.0)))
281.0ms
(- (sqrt (sqrt (sqrt (exp (* 2.0 x))))) (sqrt (sqrt (sqrt 1.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
02911286
17851228
222391210
350011206

prune541.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes44.0ms

Accuracy

75.9% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.3b

bsearch46.0ms

Steps
ItersRangePoint
7
-7.338763160096626e-07
-2.8228108650395133e-08
-5.521965690000318e-07

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05246
15246

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s6729×body10240exit
386.0ms12551×body80nan
245.0ms7458×body80valid
52.0ms686×body160valid