Details

Time bar (total: 6.6s)

sample368.0ms

Algorithm
intervals
Results
32.0ms173×body10240exit
12.0ms381×body80nan
8.0ms237×body80valid
2.0ms23×body160valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
750017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.1b
(- (exp (* 2.0 x)) 1.0)
5.2b
(- (exp x) 1.0)

rewrite36.0ms

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))
9.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms
(- (exp (* 2.0 x)) 1.0)
7.0ms
(- (exp x) 1.0)

series203.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
97.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms
(- (exp (* 2.0 x)) 1.0)
23.0ms
(- (exp x) 1.0)

simplify124.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
03871380
110541314
242871301
350031293

prune348.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.3b
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
5.2b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.2b
(- (exp x) 1.0)

rewrite107.0ms

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:
13.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
40.0ms
(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)

series524.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
322.0ms
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
53.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms
(- (exp x) 1.0)

simplify161.0ms

Algorithm
egg-herbie
Counts
393 → 393
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0112610025
147929676
250039484

prune665.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(sqrt (exp x))
0.5b
(sqrt (exp x))
5.3b
(- (sqrt (exp x)) (sqrt 1.0))
5.3b
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt sqrt-prod
18×*-un-lft-identity
13×difference-of-squares
8×add-cube-cbrt sqrt-pow1 add-log-exp
6×pow1 exp-prod
5×distribute-lft-out--
4×add-exp-log add-cbrt-cube
2×sub-neg rem-sqrt-square flip3-- pow1/2 diff-log flip--
Counts
4 → 74
Calls
4 calls:
2.0ms
(sqrt (exp x))
2.0ms
(sqrt (exp x))
7.0ms
(- (sqrt (exp x)) (sqrt 1.0))
10.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(sqrt (exp x))
12.0ms
(sqrt (exp x))
40.0ms
(- (sqrt (exp x)) (sqrt 1.0))
151.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify93.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
0177588
1409564
21003562
32903560
45001560

prune324.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(sqrt (sqrt (exp (* 2.0 x))))
0.5b
(sqrt (sqrt (exp (* 2.0 x))))
5.3b
(- (sqrt (exp x)) (sqrt 1.0))
5.3b
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
50×sqrt-prod
38×add-sqr-sqrt
18×*-un-lft-identity
16×sqrt-pow1
13×difference-of-squares
10×add-log-exp
8×pow1 add-cube-cbrt
5×distribute-lft-out--
4×add-exp-log rem-sqrt-square pow1/2 add-cbrt-cube
2×sub-neg exp-prod flip3-- exp-to-pow diff-log flip--
Counts
4 → 84
Calls
4 calls:
3.0ms
(sqrt (sqrt (exp (* 2.0 x))))
3.0ms
(sqrt (sqrt (exp (* 2.0 x))))
7.0ms
(- (sqrt (exp x)) (sqrt 1.0))
10.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(sqrt (sqrt (exp (* 2.0 x))))
107.0ms
(sqrt (sqrt (exp (* 2.0 x))))
35.0ms
(- (sqrt (exp x)) (sqrt 1.0))
146.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify85.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
0187698
1416670
21009668
32598662
45001662

prune371.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes36.0ms

Accuracy

71.4% (0.9b remaining)

Error of 1.1b against oracle of 0.2b and baseline of 3.5b

bsearch32.0ms

Steps
ItersRangePoint
5
-7.455527952367615e-16
-3.171438052781698e-16
-7.195205579931451e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03833
13833

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s6785×body10240exit
373.0ms12465×body80nan
247.0ms7407×body80valid
57.0ms729×body160valid