Details

Time bar (total: 6.6s)

sample46.0ms

Algorithm
intervals
Results
17.0ms51×body1280valid
9.0ms42×body640valid
6.0ms132×body80valid
4.0ms23×body320valid
1.0ms8×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
66×add-sqr-sqrt
61×add-cube-cbrt times-frac
54×prod-diff
18×fma-neg
16×distribute-lft-out
10×associate-/r/
5×flip3-+ flip-+ div-inv
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- distribute-lft-out--
Counts
2 → 124
Calls
2 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
40.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series123.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03761556
111701155
250011121

prune212.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
0.0b
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
2.3b
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite526.0ms

Algorithm
rewrite-expression-head
Rules
637×add-sqr-sqrt
629×*-un-lft-identity
504×prod-diff
475×times-frac
450×unpow-prod-down cube-prod
407×add-cube-cbrt
120×difference-of-squares
105×sqr-pow
86×distribute-lft-out
58×associate-/r/
55×cube-mult unpow3
42×fma-neg
39×associate-/l*
29×flip3-+ flip-+ div-inv
25×distribute-lft-out--
11×associate-/r*
10×add-exp-log add-cbrt-cube
6×add-log-exp
5×difference-cubes
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv frac-2neg div-exp clear-num
2×flip3-- flip-- associate-/l/
1×sub-neg diff-log div-sub
Counts
4 → 814
Calls
4 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
318.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
134.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series520.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
35.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
311.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
139.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify185.0ms

Algorithm
egg-herbie
Counts
826 → 826
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0148217606
1500114834

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0))))))
0.0b
(pow (+ (exp (* -2.0 x)) 1.0) 2)
0.0b
(pow (+ (exp (* -2.0 x)) 1.0) 3)
2.3b
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
19×add-sqr-sqrt add-cube-cbrt
12×times-frac
8×add-exp-log unpow-prod-down
7×add-cbrt-cube distribute-lft-out
6×pow1 pow-unpow add-log-exp
4×expm1-log1p-u cube-prod associate-/r* log1p-expm1-u
3×prod-diff associate-/l*
2×cube-div pow-to-exp flip3-- pow-pow flip3-+ pow-exp associate-/r/ flip-- flip-+ associate-/l/ sqr-pow
1×cbrt-undiv cube-mult sub-neg frac-2neg fma-neg diff-log unpow3 div-sub div-exp clear-num div-inv unpow2 rem-cube-cbrt
Counts
4 → 106
Calls
4 calls:
96.0ms
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0))))))
6.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 2)
6.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
13.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

series519.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0))))))
29.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 2)
46.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
127.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

simplify89.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
05351774
127421609
250021603

prune358.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ (exp (* -2.0 x)) 1.0) 2)
0.0b
(pow (+ (exp (* -2.0 x)) 1.0) 3)
0.0b
(cbrt (pow (/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0)))))) 3))
2.3b
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
42×cbrt-prod
27×add-sqr-sqrt add-cube-cbrt
26×unpow-prod-down
24×times-frac
22×cube-prod
9×distribute-lft-out
6×pow1 add-exp-log pow-unpow add-log-exp
5×add-cbrt-cube
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×cube-div flip3-+ prod-diff flip-+ sqr-pow
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp div-inv
1×sub-neg cbrt-div flip3-- fma-neg pow1/3 diff-log flip-- rem-cbrt-cube unpow2 rem-cube-cbrt
Counts
4 → 122
Calls
4 calls:
6.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 2)
6.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
84.0ms
(cbrt (pow (/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0)))))) 3))
17.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

series527.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 2)
48.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
317.0ms
(cbrt (pow (/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ 1.0 (+ (* 4.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 2.0 (/ 1 (+ (exp (* -2.0 x)) 1.0)))))) 3))
133.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

simplify107.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07252627
135022544
250012534

prune374.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06357
16357

end0.0ms

sample1.3s

Algorithm
intervals
Results
568.0ms1716×body1280valid
295.0ms1257×body640valid
182.0ms4088×body80valid
103.0ms631×body320valid
36.0ms308×body160valid