Details

Time bar (total: 5.9s)

sample32.0ms

Algorithm
intervals
Results
13.0ms60×body1280valid
5.0ms36×body640valid
4.0ms134×body80valid
2.0ms20×body320valid
0.0ms6×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
1.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube difference-of-squares
1×+-commutative sub-neg flip3-- flip3-+ times-frac diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
2 → 27
Calls
2 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series99.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(+ 1.0 (exp (* -2.0 x)))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0183242
1457222
21597217
35001217

prune81.0ms

Filtered
33 candidates to 24 candidates (72.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
0.0b
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
1.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
22×*-un-lft-identity
18×cbrt-prod
12×unpow-prod-down cube-prod
10×add-cube-cbrt difference-of-squares
8×add-log-exp
5×pow1 add-exp-log times-frac add-cbrt-cube distribute-lft-out--
4×cube-div
3×pow-unpow flip3-- flip--
2×cube-mult cbrt-div unpow3 sqr-pow
1×+-commutative pow-to-exp sub-neg pow-pow flip3-+ pow1/3 diff-log pow-exp sum-log rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 87
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
11.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
15.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
11.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series293.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
121.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
77.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
78.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0345909
11226864
25001849

prune180.0ms

Filtered
99 candidates to 54 candidates (54.5%)
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
(* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
0.0b
(cbrt (* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
0.3b
(pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
1.8b
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
41×*-un-lft-identity
35×sqrt-prod
29×unpow-prod-down cube-prod
28×associate-*r*
26×cube-div
18×difference-of-squares
17×add-exp-log
16×associate-*l* unswap-sqr
13×add-cube-cbrt
11×sqr-pow
9×prod-exp
8×frac-times cbrt-div distribute-lft-out
7×pow-to-exp flip3-- flip3-+ pow-exp add-cbrt-cube flip-- flip-+
6×times-frac distribute-lft-out-- add-log-exp
5×pow1
4×associate-*r/ associate-*l/
3×cube-mult pow-unpow unpow3
2×pow-prod-down
1×cbrt-prod sub-neg pow-pow pow1/3 diff-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 154
Calls
4 calls:
47.0ms
(* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
33.0ms
(cbrt (* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
16.0ms
(pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
14.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
644.0ms
(* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
373.0ms
(cbrt (* (pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
269.0ms
(pow (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
116.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify135.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
07263518
139403179
250022920

prune444.0ms

Filtered
166 candidates to 94 candidates (56.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
0.0b
(pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3)
0.0b
(cbrt (/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)))
1.4b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
392×times-frac
298×*-un-lft-identity
236×unpow-prod-down cube-prod
202×cbrt-prod
182×add-sqr-sqrt add-cube-cbrt
61×difference-of-squares
59×cube-mult unpow3 sqr-pow
58×distribute-lft-out
17×add-exp-log
14×associate-/r* associate-/l*
9×div-exp
8×cube-div
7×pow-to-exp pow-exp add-cbrt-cube
6×add-log-exp
5×pow1
4×associate-/r/
3×pow-unpow flip3-- flip--
2×flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv sub-neg cbrt-div pow-pow frac-2neg pow1/3 diff-log clear-num rem-cube-cbrt
Counts
4 → 499
Calls
4 calls:
31.0ms
(/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
13.0ms
(pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3)
36.0ms
(cbrt (/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)))
11.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series692.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
127.0ms
(pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3)
195.0ms
(cbrt (/ (pow (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) 3) (pow (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)))
87.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify272.0ms

Algorithm
egg-herbie
Counts
511 → 511
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
084317229
1441015988
2500115870

prune608.0ms

Filtered
511 candidates to 147 candidates (28.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

98% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 28.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05488
15488

end0.0ms

sample868.0ms

Algorithm
intervals
Results
349.0ms1604×body1280valid
181.0ms1279×body640valid
111.0ms4162×body80valid
60.0ms636×body320valid
20.0ms319×body160valid