Details

Time bar (total: 5.0s)

sample33.0ms

Algorithm
intervals
Results
10.0ms46×body1280valid
6.0ms41×body640valid
4.0ms137×body80valid
2.0ms19×body320valid
1.0ms13×body160valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.9b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
16×add-sqr-sqrt
13×times-frac
11×add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube distribute-lft-out add-log-exp
3×associate-/l*
2×pow1 associate-/r/ difference-of-squares
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num flip-- flip-+ div-inv distribute-lft-out--
Counts
2 → 48
Calls
2 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series114.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
78.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify63.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0220413
1613391
22032387
35001387

prune120.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
0.0b
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.9b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
80×times-frac
62×add-sqr-sqrt
50×add-cube-cbrt
24×swap-sqr distribute-lft-out
18×add-exp-log associate-*r* associate-*l* add-cbrt-cube
11×pow1
10×associate-/r/
8×add-log-exp
6×flip3-+ flip-+ difference-of-squares
5×cbrt-undiv div-exp div-inv
4×prod-exp associate-/r* cbrt-unprod associate-/l* unswap-sqr
2×flip3-- flip-- associate-/l/
1×+-commutative pow2 frac-times sub-neg frac-2neg pow-plus diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num sum-log pow-sqr *-commutative pow-prod-up
Counts
4 → 154
Calls
4 calls:
27.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
64.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
36.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series378.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
196.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
42.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
87.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify129.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
07332533
138392227
250032209

prune371.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b
(/ (- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3)) (* (+ (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (* (* (* 2.0 2.0) (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 1.0 1.0))) (pow 1.0 4)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
3.9b
(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
97×times-frac
87×add-sqr-sqrt
51×add-cube-cbrt
48×difference-of-squares
42×unpow-prod-down
25×sqr-pow
24×add-exp-log cube-prod swap-sqr
21×add-cbrt-cube distribute-lft-out associate-/l*
18×associate-*r* associate-*l* associate-/r/
12×pow1
11×flip3-+ flip-+
7×div-exp
6×cbrt-undiv div-inv add-log-exp
5×frac-times prod-exp cbrt-unprod
4×unswap-sqr
3×difference-cubes pow-unpow associate-*r/ associate-*l/ distribute-lft-out--
2×flip3-- pow-exp flip-- associate-/l/
1×pow2 pow-to-exp sub-neg pow-pow frac-2neg pow-plus diff-log div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up
Counts
4 → 219
Calls
4 calls:
35.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
183.0ms
(/ (- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3)) (* (+ (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (* (* (* 2.0 2.0) (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 1.0 1.0))) (pow 1.0 4)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
8.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
10.0ms
(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

series703.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
482.0ms
(/ (- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3)) (* (+ (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4) (* (* (* 2.0 2.0) (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 2))) (* 1.0 1.0))) (pow 1.0 4)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
51.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 4)
128.0ms
(- (pow (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 3) (pow (* 1.0 1.0) 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011565161
150014556

prune957.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1.0 x) (+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (pow x 3))))
0.1b
(* 0.3333333333333335 (pow x 3))
0.9b
(* 4.996003610813204e-16 (pow x 4))
8.0b
(+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (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) (+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (pow x 3))))
7.0ms
(* 0.3333333333333335 (pow x 3))
5.0ms
(* 4.996003610813204e-16 (pow x 4))
3.0ms
(+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (pow x 3)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* 1.0 x) (+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (pow x 3))))
40.0ms
(* 0.3333333333333335 (pow x 3))
36.0ms
(* 4.996003610813204e-16 (pow x 4))
113.0ms
(+ (* 4.996003610813204e-16 (pow x 4)) (* 0.3333333333333335 (pow x 3)))

simplify51.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0344493
11475459
25001459

prune200.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06146
16146

end0.0ms

sample904.0ms

Algorithm
intervals
Results
355.0ms1636×body1280valid
186.0ms1270×body640valid
121.0ms4140×body80valid
61.0ms633×body320valid
23.0ms321×body160valid