Details

Time bar (total: 6.7s)

sample33.0ms

Algorithm
intervals
Results
11.0ms50×body1280valid
6.0ms46×body640valid
3.0ms129×body80valid
2.0ms22×body320valid
1.0ms9×body160valid

simplify62.0ms

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: 29.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-exp-log add-cbrt-cube div-inv
4×associate-/r*
3×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
7.0ms
(+ 1.0 (exp (* -2.0 x)))
14.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series133.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
78.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03981645
112871235
250011212

prune247.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 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))
2.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
94×add-sqr-sqrt
69×add-cube-cbrt
65×times-frac
54×prod-diff
18×cbrt-prod fma-neg
16×distribute-lft-out
12×unpow-prod-down cube-prod
10×associate-/r/ difference-of-squares
7×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1 flip3-+ flip-+ div-inv distribute-lft-out--
4×cube-div expm1-log1p-u associate-/r* log1p-expm1-u
3×pow-unpow flip3-- flip-- associate-/l*
2×cube-mult cbrt-div unpow3 sqr-pow
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg pow1/3 diff-log div-exp pow-exp clear-num rem-cbrt-cube rem-cube-cbrt
Counts
4 → 188
Calls
4 calls:
14.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
74.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
63.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
83.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series316.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
119.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
78.0ms
(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)

simplify69.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05442246
120411819
250011794

prune368.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (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)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.1b
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
551×sqrt-prod
431×*-un-lft-identity
378×prod-diff
335×add-sqr-sqrt
305×add-cube-cbrt
232×times-frac
128×distribute-rgt-in distribute-lft-in
59×distribute-lft-out
38×associate-/r/
28×flip3-+ flip-+
21×fma-neg
19×div-inv
16×cube-div
12×frac-times difference-of-squares
11×associate-*r*
10×flip3-- flip--
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod cbrt-div
6×associate-*r/ associate-*l/ add-log-exp
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×sub-neg pow-unpow
2×cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×pow-to-exp pow1/3 diff-log *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 522
Calls
4 calls:
111.0ms
(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3)
8.0ms
(cbrt (pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
383.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
97.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
497.0ms
(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3)
371.0ms
(cbrt (pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
376.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
119.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify147.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0170817183
1500114509

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.1b
(* 0.33333333333333337 (pow x 3))
7.3b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*r*
8×add-exp-log
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod
Counts
3 → 53
Calls
3 calls:
0.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
16.0ms
(* 0.33333333333333337 (pow x 3))
0.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series189.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms
(* 0.33333333333333337 (pow x 3))
101.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify198.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune153.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03932
13932

end0.0ms

sample908.0ms

Algorithm
intervals
Results
341.0ms1669×body1280valid
181.0ms1316×body640valid
109.0ms4088×body80valid
57.0ms615×body320valid
18.0ms312×body160valid