Details

Time bar (total: 4.6s)

sample44.0ms

Algorithm
intervals
Results
16.0ms49×body1280valid
9.0ms41×body640valid
6.0ms145×body80valid
2.0ms13×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: 25.9b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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:
7.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
47.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series115.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03761556
111701155
250011121

prune201.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.0b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
1732×times-frac
1496×*-un-lft-identity
1023×add-sqr-sqrt
1001×sqrt-prod
996×add-cube-cbrt
585×prod-diff
249×distribute-lft-out
195×fma-neg
86×sqrt-div
84×associate-/r/
43×flip3-+ flip-+
42×div-inv
30×associate-/l*
14×associate-/r*
11×add-exp-log add-cbrt-cube
7×difference-of-squares
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log flip-- hypot-def associate-/l/ distribute-lft-out--
Counts
4 → 1110
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
24.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
230.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series234.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
36.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
70.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
83.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify207.0ms

Algorithm
egg-herbie
Counts
1122 → 1122
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0161325952
1500117156

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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)))))
0.5b
(* 0.33333333333333337 (pow x 3))
11.0b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

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)))))
7.0ms
(* 0.33333333333333337 (pow x 3))
0.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series186.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
42.0ms
(* 0.33333333333333337 (pow x 3))
98.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify205.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0170301
1655265
24046264
35002264

prune155.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 30.2b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03319
13319

end0.0ms

sample1.4s

Algorithm
intervals
Results
565.0ms1698×body1280valid
305.0ms1287×body640valid
185.0ms4045×body80valid
111.0ms639×body320valid
36.0ms331×body160valid