Details

Time bar (total: 4.9s)

sample32.0ms

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

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

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)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
58×add-sqr-sqrt
54×prod-diff
53×add-cube-cbrt
49×times-frac
18×fma-neg
13×distribute-lft-out
8×associate-/r/
6×add-log-exp
5×flip3-+ flip-+
4×div-inv
3×fma-def
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u difference-of-squares
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- distribute-lft-out--
Counts
2 → 106
Calls
2 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
13.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series97.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03621383
11096982
25001948

prune172.0ms

Filtered
112 candidates to 55 candidates (49.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(+ 1.0 (exp (* -2.0 x)))
1.6b
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-log-exp
6×fma-def
5×add-sqr-sqrt add-cube-cbrt
3×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
1×fma-udef
Counts
3 → 44
Calls
3 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
1.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series335.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
16.0ms
(+ 1.0 (exp (* -2.0 x)))
303.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0157368
1461315
21632298
35001297

prune155.0ms

Filtered
53 candidates to 44 candidates (83.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))) (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))))
1.6b
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
1.6b
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
1.6b
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 72
Calls
4 calls:
6.0ms
(* (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))) (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))))
1.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
1.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
1.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
879.0ms
(* (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))) (cbrt (fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))))
315.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
311.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
308.0ms
(fma (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03001933
112991670
250011358

prune285.0ms

Filtered
84 candidates to 64 candidates (76.2%)
Pruning

4 alts after pruning (3 fresh and 1 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))
8.8b
(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:
1.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
6.0ms
(* 0.33333333333333337 (pow x 3))
1.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series185.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
41.0ms
(* 0.33333333333333337 (pow x 3))
97.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify200.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune157.0ms

Filtered
62 candidates to 43 candidates (69.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 29.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04252
14252

end0.0ms

sample857.0ms

Algorithm
intervals
Results
333.0ms1604×body1280valid
179.0ms1279×body640valid
119.0ms4162×body80valid
58.0ms636×body320valid
19.0ms319×body160valid