Details

Time bar (total: 3.3s)

sample34.0ms

Algorithm
intervals
Results
12.0ms50×body1280valid
6.0ms47×body640valid
4.0ms130×body80valid
2.0ms18×body320valid
1.0ms11×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: 29.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
3.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite61.0ms

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:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
45.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series138.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
17.0ms
(+ 1.0 (exp (* -2.0 x)))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03981645
112871235
250011212

prune256.0ms

Filtered
150 candidates to 86 candidates (57.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
30.0b
(fma (/ 1 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 58
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.0ms
(fma (/ 1 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series772.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
133.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
139.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
361.0ms
(fma (/ 1 (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0213708
1657640
22800612
35001608

prune234.0ms

Filtered
70 candidates to 60 candidates (85.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 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)))))
0.1b
(* 0.33333333333333337 (pow x 3))
8.9b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite10.0ms

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)))

series197.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
36.0ms
(* 0.33333333333333337 (pow x 3))
107.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify202.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune154.0ms

Filtered
62 candidates to 43 candidates (69.4%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes132.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03825
13825

end0.0ms

sample908.0ms

Algorithm
intervals
Results
387.0ms1758×body1280valid
167.0ms1190×body640valid
115.0ms4126×body80valid
58.0ms615×body320valid
22.0ms311×body160valid