Details

Time bar (total: 4.1s)

sample34.0ms

Algorithm
intervals
Results
11.0ms47×body1280valid
7.0ms52×body640valid
4.0ms133×body80valid
1.0ms14×body320valid
1.0ms10×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: 28.8b

localize6.0ms

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))))
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite115.0ms

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)))
15.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
86.0ms
(- (/ 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)))
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify49.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03981645
112871235
250011212

prune258.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
29.4b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
42×times-frac
40×add-sqr-sqrt
37×add-cube-cbrt
36×sqrt-prod
14×associate-/r*
10×add-exp-log
9×distribute-lft-out
8×add-cbrt-cube
7×pow1
6×sqrt-div associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×pow-flip flip3-+ div-exp flip-+
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×rem-sqrt-square rec-exp 1-exp fma-udef hypot-def inv-pow
Counts
4 → 129
Calls
4 calls:
11.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
15.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
18.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series373.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
72.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
214.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03821270
113311133
250021081

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
29.4b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (/ (sqrt 2.0) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x))))))) (- 1.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
21×times-frac
16×sqrt-prod
8×add-exp-log cbrt-prod
7×associate-/r*
6×pow1 add-cbrt-cube distribute-lft-out
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×pow-flip flip3-+ flip-+ associate-/l*
2×pow1/3 sqrt-div div-exp associate-/r/
1×cbrt-undiv rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num fma-udef div-inv inv-pow
Counts
4 → 95
Calls
4 calls:
19.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
5.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
5.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (/ (sqrt 2.0) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x))))))) (- 1.0))

series631.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
130.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
133.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
317.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (/ (sqrt 2.0) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x))))))) (- 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04321189
117561065
250021002

prune350.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
12.0b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 43
Calls
2 calls:
13.0ms
(* 0.33333333333333337 (pow x 3))
4.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series138.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(* 0.33333333333333337 (pow x 3))
101.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify183.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0142195
1582172
23698172
35002172

prune121.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04342
14342

end0.0ms

sample911.0ms

Algorithm
intervals
Results
348.0ms1683×body1280valid
179.0ms1278×body640valid
104.0ms4024×body80valid
63.0ms674×body320valid
19.0ms341×body160valid