Details

Time bar (total: 4.2s)

sample32.0ms

Algorithm
intervals
Results
11.0ms51×body1280valid
5.0ms37×body640valid
4.0ms142×body80valid
2.0ms19×body320valid
0.0ms7×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

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))))
2.3b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite55.0ms

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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
40.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series142.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
42.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
84.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03981645
112871235
250011212

prune409.0ms

Filtered
150 candidates to 86 candidates (57.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
27.3b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite25.0ms

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:
5.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms
(/ 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:
40.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
69.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
49.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
215.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03821270
113311133
250021081

prune308.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
27.3b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
27.3b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
27.3b
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
21×times-frac
20×add-sqr-sqrt add-cube-cbrt
16×sqrt-prod
8×add-exp-log
7×associate-/r*
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u distribute-lft-out add-log-exp
3×pow-flip fma-udef associate-/l*
2×sqrt-div div-exp associate-/r/
1×cbrt-undiv rec-exp frac-2neg sqrt-pow1 flip3-+ pow1/2 1-exp clear-num flip-+ div-inv inv-pow
Counts
4 → 83
Calls
4 calls:
7.0ms
(/ 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))
0.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
0.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series688.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
217.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
211.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
211.0ms
(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02301035
1789886
22989811
35002811

prune286.0ms

Filtered
95 candidates to 61 candidates (64.2%)
Pruning

3 alts after pruning (2 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))
10.1b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

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)))

series180.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
38.0ms
(* 0.33333333333333337 (pow x 3))
95.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify196.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune155.0ms

Filtered
62 candidates to 43 candidates (69.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 30.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04149
14149

end0.0ms

sample868.0ms

Algorithm
intervals
Results
361.0ms1693×body1280valid
179.0ms1279×body640valid
104.0ms4053×body80valid
58.0ms640×body320valid
20.0ms335×body160valid