Details

Time bar (total: 5.4s)

sample33.0ms

Algorithm
intervals
Results
10.0ms47×body1280valid
7.0ms52×body640valid
4.0ms133×body80valid
1.0ms14×body320valid
1.0ms10×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

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)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 60
Calls
3 calls:
6.0ms
(+ 1.0 (exp (* -2.0 x)))
14.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
67.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
38.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
76.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35001460

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.8b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
305×*-un-lft-identity
233×sqrt-prod
214×add-sqr-sqrt
189×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
22×sqrt-div
20×associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
7×difference-of-squares
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 321
Calls
4 calls:
10.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
43.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
15.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
236.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series219.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
39.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
67.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
74.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
07905746
128715152
250014983

prune501.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.8b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
2.8b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
2.8b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
51×times-frac
34×*-un-lft-identity
31×sqrt-prod
21×difference-of-squares
20×add-cube-cbrt
10×add-log-exp
7×associate-/r*
6×add-exp-log add-cbrt-cube
4×pow1 distribute-lft-out
3×sub-neg flip3-- diff-log flip-- associate-/l* distribute-lft-out--
2×sqrt-div associate-/r/
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
15.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
234.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
236.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
237.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series303.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
80.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
79.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
80.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify117.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02761786
17811539
235861422
350011422

prune332.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-div *-un-lft-identity sqrt-div
15×add-exp-log
14×cbrt-prod
12×pow1 add-sqr-sqrt
10×add-cube-cbrt
9×pow-flip
8×flip3-+ pow1/3 sqrt-prod associate-/r/ flip-+
7×add-cbrt-cube
6×add-log-exp
4×frac-times div-exp
3×times-frac prod-exp associate-/l*
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up distribute-lft-out
1×pow2 sub-neg flip3-- frac-2neg pow-plus diff-log clear-num associate-/r* flip-- cbrt-unprod div-inv distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 91
Calls
4 calls:
6.0ms
(cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms
(cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
40.0ms
(/ 1 (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))
194.0ms
(- (/ (* (/ 1 (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (/ 2.0 (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series468.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
135.0ms
(cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
122.0ms
(/ 1 (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))
81.0ms
(- (/ (* (/ 1 (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (/ 2.0 (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03921491
112291325
250011233

prune275.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes195.0ms

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
04972
14972

end0.0ms

sample917.0ms

Algorithm
intervals
Results
352.0ms1683×body1280valid
180.0ms1278×body640valid
108.0ms4024×body80valid
60.0ms674×body320valid
20.0ms341×body160valid