Details

Time bar (total: 4.3s)

sample34.0ms

Algorithm
intervals
Results
12.0ms52×body1280valid
6.0ms34×body640valid
5.0ms146×body80valid
1.0ms13×body320valid
1.0ms11×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.7b

Counts
2 → 1

localize7.0ms

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))))
2.5b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series140.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ 1.0 (exp (* -2.0 x)))
40.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify96.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0251494
1731465
22785460
35001460

prune132.0ms

Filtered
69 candidates to 50 candidates (72.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh000
Picked101
Done000
Total67370

Merged error: 0.0b

Counts
70 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.5b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
304×*-un-lft-identity
229×sqrt-prod
212×add-sqr-sqrt
188×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
20×sqrt-div associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
8×add-log-exp
7×difference-of-squares
4×pow1 cbrt-undiv div-exp
2×frac-2neg clear-num
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 317
Calls
4 calls:
6.0ms
(+ 1.0 (exp (* -2.0 x)))
16.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
65.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series208.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
37.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
71.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
85.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify102.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07875699
127915067
250024914

prune423.0ms

Filtered
329 candidates to 142 candidates (43.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3281329
Fresh022
Picked101
Done000
Total3293332

Merged error: 0.0b

Counts
332 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(/ (+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x))))) (+ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.5b
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
49×times-frac
39×add-sqr-sqrt add-cube-cbrt
19×distribute-lft-out
16×sqrt-prod
15×associate-/r*
10×add-exp-log add-cbrt-cube associate-/l*
8×add-log-exp
6×associate-/r/
5×flip3-+ flip-+
4×pow1
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×neg-sub0 associate-+l- sqrt-div sum-log associate-/l/
1×+-commutative div-sub neg-log
Counts
4 → 133
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
70.0ms
(/ (+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x))))) (+ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0))
6.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
9.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
211.0ms
(/ (+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x))))) (+ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0))
68.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
92.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

simplify78.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05352475
121972180
250012049

prune355.0ms

Filtered
145 candidates to 100 candidates (69.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1441145
Fresh112
Picked011
Done000
Total1453148

Merged error: 0.0b

Counts
148 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.5b
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
2.5b
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
2.5b
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
21×times-frac
20×add-sqr-sqrt add-cube-cbrt
16×sqrt-prod add-log-exp
7×associate-/r* distribute-lft-out
6×add-exp-log sum-log add-cbrt-cube
4×pow1 flip3-+ flip-+
3×+-commutative neg-sub0 associate-+l- neg-log associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 87
Calls
4 calls:
6.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
9.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
9.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
9.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
89.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
90.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))
91.0ms
(+ (- (* 1.0 1.0)) (/ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 2.0) (+ 1.0 (exp (* -2.0 x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03051288
110541161
250021080

prune344.0ms

Filtered
99 candidates to 72 candidates (72.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New98199
Fresh011
Picked101
Done011
Total993102

Merged error: 0.0b

Counts
102 → 3

regimes205.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06091
16091

end0.0ms

sample1.0s

Algorithm
intervals
Results
421.0ms1735×body1280valid
200.0ms1237×body640valid
134.0ms4060×body80valid
69.0ms634×body320valid
24.0ms334×body160valid

Profiling

Loading profile data...