Details

Time bar (total: 4.5s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2

sample28.0ms

Algorithm
intervals
Results
9.0ms64×body640valid
5.0ms30×body1280valid
5.0ms126×body80valid
2.0ms22×body320valid
1.0ms14×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
026511
126511

prune5.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 22.5b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
4.5b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
33.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1.0 (sqrt x))
13.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
050761839

prune265.0ms

Filtered
103 candidates to 144 candidates (-39.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New13113144
Fresh000
Picked101
Done000
Total13213145

Merged error: 21.7b

Counts
145 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ 1.0 x)))
0.2b
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b
(/ 1.0 (sqrt x))
4.8b
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
2937×times-frac
2554×*-un-lft-identity
1354×add-sqr-sqrt
778×add-cube-cbrt
708×distribute-lft-out
508×sqrt-prod
368×distribute-lft-out--
211×div-inv
144×difference-of-squares
64×distribute-rgt-out--
45×associate-/l*
37×associate-/r/
27×associate-/r*
10×add-exp-log add-cbrt-cube
6×add-log-exp
4×pow1
3×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
2×flip3-- flip3-+ sqrt-div frac-sub flip-- flip-+
1×sub-neg diff-log div-sub frac-add
Counts
4 → 750
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
136.0ms
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
4.0ms
(/ 1.0 (sqrt x))
89.0ms
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
20.0ms
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
8.0ms
(/ 1.0 (sqrt x))
4.0ms
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify226.0ms

Algorithm
egg-herbie
Counts
762 → 762
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
0498323232
1498323232

prune1.3s

Filtered
283 candidates to 762 candidates (-169.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New7584762
Fresh10212
Picked101
Done000
Total7696775

Merged error: 4.7b

Counts
775 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ 1.0 x)))
0.2b
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b
(/ 1.0 (sqrt x))
4.1b
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
422×times-frac
403×*-un-lft-identity
160×sqrt-prod
158×distribute-lft-out
142×add-sqr-sqrt add-cube-cbrt
50×associate-/r/
40×div-inv
33×add-exp-log add-cbrt-cube
27×associate-/r*
17×cbrt-undiv div-exp
16×associate-*r/ associate-/l*
15×frac-times associate-*l/
6×add-log-exp
4×pow1 prod-exp cbrt-unprod
3×frac-2neg clear-num
2×flip3-+ sqrt-div div-sub flip-+
1×sub-neg flip3-- diff-log frac-add frac-sub flip-- associate-/l/
Counts
4 → 287
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
51.0ms
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
4.0ms
(/ 1.0 (sqrt x))
11.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

series44.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
30.0ms
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
8.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

simplify77.0ms

Algorithm
egg-herbie
Counts
299 → 299
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050229018

prune567.0ms

Filtered
158 candidates to 299 candidates (-89.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2972299
Fresh235
Picked011
Done000
Total2996305

Merged error: 4.7b

Counts
305 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ (+ 1.0 x) 1.0) (* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))
0.3b
(* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b
(/ 1.0 (sqrt x))
4.1b
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
49×times-frac
40×add-exp-log add-sqr-sqrt add-cbrt-cube
35×add-cube-cbrt
24×sqrt-prod
18×associate-*r/
16×frac-times
15×associate-/r/
14×cbrt-undiv div-exp associate-*r* distribute-lft-out
13×associate-*l*
12×prod-exp cbrt-unprod
7×associate-/r*
6×pow1 flip3-+ frac-add flip-+ associate-/l* add-log-exp
5×div-inv
4×associate-*l/
3×associate-/l/
2×flip3-- frac-2neg clear-num frac-sub flip-- unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in diff-log div-sub pow-prod-down *-commutative
Counts
4 → 152
Calls
4 calls:
49.0ms
(/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ (+ 1.0 x) 1.0) (* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))
39.0ms
(* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
4.0ms
(/ 1.0 (sqrt x))
8.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

series59.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ (+ 1.0 x) 1.0) (* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))
19.0ms
(* (/ x 1.0) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
8.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

simplify41.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
051263498

prune338.0ms

Filtered
119 candidates to 164 candidates (-37.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1622164
Fresh134
Picked101
Done011
Total1646170

Merged error: 0.8b

Counts
170 → 6

regimes42.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01723
11723

end0.0ms

sample801.0ms

Algorithm
intervals
Results
258.0ms1820×body640valid
212.0ms1158×body1280valid
149.0ms4082×body80valid
70.0ms654×body320valid
20.0ms286×body160valid

Profiling

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