Details

Time bar (total: 3.1s)

analyze1.0ms

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

sample33.0ms

Algorithm
intervals
Results
13.0ms64×body640valid
7.0ms37×body1280valid
4.0ms121×body80valid
3.0ms24×body320valid
1.0ms10×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
1911

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))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.6b
(- (/ 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))
30.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1.0 (sqrt x))
13.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify81.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
055081833

prune261.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New12915144
Fresh000
Picked101
Done000
Total13015145

Merged error: 21.9b

Counts
145 → 15

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 x))
0.1b
(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b
(* (sqrt x) (sqrt (+ 1.0 x)))
2.6b
(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-exp-log add-cbrt-cube
9×pow1 add-cube-cbrt
7×associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
4 → 92
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 x))
16.0ms
(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

series51.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 x))
31.0ms
(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
054551527

prune188.0ms

Filtered
76 candidates to 104 candidates (-36.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1013104
Fresh9514
Picked101
Done000
Total1118119

Merged error: 0.3b

Counts
119 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b
(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
35×sqrt-prod
32×distribute-lft-out
29×add-exp-log add-cbrt-cube
28×add-sqr-sqrt
25×times-frac
20×add-cube-cbrt
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×flip3-+ associate-*r/ flip-+ associate-/l*
4×sqrt-div associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative
Counts
4 → 125
Calls
4 calls:
9.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
34.0ms
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049622089
149622089

prune257.0ms

Filtered
91 candidates to 137 candidates (-50.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1298137
Fresh437
Picked101
Done000
Total13411145

Merged error: 0.0b

Counts
145 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (* 1.0 (/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.3b
(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
732×*-un-lft-identity
691×sqrt-prod
595×times-frac
273×distribute-lft-out
262×add-sqr-sqrt
254×add-cube-cbrt
45×add-exp-log add-cbrt-cube
37×associate-/l*
28×sqrt-div
26×associate-/r/
19×associate-/r*
18×cbrt-undiv div-exp
14×flip3-+ flip-+
13×div-inv
11×prod-exp cbrt-unprod
8×pow1
7×associate-*r*
6×associate-*l*
5×associate-*r/
4×add-log-exp unswap-sqr
3×frac-2neg pow-prod-down clear-num
2×sqrt-pow1 pow1/2 associate-/l/
1×sqrt-unprod *-commutative
Counts
4 → 474
Calls
4 calls:
10.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
45.0ms
(/ (* 1.0 (/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))) (* (sqrt x) (sqrt (+ 1.0 x))))
26.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
8.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))

series98.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
46.0ms
(/ (* 1.0 (/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))) (* (sqrt x) (sqrt (+ 1.0 x))))
27.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
6.0ms
(* (sqrt x) (sqrt (+ 1.0 x)))

simplify139.0ms

Algorithm
egg-herbie
Counts
486 → 486
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0497011806
1497011806

prune632.0ms

Filtered
167 candidates to 486 candidates (-191.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New4842486
Fresh01010
Picked011
Done000
Total48413497

Merged error: 0b

Counts
497 → 13

regimes73.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01629
11629

end0.0ms

analyze1.0ms

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

sample793.0ms

Algorithm
intervals
Results
262.0ms1856×body640valid
204.0ms1113×body1280valid
150.0ms4069×body80valid
65.0ms640×body320valid
22.0ms322×body160valid

Profiling

Loading profile data...