Details

Time bar (total: 5.3s)

sample31.0ms

Algorithm
intervals
Results
6.0ms321×body80nan
6.0ms62×body1280valid
3.0ms124×body80valid
2.0ms35×body640valid
1.0ms24×body320valid
0.0ms11×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.8b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
8.0ms
(sqrt (+ x 1.0))
54.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
35.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
59.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(sqrt (+ x 1.0))
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0409790
11672716
25001675

prune237.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b
(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.4b
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
18×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log1p-expm1-u
4×pow1 expm1-log1p-u associate-/l*
3×flip3-+ flip-+
2×associate-/r/ associate-/l/
1×cbrt-undiv +-commutative log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num sum-log div-inv expm1-udef
Counts
4 → 97
Calls
4 calls:
36.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0ms
(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
61.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
498.0ms
(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
144.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
302.0ms
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify67.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05421045
12186929
25002899

prune292.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
18×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×expm1-log1p-u
4×pow1 log1p-expm1-u associate-/l*
3×flip3-+ flip-+
2×associate-/r/ associate-/l/
1×cbrt-undiv +-commutative log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num sum-log div-inv expm1-udef
Counts
4 → 97
Calls
4 calls:
0.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
37.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
57.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
461.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
813.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
144.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify80.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06221165
126221024
25001993

prune279.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0148
1188
2188

end0.0ms

sample786.0ms

Algorithm
intervals
Results
168.0ms1837×body1280valid
155.0ms8004×body80nan
90.0ms1240×body640valid
81.0ms3977×body80valid
35.0ms619×body320valid
12.0ms327×body160valid