Details

Time bar (total: 5.8s)

sample25.0ms

Algorithm
intervals
Results
6.0ms65×body1280valid
4.0ms256×body80nan
3.0ms47×body640valid
2.0ms120×body80valid
1.0ms14×body320valid
0.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:
4.0ms
(sqrt (+ x 1.0))
28.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series118.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(sqrt (+ x 1.0))
78.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify43.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
02991161
1921822
25001744

prune136.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite61.0ms

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:
4.0ms
(sqrt (+ x 1.0))
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
34.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series254.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(sqrt (+ x 1.0))
64.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
152.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0409789
11675716
25001675

prune221.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0b
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite58.0ms

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:
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
35.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.8s

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
677.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
865.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
154.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify80.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06221165
126191024
25001993

prune300.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
908×sqrt-prod
774×times-frac
460×distribute-lft-out
310×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 563
Calls
4 calls:
26.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
89.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series847.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
171.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
349.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
154.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify169.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0110711444
145519783
250019783

prune612.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes42.0ms

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

sample666.0ms

Algorithm
intervals
Results
150.0ms1747×body1280valid
137.0ms7958×body80nan
97.0ms1295×body640valid
73.0ms4026×body80valid
33.0ms652×body320valid
10.0ms280×body160valid