Details

Time bar (total: 4.7s)

sample25.0ms

Algorithm
intervals
Results
5.0ms296×body80nan
5.0ms56×body1280valid
3.0ms44×body640valid
2.0ms126×body80valid
1.0ms16×body320valid
0.0ms14×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: 31.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.7b
(- (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:
7.0ms
(sqrt (+ x 1.0))
25.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(sqrt (+ x 1.0))
67.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite56.0ms

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))
18.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series241.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms
(/ (+ 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

prune231.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
24×sqrt-prod
21×add-sqr-sqrt
17×add-cube-cbrt
12×times-frac
8×pow1 sqrt-pow1 sqrt-div
6×add-exp-log add-cbrt-cube distribute-lft-out
4×expm1-log1p-u rem-sqrt-square pow1/2 log1p-expm1-u associate-/l* add-log-exp
3×flip3-+ associate-/r* flip-+
2×associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
0.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
11.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(sqrt (sqrt (+ x 1.0)))
89.0ms
(sqrt (sqrt (+ x 1.0)))
227.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
301.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

simplify81.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07431312
132301218
250031183

prune370.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

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)))
0.2b
(/ (+ 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))))

rewrite205.0ms

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:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
79.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
337.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
150.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify166.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0110711444
145519783
250019783

prune664.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample653.0ms

Algorithm
intervals
Results
146.0ms1740×body1280valid
136.0ms7974×body80nan
84.0ms1267×body640valid
73.0ms4077×body80valid
33.0ms600×body320valid
10.0ms316×body160valid