Details

Time bar (total: 8.6s)

sample38.0ms

Algorithm
intervals
Results
8.0ms273×body80nan
8.0ms51×body1280valid
6.0ms47×body640valid
4.0ms132×body80valid
2.0ms18×body320valid
0.0ms8×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: 29.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite38.0ms

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))
30.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series101.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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))
29.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series236.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0409789
11675716
25001675

prune218.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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))))

rewrite217.0ms

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)))
26.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
30.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
81.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
157.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
312.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify160.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
0110711444
145519783
250019783

prune613.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite743.0ms

Algorithm
rewrite-expression-head
Rules
2734×sqrt-prod
2274×*-un-lft-identity
1668×times-frac
924×distribute-lft-out
745×add-sqr-sqrt
607×add-cube-cbrt
411×associate-*r*
53×associate-/l*
51×sqrt-div
48×associate-/r/
45×associate-*l*
36×unswap-sqr
27×associate-/r*
26×flip3-+ flip-+
24×div-inv
15×add-exp-log add-cbrt-cube
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×sqrt-undiv prod-exp cbrt-unprod
1×frac-times sqrt-unprod associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 1122
Calls
4 calls:
31.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
456.0ms
(* (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
85.0ms
(/ (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.4s

Counts
4 → 12
Calls
4 calls:
327.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
330.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
165.0ms
(* (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
562.0ms
(/ (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify235.0ms

Algorithm
egg-herbie
Counts
1134 → 1134
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0161927555
1500126955

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes39.0ms

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

sample1.1s

Algorithm
intervals
Results
283.0ms1783×body1280valid
243.0ms8186×body80nan
153.0ms1240×body640valid
138.0ms4082×body80valid
55.0ms599×body320valid
17.0ms296×body160valid