Details

Time bar (total: 4.3s)

sample25.0ms

Algorithm
intervals
Results
6.0ms65×body1280valid
4.0ms252×body80nan
3.0ms40×body640valid
3.0ms132×body80valid
1.0ms13×body320valid
0.0ms6×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: 29.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

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:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series169.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(sqrt (+ x 1.0))
112.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify39.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02991161
1921822
25001744

prune138.0ms

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)))

rewrite32.0ms

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))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series249.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
71.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
147.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0409789
11675716
25001675

prune220.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite17.0ms

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)))
1.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
5.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (sqrt (+ x 1.0)))
94.0ms
(sqrt (sqrt (+ x 1.0)))
233.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
319.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

simplify87.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07431312
132301218
250031183

prune360.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
228×sqrt-prod
97×add-sqr-sqrt
90×sqrt-pow1
61×*-un-lft-identity
48×sqrt-div
41×pow1
35×add-cube-cbrt
30×pow1/2
27×swap-sqr
16×unswap-sqr
13×associate-*r* associate-*l* pow-prod-up
12×times-frac distribute-lft-out
9×flip3-+ flip-+
8×add-exp-log add-cbrt-cube
7×pow-prod-down pow-sqr
6×rem-sqrt-square
4×expm1-log1p-u frac-times log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 215
Calls
4 calls:
6.0ms
(sqrt (sqrt (sqrt (+ x 1.0))))
5.0ms
(sqrt (sqrt (sqrt (+ x 1.0))))
6.0ms
(/ (+ 1.0 0) (fma (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))
20.0ms
(* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0)))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (sqrt (sqrt (+ x 1.0))))
95.0ms
(sqrt (sqrt (sqrt (+ x 1.0))))
328.0ms
(/ (+ 1.0 0) (fma (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))
97.0ms
(* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0)))))

simplify120.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
08782413
143282117
250012114

prune547.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes31.0ms

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: 1 (1.0ms)

IterNodesCost
0168
1207
2207

end0.0ms

sample689.0ms

Algorithm
intervals
Results
157.0ms1716×body1280valid
141.0ms7850×body80nan
93.0ms1268×body640valid
80.0ms4123×body80valid
34.0ms583×body320valid
11.0ms310×body160valid