Details

Time bar (total: 4.2s)

sample24.0ms

Algorithm
intervals
Results
6.0ms67×body1280valid
4.0ms240×body80nan
2.0ms128×body80valid
2.0ms30×body640valid
1.0ms24×body320valid
0.0ms7×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))
2.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite21.0ms

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))
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series108.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify39.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02991161
1921822
25001744

prune139.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

4 alts after pruning (4 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)))

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:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
17.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series257.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(sqrt (+ x 1.0))
72.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
147.0ms
(/ (+ 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

prune228.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

10 alts after pruning (10 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 (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite27.0ms

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:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
1.0ms
(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
14.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.3s

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
519.0ms
(log1p (expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
148.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
527.0ms
(expm1 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify59.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05421045
12186929
25002899

prune283.0ms

Filtered
109 candidates to 72 candidates (66.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
94.0ms
(cbrt (+ x 1.0))
93.0ms
(cbrt (+ x 1.0))
91.0ms
(cbrt (+ x 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0321818
11064769
24750694
35001688

prune368.0ms

Filtered
115 candidates to 83 candidates (72.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes68.0ms

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
0148
1188
2188

end0.0ms

sample664.0ms

Algorithm
intervals
Results
149.0ms1734×body1280valid
132.0ms7943×body80nan
92.0ms1311×body640valid
74.0ms4055×body80valid
31.0ms615×body320valid
10.0ms285×body160valid