Details

Time bar (total: 4.4s)

sample33.0ms

Algorithm
intervals
Results
7.0ms56×body1280valid
7.0ms252×body80nan
4.0ms36×body640valid
3.0ms121×body80valid
2.0ms25×body320valid
1.0ms18×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.4b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
5.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite18.0ms

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))

series104.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02991161
1921822
25001744

prune131.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New92395
Fresh000
Picked101
Done000
Total93396

Merged error: 0.2b

Counts
96 → 3

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)))

rewrite30.0ms

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

series238.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0409789
11675716
25001675

prune194.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New994103
Fresh112
Picked011
Done000
Total1006106

Merged error: 0.0b

Counts
106 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.2b
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.4b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
63×add-sqr-sqrt
55×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
29×add-cube-cbrt
20×pow1/2
18×swap-sqr
12×times-frac distribute-lft-out
10×flip3-+ associate-*r* associate-*l* flip-+
9×pow-prod-up unswap-sqr
8×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/r/ 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 → 175
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
19.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
15.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (sqrt (+ x 1.0)))
93.0ms
(sqrt (sqrt (+ x 1.0)))
142.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
36.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05941528
128001345
250011318

prune340.0ms

Filtered
187 candidates to 104 candidates (55.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1852187
Fresh044
Picked011
Done011
Total1858193

Merged error: 0.0b

Counts
193 → 8

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))))

rewrite119.0ms

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:
12.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
336.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
152.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify172.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0110711444
145519783
250019783

prune536.0ms

Filtered
575 candidates to 160 candidates (27.8%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New5714575
Fresh235
Picked011
Done022
Total57310583

Merged error: 0b

Counts
583 → 10

regimes38.0ms

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

sample941.0ms

Algorithm
intervals
Results
224.0ms1696×body1280valid
214.0ms7954×body80nan
129.0ms1259×body640valid
118.0ms4128×body80valid
49.0ms619×body320valid
15.0ms298×body160valid

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