Details

Time bar (total: 6.2s)

sample40.0ms

Algorithm
intervals
Results
9.0ms66×body640valid
8.0ms230×body80nan
7.0ms38×body1280valid
5.0ms124×body80valid
2.0ms15×body320valid
1.0ms13×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0116
1146
2146

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: 20.6b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
875×*-un-lft-identity
742×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
562×sqrt-prod
73×distribute-lft-out
54×div-inv
46×sqrt-div associate-/r/
23×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 739
Calls
3 calls:
9.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
43.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series245.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ 1.0 (sqrt x))
131.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify260.0ms

Algorithm
egg-herbie
Counts
748 → 748
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
0151724924
1419718301
2500118266

prune1.0s

Filtered
748 candidates to 285 candidates (38.1%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New73315748
Fresh000
Picked011
Done000
Total73316749

Merged error: 20.0b

Counts
749 → 16

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod
58×*-un-lft-identity
51×add-sqr-sqrt
42×prod-diff
35×add-cube-cbrt
17×add-exp-log add-cbrt-cube
9×distribute-lft-out
7×pow1 fma-neg associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×expm1-log1p-u pow-prod-down log1p-expm1-u distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 132
Calls
3 calls:
23.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series397.0ms

Counts
3 → 9
Calls
3 calls:
264.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify88.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06141715
128831280
250021185

prune246.0ms

Filtered
141 candidates to 76 candidates (53.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1356141
Fresh31114
Picked101
Done101
Total14017157

Merged error: 19.6b

Counts
157 → 17

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.2b
(+ x (- 1.0 x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
41×distribute-lft-out
36×add-sqr-sqrt
35×sqrt-prod
31×times-frac
29×add-exp-log add-cbrt-cube
28×add-cube-cbrt
11×associate-+r+
9×cbrt-undiv div-exp prod-diff add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u unswap-sqr
3×fma-def pow-prod-down associate-/l/
2×associate-+r- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 156
Calls
4 calls:
15.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms
(+ x (- 1.0 x))

series690.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
490.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify114.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
07991711
142361448
250011435

prune334.0ms

Filtered
168 candidates to 106 candidates (63.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1653168
Fresh11516
Picked101
Done000
Total1778185

Merged error: 0.2b

Counts
185 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
35×sqrt-prod
29×add-exp-log add-sqr-sqrt add-cbrt-cube
22×distribute-lft-out
21×add-cube-cbrt
19×times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×fma-def associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×expm1-log1p-u flip3-+ sqrt-div associate-/r/ flip-+ log1p-expm1-u associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 131
Calls
4 calls:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
497.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify93.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07041320
136361120
250021050

prune270.0ms

Filtered
143 candidates to 94 candidates (65.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New13211143
Fresh527
Picked101
Done000
Total13813151

Merged error: 0.0b

Counts
151 → 13

regimes49.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119
1119

end0.0ms

sample1.2s

Algorithm
intervals
Results
278.0ms8056×body80nan
263.0ms1876×body640valid
198.0ms1119×body1280valid
156.0ms4111×body80valid
63.0ms596×body320valid
21.0ms298×body160valid