Details

Time bar (total: 4.0s)

sample34.0ms

Algorithm
intervals
Results
7.0ms276×body80nan
6.0ms40×body640valid
6.0ms49×body1280valid
4.0ms140×body80valid
1.0ms19×body320valid
0.0ms8×body160valid

simplify5.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.1b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.3b
(- (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))
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series106.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify44.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02991161
1921822
25001744

prune136.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh000
Picked101
Done000
Total92496

Merged error: 0.1b

Counts
96 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite31.0ms

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))
16.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series250.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(sqrt (+ x 1.0))
71.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0409789
11675716
25001675

prune199.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New967103
Fresh123
Picked011
Done000
Total9710107

Merged error: 0.0b

Counts
107 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (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:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
11.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ x 1.0))
92.0ms
(cbrt (+ x 1.0))
92.0ms
(cbrt (+ x 1.0))
113.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify157.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (146.0ms)

IterNodesCost
0321818
11071769
24756694
35001692

prune329.0ms

Filtered
115 candidates to 83 candidates (72.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1141115
Fresh178
Picked101
Done011
Total1169125

Merged error: 0.0b

Counts
125 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (fma (sqrt (pow (pow (sqrt (cbrt (+ x 1.0))) 4) 1)) (sqrt (cbrt (+ x 1.0))) (sqrt x)))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.4b
(pow (sqrt (cbrt (+ x 1.0))) 4)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
19×add-sqr-sqrt add-cube-cbrt
12×cbrt-prod times-frac
10×unpow-prod-down
7×add-exp-log sqrt-prod distribute-lft-out
6×pow1 add-cbrt-cube
4×expm1-log1p-u cbrt-div pow-pow log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow flip3-+ pow1/3 associate-/r* flip-+
2×sqrt-pow1 associate-/l/
1×cbrt-undiv pow-to-exp frac-2neg pow1/2 div-exp pow-exp clear-num sqrt-pow2 div-inv sqr-pow
Counts
4 → 97
Calls
4 calls:
5.0ms
(/ (+ 1.0 0) (fma (sqrt (pow (pow (sqrt (cbrt (+ x 1.0))) 4) 1)) (sqrt (cbrt (+ x 1.0))) (sqrt x)))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
7.0ms
(pow (sqrt (cbrt (+ x 1.0))) 4)

series667.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ (+ 1.0 0) (fma (sqrt (pow (pow (sqrt (cbrt (+ x 1.0))) 4) 1)) (sqrt (cbrt (+ x 1.0))) (sqrt x)))
91.0ms
(cbrt (+ x 1.0))
91.0ms
(cbrt (+ x 1.0))
151.0ms
(pow (sqrt (cbrt (+ x 1.0))) 4)

simplify97.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08401526
139541396
250011391

prune390.0ms

Filtered
109 candidates to 90 candidates (82.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1081109
Fresh077
Picked011
Done011
Total10810118

Merged error: 0.0b

Counts
118 → 10

regimes86.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample895.0ms

Algorithm
intervals
Results
212.0ms1687×body1280valid
201.0ms8187×body80nan
132.0ms1320×body640valid
107.0ms4069×body80valid
48.0ms625×body320valid
16.0ms299×body160valid