Details

Time bar (total: 3.4s)

sample39.0ms

Algorithm
intervals
Results
12.0ms184×body80valid
8.0ms28×body2560valid
5.0ms22×body1280valid
3.0ms9×body5120valid
1.0ms6×body640valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0198
1288
2368
3448
4468
5468

prune3.0ms

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: 40.8b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b
(- (sqrt (+ (* re re) (* im im))) re)
29.9b
(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×*-un-lft-identity
18×add-cube-cbrt prod-diff
17×sqrt-prod
7×pow1
6×fma-neg
5×add-log-exp
4×sqrt-div
3×add-exp-log expm1-log1p-u sqrt-pow1 add-cbrt-cube log1p-expm1-u
2×flip3-- pow1/2 associate-*r/ flip-- difference-of-squares
1×sub-neg rem-sqrt-square flip3-+ diff-log pow-prod-down flip-+ hypot-def distribute-lft-out--
Counts
3 → 74
Calls
3 calls:
14.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series250.0ms

Counts
3 → 9
Calls
3 calls:
165.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms
(- (sqrt (+ (* re re) (* im im))) re)
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0314760
11192522
25001473

prune177.0ms

Filtered
83 candidates to 59 candidates (71.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh000
Picked101
Done000
Total81384

Merged error: 6.5b

Counts
84 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 2.0 (- (hypot re im) re)))
1.0b
(- (hypot re im) re)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
5×pow1
4×add-log-exp
3×fma-neg
2×add-exp-log expm1-log1p-u flip3-- sqrt-pow1 sqrt-div associate-*r/ add-cbrt-cube flip-- log1p-expm1-u
1×sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
8.0ms
(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms
(- (hypot re im) re)

series232.0ms

Counts
2 → 6
Calls
2 calls:
175.0ms
(sqrt (* 2.0 (- (hypot re im) re)))
56.0ms
(- (hypot re im) re)

simplify132.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0221312
1728227
24440212
35001202

prune100.0ms

Filtered
49 candidates to 37 candidates (75.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New47249
Fresh112
Picked011
Done000
Total48452

Merged error: 6.5b

Counts
52 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
17.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1
2×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity sqrt-pow1 add-cbrt-cube log1p-expm1-u add-log-exp
1×pow1/2 pow-prod-down sqrt-prod fma-udef
Counts
2 → 23
Calls
2 calls:
3.0ms
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series390.0ms

Counts
2 → 6
Calls
2 calls:
239.0ms
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
151.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify52.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0135250
1408217
21603205
35001200

prune90.0ms

Filtered
29 candidates to 25 candidates (86.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New27229
Fresh022
Picked101
Done011
Total28533

Merged error: 6.5b

Counts
33 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
17.3b
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series470.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(cbrt (hypot re im))
115.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))
136.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify136.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 4 (131.0ms)

IterNodesCost
084329
1188287
2663279
33464272
45001263

prune189.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New58361
Fresh123
Picked101
Done011
Total60666

Merged error: 6.5b

Counts
66 → 6

regimes86.0ms

Accuracy

34.1% (3.9b remaining)

Error of 11.1b against oracle of 7.2b and baseline of 13.1b

bsearch27.0ms

Steps
ItersRangePoint
4
8.06938791009127e-11
1.1519417683705167e-10
9.902216227323653e-11

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
12913
22913

end0.0ms

sample917.0ms

Algorithm
intervals
Results
295.0ms6061×body80valid
193.0ms703×body2560valid
114.0ms487×body1280valid
93.0ms261×body5120valid
47.0ms259×body640valid
20.0ms146×body320valid
8.0ms83×body160valid

Profiling

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