Details

Time bar (total: 3.0s)

sample30.0ms

Algorithm
intervals
Results
6.0ms180×body80valid
5.0ms26×body2560valid
4.0ms15×body5120valid
3.0ms18×body1280valid
1.0ms10×body640valid
1.0msbody320valid
0.0msbody160valid

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: 38.9b

Counts
2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.7b
(- (sqrt (+ (* re re) (* im im))) re)
28.7b
(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×*-un-lft-identity
18×add-cube-cbrt prod-diff
16×sqrt-prod
add-log-exp
fma-neg
pow1
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
flip3-+ sqrt-div flip-+ difference-of-squares
+-commutative sub-neg rem-sqrt-square flip3-- fma-def sqrt-pow1 pow1/2 diff-log sum-log flip-- hypot-def distribute-lft-out--
Counts
3 → 73
Calls
3 calls:
4.0ms
(+ (* re re) (* im im))
8.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series114.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* re re) (* im im))
50.0ms
(- (sqrt (+ (* re re) (* im im))) re)
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0250664
11037430
25002381

prune175.0ms

Filtered
82 candidates to 56 candidates (68.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New78482
Fresh000
Picked101
Done000
Total79483

Merged error: 8.0b

Counts
83 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot re im)
0.7b
(- (hypot re im) re)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
add-cube-cbrt prod-diff
add-log-exp
fma-neg
pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
sub-neg hypot-udef flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 38
Calls
2 calls:
1.0ms
(hypot re im)
4.0ms
(- (hypot re im) re)

series101.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(hypot re im)
57.0ms
(- (hypot re im) re)

simplify52.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0130223
1366140
21695131
35001109

prune92.0ms

Filtered
44 candidates to 32 candidates (72.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New40444
Fresh213
Picked011
Done000
Total42648

Merged error: 7.9b

Counts
48 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot re im))
0.0b
(hypot re im)
0.0b
(hypot re im)
18.2b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
sqrt-prod
hypot-udef
rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 45
Calls
4 calls:
1.0ms
(sqrt (hypot re im))
1.0ms
(hypot re im)
1.0ms
(hypot re im)
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series322.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(sqrt (hypot re im))
47.0ms
(hypot re im)
47.0ms
(hypot re im)
141.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify51.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0130231
1357200
21503192
35001187

prune186.0ms

Filtered
57 candidates to 52 candidates (91.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New54357
Fresh134
Picked011
Done011
Total55863

Merged error: 7.9b

Counts
63 → 8

localize19.0ms

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))
18.1b
(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
cbrt-prod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity
pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
pow1/3
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 (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

series475.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))
117.0ms
(cbrt (hypot re im))
139.0ms
(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

simplify162.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
0105393
1266348
2917340
34671322
45001322

prune228.0ms

Filtered
61 candidates to 57 candidates (93.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New58361
Fresh145
Picked101
Done022
Total60969

Merged error: 7.9b

Counts
69 → 9

regimes118.0ms

Accuracy

29.9% (4.3b remaining)

Error of 11.2b against oracle of 6.9b and baseline of 13.0b

bsearch47.0ms

Steps
ItersRangePoint
8
1.501706784054669e-42
4.040994501375766e-39
2.4354963647518577e-40

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
12913
22913

end0.0ms

sample707.0ms

Algorithm
intervals
Results
222.0ms6067×body80valid
129.0ms662×body2560valid
87.0ms509×body1280valid
72.0ms287×body5120valid
32.0ms252×body640valid
16.0ms163×body320valid
4.0ms60×body160valid

Profiling

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