Details

Time bar (total: 3.7s)

sample30.0ms

Algorithm
intervals
Results
7.0ms22×body2560valid
7.0ms194×body80valid
3.0ms13×body5120valid
2.0ms14×body1280valid
1.0ms8×body640valid
0.0ms5×body320valid

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b
(+ (* re re) (* im im))
0.0b
(- (sqrt (+ (* re re) (* im im))) re)
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
17×sqrt-prod
8×pow1 add-log-exp
6×fma-neg
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square fma-def diff-log pow-prod-down sum-log hypot-def distribute-lft-out--
Counts
4 → 88
Calls
4 calls:
13.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms
(+ (* re re) (* im im))
8.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
26.0ms
(+ (* re re) (* im im))
46.0ms
(- (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0342834
11366586
25001533

prune232.0ms

Filtered
100 candidates to 72 candidates (72.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0b
(hypot re im)
0.0b
(- (hypot re im) re)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
6×pow1
5×add-log-exp
3×add-exp-log expm1-log1p-u fma-neg add-cbrt-cube log1p-expm1-u
2×sqrt-pow1 sqrt-div associate-*r/
1×sub-neg hypot-udef flip3-- flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
7.0ms
(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.0ms
(hypot re im)
4.0ms
(- (hypot re im) re)

series282.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
44.0ms
(hypot re im)
58.0ms
(- (hypot re im) re)

simplify52.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0283345
11118247
25001236

prune157.0ms

Filtered
62 candidates to 49 candidates (79.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
0.0b
(hypot re im)
0.0b
(hypot re im)
14.9b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
4×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
2×hypot-udef sqrt-pow1 sqrt-div associate-*r/
1×flip3-+ pow1/2 pow-prod-down sqrt-prod flip-+ fma-udef
Counts
4 → 45
Calls
4 calls:
5.0ms
(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
1.0ms
(hypot re im)
1.0ms
(hypot re im)
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series484.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
44.0ms
(hypot re im)
49.0ms
(hypot re im)
143.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify38.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0207358
1759315
25001299

prune224.0ms

Filtered
57 candidates to 53 candidates (93.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
14.9b
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (* -1 re))

rewrite6.0ms

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)) (* -1 re))

series477.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(cbrt (hypot re im))
111.0ms
(cbrt (hypot re im))
112.0ms
(cbrt (hypot re im))
145.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (* -1 re))

simplify154.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 4 (142.0ms)

IterNodesCost
086329
1193286
2704278
33770271
45001262

prune210.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

regimes140.0ms

Accuracy

22.9% (4.4b remaining)

Error of 11.5b against oracle of 7.0b and baseline of 12.8b

bsearch52.0ms

Steps
ItersRangePoint
7
3.3765927396946256e+151
1.3584121836592172e+153
4.412835503564449e+151

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
13314
23314

end0.0ms

sample690.0ms

Algorithm
intervals
Results
214.0ms6089×body80valid
135.0ms656×body2560valid
76.0ms460×body1280valid
69.0ms287×body5120valid
35.0ms266×body640valid
15.0ms159×body320valid
5.0ms83×body160valid