Details

Time bar (total: 3.6s)

sample25.0ms

Algorithm
intervals
Results
6.0ms198×body80valid
5.0ms25×body2560valid
2.0ms14×body1280valid
1.0ms6×body5120valid
1.0ms8×body640valid
0.0ms5×body320valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0198
1288
2368
3448
4468
5468

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b
(- (sqrt (+ (* re re) (* im im))) re)
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

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:
3.0ms
(+ (* re re) (* im im))
27.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms
(- (sqrt (+ (* re re) (* im im))) re)
3.0ms
(sqrt (+ (* re re) (* im im)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* re re) (* im im))
169.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms
(- (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0342834
11366586
25001533

prune226.0ms

Filtered
100 candidates to 72 candidates (72.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.2b
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.5b
(- (* 1 (hypot re im)) re)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1
5×*-un-lft-identity add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×add-exp-log expm1-log1p-u prod-diff add-cbrt-cube log1p-expm1-u
2×flip3-- sqrt-pow1 sqrt-div associate-*r/ flip--
1×sub-neg hypot-udef pow1/2 fma-neg diff-log pow-prod-down sqrt-prod distribute-lft-out--
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot re im)
7.0ms
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
3.0ms
(- (* 1 (hypot re im)) re)

series284.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(hypot re im)
177.0ms
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
59.0ms
(- (* 1 (hypot re im)) re)

simplify33.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0235265
1803220
25002213

prune146.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize16.0ms

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))
10.2b
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod *-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3 prod-diff
1×sub-neg flip3-- fma-neg diff-log flip-- distribute-lft-out--
Counts
4 → 58
Calls
4 calls:
0.0ms
(cbrt (hypot re im))
0.0ms
(cbrt (hypot re im))
0.0ms
(cbrt (hypot re im))
37.0ms
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

series394.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))
59.0ms
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

simplify112.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0175475
1630366
23981323
35001314

prune233.0ms

Filtered
70 candidates to 59 candidates (84.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize15.0ms

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))
9.2b
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))) re)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod *-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3 prod-diff
1×sub-neg flip3-- fma-neg diff-log flip-- distribute-lft-out--
Counts
4 → 58
Calls
4 calls:
0.0ms
(cbrt (hypot re im))
0.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
100.0ms
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))) re)

series392.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(cbrt (hypot re im))
115.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))
60.0ms
(- (* 1 (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))) re)

simplify34.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0184561
1730406
25001364

prune235.0ms

Filtered
70 candidates to 58 candidates (82.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

regimes161.0ms

Accuracy

30.5% (4.1b remaining)

Error of 11.6b against oracle of 7.5b and baseline of 13.4b

bsearch26.0ms

Steps
ItersRangePoint
4
4.0640115501986475e+51
5.867938426223691e+51
5.4733294220932124e+51

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03114
13714
23714

end0.0ms

sample675.0ms

Algorithm
intervals
Results
199.0ms5993×body80valid
130.0ms691×body2560valid
79.0ms492×body1280valid
69.0ms300×body5120valid
35.0ms278×body640valid
14.0ms156×body320valid
5.0ms90×body160valid