Details

Time bar (total: 3.7s)

sample35.0ms

Algorithm
intervals
Results
9.0ms187×body80valid
5.0ms18×body2560valid
4.0ms12×body5120valid
4.0ms18×body1280valid
2.0ms12×body640valid
1.0ms6×body160valid
0.0ms3×body320valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0248
1308
2338
3338

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: 39.0b

Counts
2 → 1

localize14.0ms

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)))
1.8b
(+ (sqrt (+ (* re re) (* im im))) re)
28.7b
(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×pow1 add-sqr-sqrt add-log-exp
7×add-cube-cbrt fma-def sqrt-prod
4×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-pow1
2×+-commutative pow1/2 associate-*r/ sum-log
1×rem-sqrt-square pow-prod-down hypot-def distribute-lft-out
Counts
4 → 67
Calls
4 calls:
4.0ms
(+ (* re re) (* im im))
8.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* re re) (* im im))
174.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0296446
11086401
23561382
35001381

prune207.0ms

Filtered
79 candidates to 69 candidates (87.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New75479
Fresh000
Picked101
Done000
Total76480

Merged error: 7.6b

Counts
80 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.2b
(sqrt (* 2.0 (+ (hypot re im) re)))
1.6b
(+ (hypot re im) re)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 *-un-lft-identity
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×add-exp-log expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative hypot-udef pow1/2 pow-prod-down sum-log sqrt-prod distribute-lft-out
Counts
3 → 42
Calls
3 calls:
1.0ms
(hypot re im)
5.0ms
(sqrt (* 2.0 (+ (hypot re im) re)))
7.0ms
(+ (hypot re im) re)

series290.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(hypot re im)
186.0ms
(sqrt (* 2.0 (+ (hypot re im) re)))
54.0ms
(+ (hypot re im) re)

simplify56.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0196197
1536180
21779174
35002172

prune126.0ms

Filtered
51 candidates to 46 candidates (90.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New47451
Fresh213
Picked011
Done000
Total49655

Merged error: 7.3b

Counts
55 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (hypot re im) re))
0.0b
(hypot re im)
0.3b
(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
1.6b
(+ (hypot re im) re)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
15×sqrt-prod
10×add-cube-cbrt
9×pow1
7×associate-*r*
6×add-exp-log associate-*l* add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u unswap-sqr
3×fma-def sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out
2×associate-*r/
1×+-commutative rem-sqrt-square hypot-udef sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod hypot-def
Counts
4 → 81
Calls
4 calls:
3.0ms
(sqrt (+ (hypot re im) re))
1.0ms
(hypot re im)
8.0ms
(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
3.0ms
(+ (hypot re im) re)

series422.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (+ (hypot re im) re))
51.0ms
(hypot re im)
188.0ms
(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
59.0ms
(+ (hypot re im) re)

simplify118.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0300457
11015427
24386412
35001411

prune205.0ms

Filtered
93 candidates to 74 candidates (79.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh044
Picked011
Done011
Total93699

Merged error: 7.3b

Counts
99 → 6

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))
10.8b
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
9.0ms
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series397.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(cbrt (hypot re im))
115.0ms
(cbrt (hypot re im))
109.0ms
(cbrt (hypot re im))
58.0ms
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify51.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0146395
1420316
21490274
35002272

prune189.0ms

Filtered
65 candidates to 60 candidates (92.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New63265
Fresh033
Picked101
Done022
Total64771

Merged error: 7.3b

Counts
71 → 7

regimes65.0ms

Accuracy

29% (4.4b remaining)

Error of 12.1b against oracle of 7.7b and baseline of 13.9b

bsearch40.0ms

Steps
ItersRangePoint
6
-6.273963436367294e-104
-4.339042744353832e-105
-6.104780096278364e-104

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
12913
22913

end0.0ms

sample960.0ms

Algorithm
intervals
Results
295.0ms5931×body80valid
205.0ms720×body2560valid
117.0ms506×body1280valid
102.0ms298×body5120valid
58.0ms309×body640valid
20.0ms148×body320valid
8.0ms88×body160valid