Details

Time bar (total: 3.7s)

sample29.0ms

Algorithm
intervals
Results
7.0ms203×body80valid
6.0ms19×body2560valid
2.0ms9×body5120valid
2.0ms10×body1280valid
1.0ms6×body640valid
0.0ms6×body160valid
0.0ms3×body320valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

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))
1.4b
(+ (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-log-exp
7×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt
4×add-exp-log flip3-+ sqrt-div sqrt-prod add-cbrt-cube flip-+
3×sqrt-pow1
2×+-commutative pow1/2 associate-*r/ sum-log
1×rem-sqrt-square pow-prod-down distribute-lft-out
Counts
4 → 51
Calls
4 calls:
24.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
10.0ms
(+ (* re re) (* im im))
31.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
29.0ms
(+ (* re re) (* im im))
54.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0274428
1986391
23089381
35002379

prune201.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.3b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 57
Calls
4 calls:
34.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series170.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
44.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0141392
1358380
2866376
32557375
45001375

prune312.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
57.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
34.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
43.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02671096
1974974
25001950

prune301.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.3b

localize22.0ms

Local error

Found 4 expressions with local error:

31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))
42.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify141.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (135.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune321.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 17.3b

regimes316.0ms

Accuracy

58.7% (8.9b remaining)

Error of 26.7b against oracle of 17.8b and baseline of 39.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05145
15545
25545

end0.0ms

sample733.0ms

Algorithm
intervals
Results
205.0ms6015×body80valid
138.0ms682×body2560valid
81.0ms497×body1280valid
69.0ms264×body5120valid
36.0ms288×body640valid
16.0ms167×body320valid
6.0ms87×body160valid