Details

Time bar (total: 3.4s)

sample25.0ms

Algorithm
intervals
Results
7.0ms203×body80valid
3.0ms13×body5120valid
3.0ms16×body1280valid
3.0ms13×body2560valid
1.0ms7×body640valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(+ (sqrt (+ (* re re) (* im im))) re)
0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:
4.0ms
(+ (* re re) (* im im))
6.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* re re) (* im im))
48.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
173.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0274428
1986391
23089381
35002379

prune191.0ms

Filtered
63 candidates to 52 candidates (82.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
5.8b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

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:
14.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02671096
1974974
25001950

prune291.0ms

Filtered
136 candidates to 74 candidates (54.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.0b

localize19.0ms

Local error

Found 4 expressions with local error:

11.0b
(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
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
Counts
4 → 56
Calls
4 calls:
25.0ms
(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
39.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0172663
1540575
21978556
35002527

prune293.0ms

Filtered
68 candidates to 58 candidates (85.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.9b

localize30.0ms

Local error

Found 4 expressions with local error:

32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
33.9b
(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
Calls
4 calls:
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))
92.0ms
(cbrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0141422
1440404
21469402
35002399

prune380.0ms

Filtered
70 candidates to 60 candidates (85.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.9b

regimes159.0ms

Accuracy

59.4% (8.8b remaining)

Error of 26.3b against oracle of 17.4b and baseline of 39.2b

bsearch72.0ms

Steps
ItersRangePoint
7
8.038692978176935e+71
1.1196446523800873e+74
1.1038304751290051e+74
7
-8.600867818901156e-299
-2.096985094049225e-300
-2.1284573403280654e-300

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04531
14931
24931

end0.0ms

sample687.0ms

Algorithm
intervals
Results
201.0ms6028×body80valid
134.0ms664×body2560valid
83.0ms301×body5120valid
80.0ms492×body1280valid
34.0ms268×body640valid
16.0ms171×body320valid
5.0ms76×body160valid