Details

Time bar (total: 3.5s)

sample33.0ms

Algorithm
intervals
Results
9.0ms192×body80valid
7.0ms24×body2560valid
4.0ms11×body5120valid
3.0ms16×body1280valid
1.0ms8×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune2.0ms

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: 37.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
11.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series316.0ms

Counts
3 → 9
Calls
3 calls:
231.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0247351
1781333
22656327
35001325

prune144.0ms

Filtered
49 candidates to 42 candidates (85.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New44549
Fresh000
Picked011
Done000
Total44650

Merged error: 18.1b

Counts
50 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

9.5b
(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:
21.0ms
(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (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)))

series158.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0160641
1431527
21354481
35001477

prune221.0ms

Filtered
68 candidates to 61 candidates (89.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New67168
Fresh044
Picked101
Done101
Total69574

Merged error: 18.1b

Counts
74 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

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

series145.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
41.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify147.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (136.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune305.0ms

Filtered
72 candidates to 60 candidates (83.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh044
Picked011
Done000
Total72577

Merged error: 18.1b

Counts
77 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (+ (* re re) (* im im))) re)
6.3b
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
19.1b
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×pow1
7×add-cube-cbrt sqrt-prod
6×times-frac associate-/r* add-log-exp difference-of-squares
3×sqrt-pow1 sqrt-div distribute-lft-out--
2×cbrt-undiv flip3-- pow1/2 div-exp associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
12.0ms
(- (sqrt (+ (* re re) (* im im))) re)
10.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms
(sqrt (+ (* re re) (* im im)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (sqrt (+ (* re re) (* im im))) re)
225.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
74.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0362695
11503628
25001624

prune192.0ms

Filtered
83 candidates to 65 candidates (78.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New78583
Fresh123
Picked101
Done101
Total81788

Merged error: 14.3b

Counts
88 → 7

regimes157.0ms

Accuracy

50.3% (13.3b remaining)

Error of 27.7b against oracle of 14.4b and baseline of 41.2b

bsearch102.0ms

Steps
ItersRangePoint
9
8.850304217014897e-16
2.8262556577633816e-09
6.35425561113628e-15
7
-1.269270905055957e+156
-6.523895171398485e+153
-1.324813134382297e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03821
13821

end0.0ms

sample884.0ms

Algorithm
intervals
Results
284.0ms6011×body80valid
197.0ms723×body2560valid
117.0ms512×body1280valid
78.0ms244×body5120valid
48.0ms279×body640valid
19.0ms149×body320valid
7.0ms82×body160valid

Profiling

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