Details

Time bar (total: 4.0s)

sample27.0ms

Algorithm
intervals
Results
7.0ms196×body80valid
5.0ms27×body2560valid
3.0ms16×body1280valid
1.0ms8×body640valid
1.0ms4×body5120valid
0.0ms3×body320valid
0.0ms2×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 add-cube-cbrt
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 38
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
32.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series123.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* re re) (* im im))
54.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0178275
1689252
22017248
35001246

prune159.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

28.2b
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
29.1b
(cbrt (+ (* re re) (* im im)))
29.1b
(cbrt (+ (* re re) (* im im)))
29.1b
(cbrt (+ (* re re) (* im im)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
68.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
104.0ms
(cbrt (+ (* re re) (* im im)))
104.0ms
(cbrt (+ (* re re) (* im im)))
104.0ms
(cbrt (+ (* re re) (* im im)))

simplify223.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (210.0ms)

IterNodesCost
02871504
17011463
230661446
350011379

prune303.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 16.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.7b
(exp (log (sqrt (+ (* re re) (* im im)))))
14.5b
(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
3×log-pow
2×+-commutative log-div sqrt-pow1 pow1/2 exp-diff sum-log
1×rem-sqrt-square rem-exp-log distribute-lft-out
Counts
4 → 60
Calls
4 calls:
8.0ms
(+ (* re re) (* im im))
10.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
47.0ms
(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series175.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* re re) (* im im))
45.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
53.0ms
(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
46.0ms
(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0225472
1761420
22155403
35002394

prune211.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
6.1b
(pow (exp 1/2) (log (+ (* re re) (* im im))))
14.5b
(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
29.1b
(log (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt add-cube-cbrt
8×add-log-exp
7×pow1
6×log-prod
5×add-exp-log
4×log-div pow-unpow pow-pow flip3-+ add-cbrt-cube flip-+
3×unpow-prod-up unpow-prod-down exp-prod
2×+-commutative sum-log log-pow pow-sub
1×pow-to-exp rem-log-exp pow-exp distribute-lft-out sqr-pow
Counts
4 → 63
Calls
4 calls:
10.0ms
(+ (* re re) (* im im))
10.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
46.0ms
(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
6.0ms
(log (+ (* re re) (* im im)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* re re) (* im im))
103.0ms
(pow (exp 1/2) (log (+ (* re re) (* im im))))
92.0ms
(+ (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
51.0ms
(log (+ (* re re) (* im im)))

simplify110.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0294578
11016535
23325530
35001530

prune224.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 16.8b

regimes495.0ms

Accuracy

55.8% (9.2b remaining)

Error of 26.7b against oracle of 17.5b and baseline of 38.3b

bsearch111.0ms

Steps
ItersRangePoint
9
1.0503009045500217e+63
8.52518331542308e+67
8.439330033545885e+67
7
1.8198961796190227e-246
5.008869003657369e-245
3.6148118604621735e-246
9
-4.394634857083432e-256
-8.20373527102732e-264
-8.500232528907394e-258

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
14826

end0.0ms

sample724.0ms

Algorithm
intervals
Results
204.0ms6034×body80valid
142.0ms716×body2560valid
75.0ms463×body1280valid
66.0ms279×body5120valid
38.0ms262×body640valid
15.0ms158×body320valid
5.0ms88×body160valid