Details

Time bar (total: 6.2s)

sample24.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

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: 36.1b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
33.4b
(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms
(sqrt (+ (* re re) (* im im)))

series169.0ms

Counts
2 → 6
Calls
2 calls:
130.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify133.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (121.0ms)

IterNodesCost
0221664
1556631
21309628
34251628
45001627

prune201.0ms

Filtered
69 candidates to 45 candidates (65.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New551469
Fresh000
Picked101
Done000
Total561470

Merged error: 9.6b

Counts
70 → 14

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
34.7b
(log (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
82×add-sqr-sqrt
54×sqrt-prod
52×add-cube-cbrt *-un-lft-identity
33×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
18×add-exp-log
17×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod div-inv add-log-exp
2×flip3-+ div-sub flip-+
1×frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 153
Calls
3 calls:
22.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms
(log (+ (* re re) (* im im)))

series383.0ms

Counts
3 → 9
Calls
3 calls:
141.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
191.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
51.0ms
(log (+ (* re re) (* im im)))

simplify60.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05282080
120811913
250011831

prune390.0ms

Filtered
162 candidates to 94 candidates (58.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1548162
Fresh9413
Picked101
Done000
Total16412176

Merged error: 9.4b

Counts
176 → 12

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
17.4b
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.0b
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
44×times-frac
39×add-cube-cbrt *-un-lft-identity
25×pow-unpow associate-*l* sqrt-prod
21×log-prod
12×pow1 unpow-prod-down
11×add-exp-log
8×log-pow add-cbrt-cube
7×distribute-rgt-in distribute-lft-in
4×associate-*r* sqr-pow
3×rem-log-exp add-log-exp unswap-sqr
2×pow-to-exp pow-exp prod-exp cbrt-unprod div-inv
1×cbrt-undiv pow-pow div-exp pow-prod-down associate-*l/ *-commutative
Counts
3 → 117
Calls
3 calls:
17.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
4.0ms
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
7.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts
3 → 9
Calls
3 calls:
522.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
295.0ms
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
311.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify58.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04631699
119901501
250011310

prune345.0ms

Filtered
126 candidates to 80 candidates (63.5%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1233126
Fresh01111
Picked011
Done000
Total12315138

Merged error: 9.3b

Counts
138 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
34.7b
(log (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
126×sqrt-prod
112×times-frac
107×add-sqr-sqrt
69×add-cube-cbrt *-un-lft-identity
56×associate-*l*
42×pow1
33×associate-*r*
31×log-pow
21×add-exp-log
20×add-cbrt-cube
12×unswap-sqr
10×sqrt-div
7×prod-exp associate-/r* cbrt-unprod
6×frac-times associate-*r/
4×log-div pow-prod-down associate-*l/ div-inv associate-/l* add-log-exp
3×cbrt-undiv log-prod div-exp
2×flip3-+ div-sub *-commutative flip-+
1×frac-2neg rem-log-exp clear-num
Counts
4 → 207
Calls
4 calls:
19.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
27.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms
(log (+ (* re re) (* im im)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
455.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
184.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
51.0ms
(log (+ (* re re) (* im im)))

simplify93.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06403171
128052920
250012882

prune586.0ms

Filtered
219 candidates to 136 candidates (62.1%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New2145219
Fresh31013
Picked011
Done011
Total21717234

Merged error: 9.3b

Counts
234 → 17

regimes603.0ms

Accuracy

55.8% (10.9b remaining)

Error of 18.4b against oracle of 7.5b and baseline of 32.2b

bsearch226.0ms

Steps
ItersRangePoint
1
8.549531690056054e+66
9.237151171742518e+66
8.721436560477669e+66
9
9.511891588263079e-214
1.625473957011741e-208
1.9800036494721456e-210
4
1.4426124596063804e-295
2.578047702902632e-295
1.8808986097929313e-295
9
-1.6613505346969782e-234
-1.1875715719458275e-240
-5.684970364589658e-240
8
-3.054829626739183e-209
-4.6249165735205644e-212
-2.268704362676497e-210
8
-8716053662791948.0
-13967805288982.43
-8633833088570918.0

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07088
17088

end0.0ms

sample662.0ms

Algorithm
intervals
Results
506.0ms8000×body80valid

Profiling

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