Details

Time bar (total: 4.3s)

analyze5.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
74.9%25%0.1%3
87.4%12.5%0.1%4
93.7%6.2%0.1%5
96.8%3.1%0.1%6
98.3%1.6%0.1%7
99.1%0.8%0.1%8
99.5%0.4%0.1%9
99.7%0.2%0.1%10
99.8%0.1%0.1%11
99.9%0%0.1%12
99.9%0%0.1%13
99.9%0%0.1%14

sample22.0ms (0.5%)

Algorithm
intervals
Results
14.0ms256×body80valid

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01112
11112

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 1

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.7b
(sqrt (+ (* re re) (* im im)))

rewrite21.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
sqrt-pow1 pow1/2 associate-/l*
add-exp-log add-cbrt-cube add-log-exp
sqrt-div associate-/r*
flip3-+ sqrt-prod flip-+
log-div div-sub
cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls

3 calls:

8.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(+ (* re re) (* im im))

series28.0ms (0.6%)

Counts
3 → 9
Calls

3 calls:

17.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(+ (* re re) (* im im))

simplify52.0ms (1.2%)

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049161166
149161166

prune302.0ms (7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New691483
Fresh000
Picked101
Done000
Total701484

Merged error: 6.0b

Counts
84 → 14

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.8b
(log (+ (* re re) (* im im)))

rewrite42.0ms (1%)

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×add-cube-cbrt *-un-lft-identity
34×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
19×add-exp-log
18×add-cbrt-cube
unswap-sqr
associate-/r*
add-log-exp
cbrt-undiv div-exp
log-div prod-exp cbrt-unprod associate-/l*
log-prod flip3-+ flip-+ div-inv
div-sub
+-commutative frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
4 → 164
Calls

4 calls:

21.0ms
(* (/ 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)))
4.0ms
(+ (* re re) (* im im))

series58.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
20.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
9.0ms
(log (+ (* re re) (* im im)))
5.0ms
(+ (* re re) (* im im))

simplify97.0ms (2.2%)

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
049843029
149843029

prune498.0ms (11.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1697176
Fresh11213
Picked101
Done000
Total1819190

Merged error: 5.8b

Counts
190 → 9

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
29.8b
(log (+ (* re re) (* im im)))

rewrite39.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
46×add-sqr-sqrt times-frac
36×*-un-lft-identity
34×add-cube-cbrt
30×add-cbrt-cube
29×associate-*l*
26×associate-*r* sqrt-prod
22×prod-exp
19×pow1
12×cbrt-unprod
11×div-exp
log-pow
cbrt-undiv add-log-exp
associate-*r/ unswap-sqr
pow-prod-down
rec-exp log-prod 1-exp un-div-inv
frac-times log-div flip3-+ *-commutative flip-+ div-inv
+-commutative rem-log-exp associate-*l/ sum-log
Counts
4 → 133
Calls

4 calls:

13.0ms
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
11.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
6.0ms
(log (+ (* re re) (* im im)))
4.0ms
(+ (* re re) (* im im))

series59.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

23.0ms
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
21.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
9.0ms
(log (+ (* re re) (* im im)))
5.0ms
(+ (* re re) (* im im))

simplify69.0ms (1.6%)

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049491970
149491970

prune357.0ms (8.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1450145
Fresh088
Picked011
Done000
Total1459154

Merged error: 5.8b

Counts
154 → 9

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
0.4b
(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.8b
(log (+ (* re re) (* im im)))

rewrite63.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
126×sqrt-prod
112×times-frac
107×add-sqr-sqrt
69×add-cube-cbrt *-un-lft-identity
60×associate-*l*
42×pow1
31×log-pow
29×associate-*r*
21×add-exp-log
20×add-cbrt-cube
12×unswap-sqr
10×sqrt-div
prod-exp associate-/r* cbrt-unprod
frac-times associate-*r/
log-div pow-prod-down associate-*l/ div-inv associate-/l* add-log-exp
cbrt-undiv log-prod div-exp
flip3-+ div-sub *-commutative flip-+
frac-2neg rem-log-exp clear-num
Counts
4 → 207
Calls

4 calls:

23.0ms
(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
20.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
7.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms
(log (+ (* re re) (* im im)))

series105.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

48.0ms
(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
26.0ms
(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
21.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms
(log (+ (* re re) (* im im)))

simplify63.0ms (1.5%)

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049404416
149404416

prune857.0ms (19.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2145219
Fresh167
Picked011
Done011
Total21513228

Merged error: 5.7b

Counts
228 → 13

regimes694.0ms (16%)

Accuracy

Total 10.5b remaining (58%)

Threshold costs 0b (0%)

bsearch31.0ms (0.7%)

Steps
ItersRangePoint
8
4.968976558356122e+91
5.8774745178997e+94
8.860843829360954e+93
6
-2.0192875199418532e+51
-3.1573391340994785e+50
-1.8014590457402938e+51

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07268
17268

end0.0ms (0%)

sample797.0ms (18.4%)

Algorithm
intervals
Results
661.0ms8000×body80valid

Profiling

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