Details

Time bar (total: 5.4s)

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: 31.1b

Counts
2 → 1

localize10.0ms

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))
28.6b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div associate-/r*
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls
3 calls:
4.0ms
(+ (* re re) (* im im))
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))

series199.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* re re) (* im im))
133.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0256741
1895697
22846694
35001694

prune206.0ms

Filtered
83 candidates to 55 candidates (66.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New701383
Fresh000
Picked101
Done000
Total711384

Merged error: 7.6b

Counts
84 → 13

localize12.0ms

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)))

rewrite48.0ms

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
9×unswap-sqr
7×associate-/r*
6×add-log-exp
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×div-sub
1×+-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:
4.0ms
(+ (* re re) (* im im))
23.0ms
(* (/ 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)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* re re) (* im im))
147.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
186.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
49.0ms
(log (+ (* re re) (* im im)))

simplify72.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05632163
123951981
250021899

prune377.0ms

Filtered
176 candidates to 104 candidates (59.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1688176
Fresh6612
Picked101
Done000
Total17514189

Merged error: 7.5b

Counts
189 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
14.6b
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
16.4b
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
44×times-frac
40×add-cube-cbrt *-un-lft-identity
25×pow-unpow associate-*l* sqrt-prod
21×log-prod
13×pow1
12×add-exp-log unpow-prod-down
9×add-cbrt-cube
8×log-pow
7×distribute-rgt-in distribute-lft-in
6×add-log-exp
4×associate-*r* sqr-pow
3×rem-log-exp unswap-sqr
2×pow-to-exp pow-exp prod-exp cbrt-unprod div-inv
1×cbrt-undiv +-commutative pow-pow flip3-+ div-exp pow-prod-down associate-*l/ sum-log *-commutative flip-+
Counts
4 → 128
Calls
4 calls:
4.0ms
(+ (* re re) (* im im))
13.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
5.0ms
(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
4 → 12
Calls
4 calls:
26.0ms
(+ (* re re) (* im im))
412.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
296.0ms
(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
326.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify69.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05541776
125191567
250021445

prune354.0ms

Filtered
140 candidates to 89 candidates (63.6%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1364140
Fresh11213
Picked011
Done000
Total13717154

Merged error: 7.5b

Counts
154 → 17

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
29.8b
(log (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
332×times-frac
189×sqrt-prod
179×associate-*r*
178×add-sqr-sqrt
154×add-cube-cbrt *-un-lft-identity
53×pow1
48×log-pow
13×add-exp-log
12×add-cbrt-cube
8×div-inv
7×unswap-sqr
5×add-log-exp
4×associate-*l*
3×cbrt-undiv log-prod div-exp prod-exp cbrt-unprod
2×log-div flip3-+ flip-+
1×+-commutative associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative
Counts
3 → 231
Calls
3 calls:
4.0ms
(+ (* re re) (* im im))
47.0ms
(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
4.0ms
(log (+ (* re re) (* im im)))

series225.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* re re) (* im im))
149.0ms
(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
48.0ms
(log (+ (* re re) (* im im)))

simplify94.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
08812994
143802543
250012530

prune410.0ms

Filtered
240 candidates to 105 candidates (43.8%)
Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New2373240
Fresh11415
Picked011
Done011
Total23819257

Merged error: 7.4b

Counts
257 → 19

regimes892.0ms

Accuracy

58% (10.4b remaining)

Error of 17.9b against oracle of 7.6b and baseline of 32.2b

bsearch98.0ms

Steps
ItersRangePoint
9
3756363593819.6455
2.7003150980902443e+20
1.9097657948152755e+20
8
-9.551618771889815e+129
-1.155698580497464e+126
-1.276151183917047e+126

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04533
14533

end0.0ms

sample614.0ms

Algorithm
intervals
Results
468.0ms8000×body80valid