Details

Time bar (total: 6.1s)

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

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))
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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)))

series197.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* re re) (* im im))
138.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
34.0ms
(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0256741
1895697
22846694
35001694

prune221.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
108×add-sqr-sqrt
78×sqrt-prod
67×*-un-lft-identity
61×add-cube-cbrt log-pow
53×pow1
46×associate-*r*
28×add-exp-log
25×associate-*l*
18×add-cbrt-cube
16×sqrt-pow1 pow1/2
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
6×associate-/l* add-log-exp
5×cbrt-undiv
4×sqrt-div cbrt-unprod
3×flip3-+ flip-+ div-inv
2×log-div rec-exp 1-exp div-sub
1×+-commutative frac-times rem-sqrt-square frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
4 → 205
Calls
4 calls:
4.0ms
(+ (* re re) (* im im))
29.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
8.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* re re) (* im im))
132.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
194.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06482798
128782493
250022395

prune456.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
45×add-cube-cbrt
41×sqrt-prod
30×log-prod
25×pow-unpow associate-*l*
24×unpow-prod-down
16×add-exp-log
15×pow1
10×distribute-rgt-in distribute-lft-in
9×add-cbrt-cube
8×log-pow
5×unswap-sqr
4×associate-*r* prod-exp add-log-exp sqr-pow
3×pow-pow rem-log-exp
2×pow-to-exp sqrt-pow1 pow1/2 sqrt-div div-exp pow-exp cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square rec-exp flip3-+ 1-exp pow-prod-down associate-*l/ *-commutative sqrt-pow2 flip-+
Counts
4 → 151
Calls
4 calls:
5.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
17.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
8.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series1.1s

Counts
4 → 12
Calls
4 calls:
298.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
478.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
331.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
34.0ms
(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05582291
123431895
250011744

prune435.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.6b

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.8b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
29.2b
(sqrt (+ (* re re) (* im im)))
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
50×pow-unpow
42×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt *-un-lft-identity
36×sqrt-prod
16×pow1
12×unpow-prod-down
6×add-exp-log pow-pow log-pow
4×sqrt-pow1 pow1/2 sqrt-div add-cbrt-cube add-log-exp
2×pow-to-exp rem-sqrt-square flip3-+ pow-exp sqrt-pow2 flip-+ div-inv sqr-pow
Counts
4 → 120
Calls
4 calls:
8.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
11.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
336.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
336.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
39.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03051184
110011106
233381032
350021028

prune524.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.6b

regimes859.0ms

Accuracy

55.5% (11.2b remaining)

Error of 18.1b against oracle of 6.9b and baseline of 32.1b

bsearch124.0ms

Steps
ItersRangePoint
10
7.491092794297452e+92
1.1133938054187134e+105
6.127379446422431e+97
8
-6.229466306237523e+17
-1134389816868286.8
-6.127312286411e+17

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05956
15956

end0.0ms

sample494.0ms

Algorithm
intervals
Results
348.0ms8000×body80valid