Details

Time bar (total: 5.7s)

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: 29.7b

localize11.0ms

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))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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:
3.0ms
(+ (* re re) (* im im))
11.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))

series200.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* re re) (* im im))
133.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify96.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0256741
1895697
22846694
35001694

prune233.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

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))))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

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:
3.0ms
(+ (* re re) (* im im))
44.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
12.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* re re) (* im im))
137.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
212.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06482798
128782493
250022395

prune471.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.7b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
46×times-frac
44×*-un-lft-identity
42×add-cube-cbrt
38×sqrt-prod
25×pow-unpow associate-*l*
20×log-prod
18×unpow-prod-down
15×pow1
14×add-exp-log
10×distribute-rgt-in distribute-lft-in
9×add-cbrt-cube
7×log-pow
6×add-log-exp
5×unswap-sqr
4×associate-*r* prod-exp
3×pow-pow sqr-pow
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp cbrt-unprod flip-+ div-inv
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square rec-exp 1-exp pow-prod-down associate-*l/ pow-exp sum-log *-commutative sqrt-pow2
Counts
4 → 141
Calls
4 calls:
3.0ms
(+ (* re re) (* im im))
24.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
7.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series910.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* re re) (* im im))
495.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
349.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05932050
127441681
250011554

prune407.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.0b

localize26.0ms

Local error

Found 4 expressions with local error:

3.7b
(pow (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10.0))))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
25×pow-unpow
24×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity times-frac sqrt-prod
15×pow-pow
10×add-exp-log
9×pow1/3 pow-prod-up
6×pow-plus sqrt-div
5×pow-prod-down
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp prod-exp pow-sqr log-pow flip-+
2×pow2
1×pow-to-exp unpow-prod-down pow3 div-inv sqr-pow
Counts
4 → 98
Calls
4 calls:
39.0ms
(pow (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10.0))))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
334.0ms
(pow (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03501263
11158908
25002846

prune356.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.0b

regimes980.0ms

Accuracy

56.6% (10.7b remaining)

Error of 18.3b against oracle of 7.6b and baseline of 32.2b

bsearch186.0ms

Steps
ItersRangePoint
11
5.10808278574109e+145
3.366560557353129e+171
1.7188497108846366e+152
8
3.382408398818948e-133
1.7648023804592677e-130
3.4134902923337802e-133
7
2.00818341296373e-296
3.449635196547704e-295
9.194803090293717e-296
7
-6.579287999353623e+83
-2.1130938932944453e+82
-6.296857350600111e+83

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05987
16887
27187
37387
47387

end0.0ms

sample486.0ms

Algorithm
intervals
Results
347.0ms8000×body80valid