Details

Time bar (total: 16.5s)

sample131.0ms

Algorithm
intervals
Results
61.0ms256×body80valid
47.0ms238×body80nan

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2408
82408
71116
6232
578
453
339
224
122
018

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.7b

localize30.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
30.3b
(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
4×associate-/r* add-cbrt-cube sqrt-div add-exp-log
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ insert-posit16 add-log-exp
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-exp div-inv
Counts
2 → 65
Calls
2 calls:
30.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms
(sqrt (+ (* re re) (* im im)))

series166.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
71 → 71
Iterations
IterNodes
done2070
42070
31336
2524
1233
0123

prune349.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1 (log base))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
30.3b
(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×times-frac
23×*-un-lft-identity
22×add-cube-cbrt
16×pow1 associate-*r* add-exp-log
10×add-cbrt-cube log-pow
6×associate-*l*
4×associate-/r* div-exp prod-exp
3×sqrt-prod insert-posit16 associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 sqrt-div 1-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg flip3-+ pow-prod-down associate-*r/ un-div-inv *-commutative flip-+ pow-flip inv-pow
Counts
3 → 95
Calls
3 calls:
8.0ms
(/ 1 (log base))
32.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
10.0ms
(sqrt (+ (* re re) (* im im)))

series376.0ms

Counts
3 → 9
Calls
3 calls:
198.0ms
(/ 1 (log base))
124.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
104 → 104
Iterations
IterNodes
done2000
42000
31616
2800
1319
0142

prune498.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b
(* (log base) (log base))
30.3b
(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×pow1 add-cube-cbrt
12×log-prod
10×add-cbrt-cube associate-*l* add-exp-log log-pow
9×times-frac
8×associate-*r*
6×distribute-rgt-in distribute-lft-in swap-sqr
4×insert-posit16 add-log-exp
3×associate-/r* flip3-+ sqrt-prod flip-+ associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod unswap-sqr associate-/l/
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg pow-plus div-exp pow-sqr pow-prod-up div-inv
Counts
4 → 114
Calls
4 calls:
60.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
18.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms
(* (log base) (log base))
9.0ms
(sqrt (+ (* re re) (* im im)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
119.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
246.0ms
(* (log base) (log base))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
done2003
32003
21099
1492
0204

prune760.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.7b

localize33.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1 (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log base))))
0.3b
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
30.3b
(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
27×times-frac
24×pow1
23×add-cbrt-cube div-exp
22×log-pow
19×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
12×prod-exp
10×cbrt-undiv
7×associate-/r* associate-/l*
6×sqrt-pow1 pow1/2
5×rec-exp 1-exp
4×cbrt-unprod
3×associate-/r/ sqrt-prod insert-posit16 add-log-exp
2×clear-num frac-2neg sqrt-div div-inv pow-flip
1×frac-times rem-sqrt-square flip3-+ pow-prod-down associate-*l/ associate-*r/ flip-+ inv-pow
Counts
3 → 107
Calls
3 calls:
28.0ms
(/ 1 (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log base))))
7.0ms
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
7.0ms
(sqrt (+ (* re re) (* im im)))

series394.0ms

Counts
3 → 9
Calls
3 calls:
167.0ms
(/ 1 (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log base))))
181.0ms
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
45.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts
116 → 116
Iterations
IterNodes
done2011
42011
31979
2800
1404
0189

prune400.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 5.7b

regimes757.0ms

Accuracy

55.5% (10.5b remaining)

Error of 17.7b against oracle of 7.3b and baseline of 30.8b

bsearch421.0ms

Steps
ItersRangePoint
6
2.740698701752476e+54
2.0621309002659428e+55
1.923554289447892e+55
7
-1.919784781288074e-306
-4.593510748503278e-308
-1.7888060498818623e-307
6
-6.126291507130798e-234
-1.5186925114434545e-234
-2.289233214842376e-234
9
-16883.399250034305
-6.558941820044306e-05
-16436.105427898932

simplify15.0ms

Iterations
IterNodes
done55
355
253
152
044

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.2s8000×body80valid
2.0s8086×body80nan