Details

Time bar (total: 20.8s)

sample80.0ms

Algorithm
intervals
Results
32.0ms274×body80nan
28.0ms256×body80valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5174
71116
6232
578
453
339
224
122
018

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
27.8b
(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div
3×flip3-+ sqrt-prod flip-+ insert-posit16
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Counts
3 → 77
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
48.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms
(sqrt (+ (* re re) (* im im)))

series273.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (* re re) (* im im))
168.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
59.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts
86 → 86
Iterations
IterNodes
done5003
32220
2686
1269
0133

prune549.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
27.8b
(sqrt (+ (* re re) (* im im)))
27.8b
(sqrt (+ (* re re) (* im im)))
27.8b
(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
7×pow1
6×cbrt-prod
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 65
Calls
4 calls:
9.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
16.0ms
(sqrt (+ (* re re) (* im im)))
15.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(sqrt (+ (* re re) (* im im)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
48.0ms
(sqrt (+ (* re re) (* im im)))
42.0ms
(sqrt (+ (* re re) (* im im)))
49.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts
77 → 77
Iterations
IterNodes
done5001
43626
31040
2341
1149
072

prune555.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
0.4b
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
27.8b
(sqrt (+ (* re re) (* im im)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
94×log-pow
91×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
79×pow1
34×associate-/r*
22×sqrt-pow1 pow1/2
17×add-exp-log
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv add-log-exp
4×cbrt-undiv insert-posit16
3×sqrt-prod
2×rec-exp clear-num frac-2neg flip3-+ sqrt-div 1-exp flip-+
1×+-commutative rem-sqrt-square sum-log associate-/r/ pow-flip inv-pow
Counts
4 → 212
Calls
4 calls:
9.0ms
(+ (* re re) (* im im))
27.0ms
(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
8.0ms
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
14.0ms
(sqrt (+ (* re re) (* im im)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* re re) (* im im))
158.0ms
(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
199.0ms
(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts
224 → 224
Iterations
IterNodes
done5000
34444
21558
1619
0254

prune718.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 8.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
0.5b
(* (log base) (log base))
27.8b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

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:
14.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
42.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
10.0ms
(* (log base) (log base))
8.0ms
(sqrt (+ (* re re) (* im im)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
122.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
164.0ms
(* (log base) (log base))
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts
126 → 126
Iterations
IterNodes
done5004
32717
21087
1492
0204

prune750.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.0b

regimes555.0ms

Accuracy

57.9% (10.1b remaining)

Error of 17.2b against oracle of 7.1b and baseline of 31.1b

bsearch172.0ms

Steps
ItersRangePoint
7
1.1272042506659227e+118
2.1601548166741077e+119
1.9754095442502022e+118
9
-1.753594842855003e+109
-5.168447646878728e+103
-4.976637077884882e+106

simplify4.0ms

Iterations
IterNodes
done26
126
023

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.7s8083×body80nan
1.7s8000×body80valid