Details

Time bar (total: 19.4s)

sample62.0ms

Algorithm
intervals
Results
45.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
211
111
010

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize59.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
26.6b
(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:
15.0ms
(+ (* re re) (* im im))
42.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
14.0ms
(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* re re) (* im im))
182.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
70.0ms
(sqrt (+ (* re re) (* im im)))

simplify742.0ms

Counts
86 → 86
Iterations
IterNodes
32282
2717
1265
0128

prune908.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.6b

localize30.0ms

Local error

Found 4 expressions with local error:

26.6b
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
27.7b
(cbrt (+ (* re re) (* im im)))
27.7b
(cbrt (+ (* re re) (* im im)))
27.7b
(cbrt (+ (* re re) (* im im)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 93
Calls
4 calls:
63.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
125.0ms
(cbrt (+ (* re re) (* im im)))
106.0ms
(cbrt (+ (* re re) (* im im)))
103.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.3s

Counts
105 → 105
Iterations
IterNodes
42816
31103
2492
1287
0166

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
27.8b
(log (+ (* re re) (* im im)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×*-un-lft-identity add-cube-cbrt
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 insert-posit16 associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×div-sub
1×frac-times +-commutative clear-num sum-log frac-2neg rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 168
Calls
4 calls:
14.0ms
(+ (* re re) (* im im))
45.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
41.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
11.0ms
(log (+ (* re re) (* im im)))

series622.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (* re re) (* im im))
184.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
292.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
90.0ms
(log (+ (* re re) (* im im)))

simplify3.6s

Counts
180 → 180
Iterations
IterNodes
36721
21913
1584
0218

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt 1/2) (cbrt 1/2))
1.0b
(sqrt (sqrt (log 10)))
1.0b
(sqrt (sqrt (log 10)))
27.8b
(log (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
24×sqrt-prod
18×pow1
17×*-un-lft-identity add-cube-cbrt
16×cbrt-prod
8×sqrt-pow1
7×add-exp-log
6×pow1/3 swap-sqr associate-*r* associate-*l*
4×rem-sqrt-square add-cbrt-cube pow1/2 insert-posit16 add-log-exp unswap-sqr
3×log-prod log-pow
2×log-div pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus rem-log-exp prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 98
Calls
4 calls:
7.0ms
(* (cbrt 1/2) (cbrt 1/2))
2.0ms
(sqrt (sqrt (log 10)))
2.0ms
(sqrt (sqrt (log 10)))
6.0ms
(log (+ (* re re) (* im im)))

series58.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(* (cbrt 1/2) (cbrt 1/2))
0.0ms
(sqrt (sqrt (log 10)))
0.0ms
(sqrt (sqrt (log 10)))
58.0ms
(log (+ (* re re) (* im im)))

simplify3.0s

Counts
104 → 104
Iterations
IterNodes
55740
41974
3896
2453
1234
0120

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

regimes733.0ms

Accuracy

56.6% (10.3b remaining)

Error of 17.4b against oracle of 7.1b and baseline of 30.8b

bsearch210.0ms

Steps
ItersRangePoint
10
0.0027002530800994988
446233850.42817044
441347509.722609
10
-5.9888586822218275e+144
-4.398408557398186e+133
-1.5084829120832133e+136

simplify9.0ms

Iterations
IterNodes
251
151
040

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.7s8000×body80valid