Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
4×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`log-div` `flip3-+` `div-sub` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 63

Calls

2 calls:

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

series168.0ms

Counts

2 → 6

Calls

2 calls:

129.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

69 → 69

Iterations

Useful iterations: 3 (204.0ms)

Iter	Nodes	Cost
0	116	1191
1	225	1120
2	554	1046
3	1373	1032
4	3872	1032
done	5001	1032

prune203.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 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)))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
107×	`add-sqr-sqrt`
78×	`sqrt-prod`
66×	`*-un-lft-identity`
61×	`log-pow`
60×	`add-cube-cbrt`
52×	`pow1`
46×	`associate-r`
27×	`add-exp-log`
25×	`associate-l`
17×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`div-inv` `add-log-exp`
2×	`log-div` `rec-exp` `flip3-+` `1-exp` `div-sub` `flip-+`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 194

Calls

3 calls:

46.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
13.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series377.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
202.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify980.0ms

Counts

203 → 203

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	238	4455
1	620	4097
2	2074	3528
done	5000	3528

prune433.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
46×	`add-sqr-sqrt` `times-frac`
40×	`prod-exp`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
31×	`associate-l`
29×	`sqrt-prod` `add-cbrt-cube`
26×	`associate-r`
20×	`div-exp`
19×	`pow1`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
9×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`un-div-inv` `add-log-exp`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `flip3-+` `associate-*l/` `flip-+`

Counts

3 → 135

Calls

3 calls:

36.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
17.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series387.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
210.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.7s

Counts

144 → 144

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	205	3101
1	523	2613
2	1518	1930
3	3915	1920
done	5000	1920

prune346.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b	(* (/ 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))))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

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:

6.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
26.0ms	(* (/ 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))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

295.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
354.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
339.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

163 → 163

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	229	3870
1	565	3539
2	1874	2753
done	5000	2733

prune407.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

regimes757.0ms

Accuracy

57.3% (10.2b remaining)

Error of 17.6b against oracle of 7.3b and baseline of 31.3b

bsearch186.0ms

Steps

Iters	Range		Point
9	6.3129433769575865e+100	1.1419719569126802e+107	4.4853367152010175e+105
10	-6.170392859290159e-228	-5.7033062948028695e-238	-6.084564628966416e-228
9	-7.407647349127261e-206	-2.5535425374078063e-212	-2.6032323348577763e-212
10	-2.7283838574175814e+156	-2.4047927607493394e+144	-2.8015950926867568e+144

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	39	99
1	48	95
2	50	95
done	50	95

end0.0ms

sample471.0ms

Algorithm

intervals

Results

335.0ms

8000×

body

valid