Details

sample25.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 31.0b

localize22.0ms

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))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

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:

8.0ms	(+ (* re re) (* im im))
47.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
11.0ms	(sqrt (+ (* re re) (* im im)))

series342.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ (* re re) (* im im))
247.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.4s

Counts

83 → 83

Iterations

Useful iterations: 3 (964.0ms)

Iter	Nodes	Cost
0	125	1357
1	254	1281
2	588	1165
3	1394	1163
4	3509	1163
done	5001	1163

prune385.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite210.0ms

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:

9.0ms	(+ (* re re) (* im im))
100.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
60.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
25.0ms	(sqrt (+ (* re re) (* im im)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* re re) (* im im))
241.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
336.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.8s

Counts

217 → 217

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	247	4621
1	620	4164
2	1705	3647
3	4488	3643
done	5000	3547

prune519.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
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))))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

15.0ms	(+ (* re re) (* im im))
109.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
43.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* re re) (* im im))
181.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
295.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

158 → 158

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	214	3267
1	508	2700
2	1329	2055
3	3184	2051
done	5001	2051

prune526.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite154.0ms

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:

16.0ms	(+ (* re re) (* im im))
88.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
25.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
15.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* re re) (* im im))
459.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
483.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.4s

Counts

153 → 153

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	238	3510
1	573	3107
2	1436	2450
3	3742	2372
done	5000	2336

prune498.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.0b

regimes1.3s

Accuracy

59% (10.2b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 32.2b

bsearch144.0ms

Steps

Iters	Range		Point
10	1.2073698495971617e+61	3.217811591970086e+74	2.7153468834491098e+73
5	-1.7457635943519997e+137	-5.665103565004941e+136	-9.983262521343274e+136

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	60
1	37	60
done	37	60

end0.0ms

sample1.0s

Algorithm

intervals

Results

764.0ms

8000×

body

valid