Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	185×	body	80	valid
8.0ms	29×	body	2560	valid
5.0ms	13×	body	5120	valid
3.0ms	14×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	24	15
done	24	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

37.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
32.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
18.0ms	(sqrt (+ (* re re) (* im im)))

series339.0ms

Counts

3 → 9

Calls

3 calls:

233.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify549.0ms

Counts

49 → 49

Iterations

Useful iterations: done (547.0ms)

Iter	Nodes	Cost
0	99	722
1	251	621
2	954	569
done	5001	545

prune270.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

68.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
36.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
62.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
60.0ms	(sqrt (+ (* re re) (* im im)))
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	133	3041
1	300	1750
2	1110	1579
done	5000	1544

prune559.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)))
0.6b	(+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)
28.0b	(sqrt (+ (* im im) (* re re)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log`

Counts

3 → 39

Calls

3 calls:

56.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)))
33.0ms	(+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)
9.0ms	(sqrt (+ (* im im) (* re re)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)))
67.0ms	(+ (* (sqrt (sqrt 1)) (sqrt (+ (* im im) (* re re)))) re)
47.0ms	(sqrt (+ (* im im) (* re re)))

simplify852.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (315.0ms)

Iter	Nodes	Cost
0	118	895
1	325	724
2	1422	592
done	5000	592

prune255.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
13.7b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

25.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
65.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
69.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
65.0ms	(sqrt (+ (* re re) (* im im)))
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	151	1948
1	488	1500
2	1770	1345
done	5002	1287

prune561.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.7b

regimes389.0ms

Accuracy

53.7% (13.3b remaining)

Error of 23.3b against oracle of 10.0b and baseline of 38.7b

bsearch509.0ms

Steps

Iters	Range		Point
6	8.279266058261865e+86	5.158400896377674e+87	3.218748827894776e+87
10	4.55069835955133e+33	3.3925201621099505e+51	4.757023444309772e+34
7	6.605278399860118e-92	2.2238042519166395e-90	1.7640701635345317e-90
9	8.586179648932124e-129	2.453329268167905e-120	4.9892708591511305e-124
8	-4.56186421133043e-258	-8.235648826256163e-262	-9.014365595105152e-259
10	-2.1595158930405206e+94	-1.4003310428377996e+80	-1.9799446773568452e+87

simplify1.2s

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	63	134
1	87	124
2	106	118
3	132	118
4	188	118
5	311	118
6	593	118
7	1256	118
8	2836	118
done	5001	118

end0.0ms

sample2.3s

Algorithm

intervals

Results

762.0ms	694×	body	2560	valid
640.0ms	6000×	body	80	valid
232.0ms	306×	body	5120	valid
186.0ms	523×	body	1280	valid
156.0ms	254×	body	640	valid
29.0ms	144×	body	320	valid
11.0ms	79×	body	160	valid