Details

sample205.0ms

Algorithm

intervals

Results

59.0ms	8×	body	5120	valid
31.0ms	197×	body	80	valid
20.0ms	24×	body	1280	valid
15.0ms	15×	body	2560	valid
5.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	35
4	35
3	30
2	24
1	17
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize38.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--` `distribute-lft-out--`

Counts

2 → 32

Calls

2 calls:

53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series325.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(- (sqrt (+ (* re re) (* im im))) re)
74.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2000
4	1983
3	761
2	328
1	139
0	66

prune240.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.6b

localize53.0ms

Local error

Found 4 expressions with local error:

9.0b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
31.5b	(sqrt (+ (* re re) (* im im)))
31.5b	(sqrt (+ (* re re) (* im im)))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

122.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
59.0ms	(sqrt (+ (* re re) (* im im)))
54.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify775.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2001
3	860
2	340
1	152
0	66

prune453.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.6b

localize21.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune33.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
5.6b	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
23.3b	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `pow1`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`associate-/r*` `times-frac` `sqrt-prod` `insert-posit16`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `pow1/2` `div-exp` `associate-/r/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `prod-exp` `associate-r/` `cbrt-unprod` `div-inv` `associate-/l`

Counts

4 → 68

Calls

4 calls:

26.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
25.0ms	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
46.0ms	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
11.0ms	(sqrt (+ (* re re) (* im im)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
242.0ms	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
83.0ms	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify722.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	2000
2	1423
1	405
0	149

prune388.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.9b

regimes220.0ms

Accuracy

53.3% (17.3b remaining)

Error of 24.0b against oracle of 6.7b and baseline of 43.7b

bsearch420.0ms

Steps

Iters	Range		Point
4	1.5484804938959987e+60	2.762302480820347e+60	2.0068865055559888e+60
9	9.119704175166538e-140	1.858800197845562e-131	1.3866396419306994e-139
9	6.216905896957421e-145	8.385922303039764e-140	2.5714137250259334e-143
7	5.669202008519774e-190	1.0166545693391138e-187	9.324165927345474e-188
9	-8.206475012289342e-137	-8.137733917587764e-146	-1.3770145852390023e-143

simplify19.0ms

Iterations

Iter	Nodes
done	67
3	67
2	66
1	61
0	44

end0.0ms

sample2.6s

Algorithm

intervals

Results

899.0ms	648×	body	2560	valid
729.0ms	6067×	body	80	valid
288.0ms	325×	body	5120	valid
241.0ms	484×	body	1280	valid
155.0ms	263×	body	640	valid
77.0ms	144×	body	320	valid
46.0ms	69×	body	160	valid