Details

sample102.0ms

Algorithm

intervals

Results

39.0ms	187×	body	80	valid
18.0ms	22×	body	2560	valid
16.0ms	21×	body	1280	valid
6.0ms	11×	body	640	valid
6.0ms	9×	body	5120	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

21.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
34.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

series343.0ms

Counts

3 → 9

Calls

3 calls:

222.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
75.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify988.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
3	2001
2	669
1	246
0	102

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
29.7b	(sqrt (+ (* re re) (* im im)))
31.0b	(sqrt (* 2.0 (+ (* im im) 0)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/r*`
8×	`pow1` `sqrt-div`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`associate-r/` `insert-posit16` `associate-/l`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `div-inv`

Counts

4 → 113

Calls

4 calls:

34.0ms	(- (sqrt (+ (* re re) (* im im))) re)
66.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (sqrt (+ (* re re) (* im im))) re)
256.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(sqrt (+ (* re re) (* im im)))
71.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

simplify1.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
3	2000
2	1122
1	453
0	216

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(* (sqrt 2.0) (fabs im))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `times-frac`
7×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div` `insert-posit16`
3×	`associate-r` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

35.0ms	(- (sqrt (+ (* re re) (* im im))) re)
70.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
12.0ms	(* (sqrt 2.0) (fabs im))
17.0ms	(sqrt (+ (* re re) (* im im)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (sqrt (+ (* re re) (* im im))) re)
193.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
63.0ms	(* (sqrt 2.0) (fabs im))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2041
3	2041
2	1546
1	463
0	194

prune595.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
0.5b	(* (sqrt 2.0) (fabs im))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `sqrt-prod`
54×	`times-frac`
42×	`add-cube-cbrt`
36×	`associate-r`
32×	`add-exp-log`
20×	`add-cbrt-cube`
14×	`pow1` `difference-of-squares`
13×	`prod-exp`
9×	`associate-/r*`
7×	`associate-l` `cbrt-unprod` `distribute-lft-out--`
6×	`sqrt-div` `div-exp`
4×	`pow-prod-down` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `flip3--` `pow1/2` `*-commutative` `div-inv` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `flip3-+` `associate-*r/` `un-div-inv` `flip-+` `inv-pow`

Counts

4 → 158

Calls

4 calls:

31.0ms	(/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
127.0ms	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
19.0ms	(* (sqrt 2.0) (fabs im))
12.0ms	(sqrt (+ (* re re) (* im im)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
261.0ms	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
65.0ms	(* (sqrt 2.0) (fabs im))
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

170 → 170

Iterations

Iter	Nodes
done	2001
2	2001
1	706
0	270

prune729.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.0b

regimes400.0ms

Accuracy

64.2% (10.4b remaining)

Error of 18.4b against oracle of 8.0b and baseline of 37.1b

bsearch332.0ms

Steps

Iters	Range		Point
6	1.0720302096475472e+92	7.938065894163254e+92	3.4696741244957e+92
8	2.682856457515952e-293	3.682879132878819e-290	1.3130508878524708e-291
7	-1.5942858179205256e-248	-4.44103357617797e-250	-9.529220942855773e-250
9	-4.397076889216472e+51	-6.689715143507821e+43	-3.106642014201959e+51

simplify26.0ms

Iterations

Iter	Nodes
done	64
1	64
0	48

end0.0ms

sample2.8s

Algorithm

intervals

Results

800.0ms	5992×	body	80	valid
743.0ms	525×	body	1280	valid
601.0ms	682×	body	2560	valid
279.0ms	306×	body	5120	valid
162.0ms	285×	body	640	valid
43.0ms	132×	body	320	valid
18.0ms	78×	body	160	valid