Details

sample65.0ms

Algorithm

intervals

Results

19.0ms	16×	body	2560	valid
14.0ms	188×	body	80	valid
7.0ms	17×	body	1280	valid
6.0ms	11×	body	5120	valid
4.0ms	14×	body	640	valid
2.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

31.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (* re re) (* im im))
21.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
34.0ms	(+ (* re re) (* im im))
59.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	2005
3	2005
2	814
1	280
0	112

prune759.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
26.2b	(sqrt (* 2.0 (+ (* im im) 0)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite123.0ms

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:

53.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(- (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
66.0ms	(- (sqrt (+ (* re re) (* im im))) re)
64.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
62.0ms	(sqrt (+ (* re re) (* im im)))

simplify991.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
3	2000
2	1114
1	452
0	216

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
0.3b	(/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
0.6b	(- (sqrt (+ (* im im) (* re re))) re)
29.8b	(sqrt (+ (* im im) (* re re)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

111.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
46.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
53.0ms	(- (sqrt (+ (* im im) (* re re))) re)
12.0ms	(sqrt (+ (* im im) (* re re)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
163.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
50.0ms	(- (sqrt (+ (* im im) (* re re))) re)
42.0ms	(sqrt (+ (* im im) (* re re)))

simplify1.2s

Counts

158 → 158

Iterations

Iter	Nodes
done	2003
2	2003
1	668
0	267

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fabs im)) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
0.4b	(* (sqrt 2.0) (sqrt (fabs im)))
0.6b	(- (sqrt (+ (* im im) (* re re))) re)
29.8b	(sqrt (+ (* im im) (* re re)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

43.0ms	(/ (sqrt (fabs im)) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
8.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
63.0ms	(- (sqrt (+ (* im im) (* re re))) re)
12.0ms	(sqrt (+ (* im im) (* re re)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sqrt (fabs im)) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
55.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
54.0ms	(- (sqrt (+ (* im im) (* re re))) re)
61.0ms	(sqrt (+ (* im im) (* re re)))

simplify1.2s

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
3	2000
2	1352
1	488
0	237

prune2.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.9b

regimes372.0ms

Accuracy

53.2% (16.4b remaining)

Error of 18.6b against oracle of 2.3b and baseline of 37.2b

bsearch346.0ms

Steps

Iters	Range		Point
8	3.807534648988377e+65	1.3176703569903367e+68	1.2290590931535932e+68
8	6.044418216813967e-222	6.507846128246995e-219	7.239807700907349e-222
8	-7.581771154583152e-270	-3.560522852506786e-274	-2.053769551615154e-273
9	-2.358440659027997e+139	-1.7312143184102848e+134	-1.1292868428778451e+139

simplify22.0ms

Iterations

Iter	Nodes
done	71
1	71
0	54

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	5994×	body	80	valid
479.0ms	694×	body	2560	valid
368.0ms	517×	body	1280	valid
278.0ms	290×	body	5120	valid
188.0ms	286×	body	640	valid
69.0ms	147×	body	320	valid
15.0ms	72×	body	160	valid