Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	195×	body	80	valid
5.0ms	10×	body	5120	valid
4.0ms	23×	body	2560	valid
2.0ms	11×	body	1280	valid
2.0ms	13×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	35	10
4	41	10
5	43	10
done	43	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.5b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

4.0ms	(sqrt (* (- (hypot re im) re) 2.0))
3.0ms	(- (hypot re im) re)

series233.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(sqrt (* (- (hypot re im) re) 2.0))
59.0ms	(- (hypot re im) re)

simplify1.0s

Counts

49 → 49

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	107	626
1	220	520
2	540	446
3	1928	400
done	5000	399

prune117.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
14.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

2.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series371.0ms

Counts

2 → 6

Calls

2 calls:

237.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
134.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.7s

Counts

29 → 29

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	63	457
1	136	303
2	395	254
3	1401	241
4	4879	239
done	5000	239

prune78.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (- re re)) 2.0))
0.5b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
9.7b	(- (pow (cbrt (hypot re im)) 3) re)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
54×	`prod-diff`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
35×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
18×	`fma-neg`
8×	`pow1`
6×	`sqrt-div` `associate-*l/` `add-log-exp` `difference-of-squares` `sqr-pow`
5×	`add-exp-log` `cube-mult` `flip3--` `unpow3` `flip--`
4×	`expm1-log1p-u` `frac-add` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-pow` `sqrt-pow1` `pow1/3`
1×	`pow-to-exp` `sub-neg` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `pow-exp` `sqrt-prod` `flip-+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

54.0ms	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (- re re)) 2.0))
0.0ms	(cbrt (hypot re im))
2.0ms	(pow (cbrt (hypot re im)) 3)
21.0ms	(- (pow (cbrt (hypot re im)) 3) re)

series427.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (* (+ (- (pow (cbrt (hypot re im)) 3) re) (- re re)) 2.0))
105.0ms	(cbrt (hypot re im))
87.0ms	(pow (cbrt (hypot re im)) 3)
58.0ms	(- (pow (cbrt (hypot re im)) 3) re)

simplify806.0ms

Counts

169 → 169

Iterations

Useful iterations: done (797.0ms)

Iter	Nodes	Cost
0	239	3284
1	540	1823
2	1620	1230
done	5000	1228

prune307.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (- re re)) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.8b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`pow1`
19×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`sqrt-div` `associate-r` `associate-l` `associate-*l/`
5×	`add-exp-log` `flip3--` `pow-prod-up` `add-cbrt-cube` `flip--` `add-log-exp`
4×	`pow-prod-down` `frac-add` `unswap-sqr`
3×	`expm1-log1p-u` `prod-diff` `pow-sqr` `log1p-expm1-u`
1×	`pow2` `sub-neg` `flip3-+` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

3 → 89

Calls

3 calls:

29.0ms	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (- re re)) 2.0))
6.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series293.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(sqrt (* (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) (- re re)) 2.0))
51.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
56.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	190	1770
1	432	910
2	1306	796
done	5000	734

prune206.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.4b

regimes92.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample688.0ms

Algorithm

intervals

Results

210.0ms	6030×	body	80	valid
142.0ms	699×	body	2560	valid
78.0ms	489×	body	1280	valid
69.0ms	280×	body	5120	valid
36.0ms	284×	body	640	valid
13.0ms	141×	body	320	valid
5.0ms	77×	body	160	valid