Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	21×	body	2560	valid
6.0ms	198×	body	80	valid
2.0ms	16×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8
done	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

55.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473
done	5001	473

prune182.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.7b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0b	(hypot re im)
1.2b	(- (hypot re im) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

21.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0ms	(hypot re im)
7.0ms	(- (hypot re im) re)

series287.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
48.0ms	(hypot re im)
61.0ms	(- (hypot re im) re)

simplify46.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236
done	5001	236

prune149.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
13.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series200.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
48.0ms	(hypot re im)
46.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
60.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify37.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	198	388
1	788	297
2	5002	285
done	5002	285

prune227.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.2b	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
10.2b	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-r`
8×	`sqrt-pow1`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `flip--` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 154

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
31.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
21.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

series352.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (sqrt (hypot re im)))
46.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
137.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
58.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

simplify69.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	384	1225
1	1775	953
2	5002	812
done	5002	812

prune339.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

regimes115.0ms

Accuracy

0.1% (5.7b remaining)

Error of 13.1b against oracle of 7.4b and baseline of 13.1b

bsearch185.0ms

Steps

Iters	Range		Point
8	-3.80808233067461e-41	-9.726232553466861e-46	-2.7809543568425416e-41
9	-3.649797396570063e+16	-66911392.43097515	-645644762598500.5
9	-6.261927662807804e+61	-1.691923950948768e+56	-5.9156754413410994e+60
8	-2.519337225575135e+155	-5.776441892175825e+150	-2.0479595210044226e+153

simplify4.0ms

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	41	34
1	48	34
2	54	14
3	57	14
4	63	14
5	74	14
6	81	14
7	82	14
8	82	14
done	82	14

end0.0ms

sample688.0ms

Algorithm

intervals

Results

190.0ms	6037×	body	80	valid
127.0ms	712×	body	2560	valid
74.0ms	462×	body	1280	valid
73.0ms	305×	body	5120	valid
31.0ms	270×	body	640	valid
14.0ms	131×	body	320	valid
5.0ms	83×	body	160	valid