Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	186×	body	80	valid
4.0ms	22×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	11×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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:

0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

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:

51.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

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)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

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

prune182.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.3b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.5b	(- (hypot re im) re)

rewrite28.0ms

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:

0.0ms	(hypot re im)
20.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
6.0ms	(- (hypot re im) re)

series288.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(hypot re im)
180.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
59.0ms	(- (hypot re im) re)

simplify45.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (41.0ms)

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

prune154.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (- (hypot re im) re))
0.3b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
1.5b	(- (hypot re im) re)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
17×	`sqrt-prod`
16×	`add-cube-cbrt`
9×	`pow1` `prod-diff`
8×	`associate-r`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

0.0ms	(hypot re im)
9.0ms	(sqrt (- (hypot re im) re))
24.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
6.0ms	(- (hypot re im) re)

series416.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot re im)
123.0ms	(sqrt (- (hypot re im) re))
183.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
60.0ms	(- (hypot re im) re)

simplify41.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	348	614
1	1286	509
2	5002	488
done	5002	488

prune247.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (* 2.0 (+ (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 0)))
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
1.5b	(- (hypot re im) re)
1.5b	(- (hypot re im) re)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

27.0ms	(sqrt (* 2.0 (+ (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 0)))
38.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
6.0ms	(- (hypot re im) re)
6.0ms	(- (hypot re im) re)

series355.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (* 2.0 (+ (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 0)))
60.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
56.0ms	(- (hypot re im) re)
60.0ms	(- (hypot re im) re)

simplify79.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	377	983
1	1654	768
2	5002	755
done	5002	755

prune313.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

regimes101.0ms

Accuracy

-8.8% (6.5b remaining)

Error of 14.1b against oracle of 7.6b and baseline of 13.5b

bsearch175.0ms

Steps

Iters	Range		Point
9	4.310439048164553e+59	9.389232274922462e+67	1.2960687720432806e+60
7	1.0234318601461633e-26	1.380851535651534e-24	2.3641995363355918e-26
9	3.3591430669182463e-102	1.1893945553223457e-95	3.3970012564759815e-102
9	2.6119986309082814e-155	2.5989129199139394e-149	2.5608629010698907e-149

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

sample700.0ms

Algorithm

intervals

Results

191.0ms	5982×	body	80	valid
136.0ms	731×	body	2560	valid
79.0ms	518×	body	1280	valid
59.0ms	274×	body	5120	valid
30.0ms	270×	body	640	valid
13.0ms	149×	body	320	valid
4.0ms	76×	body	160	valid