Details

sample175.0ms

Algorithm

intervals

Results

14.0ms	181×	body	80	valid
13.0ms	22×	body	2560	valid
11.0ms	19×	body	5120	valid
7.0ms	16×	body	1280	valid
4.0ms	13×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	42
3	35
2	27
1	19
0	12

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(- (hypot re im) re)
0.2b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite41.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

0.0ms	(hypot re im)
12.0ms	(- (hypot re im) re)
25.0ms	(sqrt (* (- (hypot re im) re) 2.0))

series448.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(hypot re im)
96.0ms	(- (hypot re im) re)
268.0ms	(sqrt (* (- (hypot re im) re) 2.0))

simplify2.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	1780
2	569
1	247
0	118

prune322.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (- (hypot re im) re))
0.2b	(- (hypot re im) re)
0.3b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

rewrite60.0ms

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-l`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`rem-sqrt-square` `hypot-udef` `sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

0.0ms	(hypot re im)
11.0ms	(sqrt (- (hypot re im) re))
13.0ms	(- (hypot re im) re)
33.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

series600.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot re im)
178.0ms	(sqrt (- (hypot re im) re))
102.0ms	(- (hypot re im) re)
259.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

simplify2.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
3	2581
2	878
1	374
0	171

prune540.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.2b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
0.2b	(- (hypot re im) re)
0.2b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
37×	`sqrt-prod`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-r`
17×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
9×	`associate-l` `prod-diff`
6×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`fma-neg` `sqrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`rem-sqrt-square` `sub-neg` `diff-log`

Counts

4 → 123

Calls

4 calls:

18.0ms	(sqrt (- (hypot re im) re))
60.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
13.0ms	(- (hypot re im) re)
83.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (- (hypot re im) re))
370.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
87.0ms	(- (hypot re im) re)
271.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.8s

Counts

135 → 135

Iterations

Iter	Nodes
done	5002
2	1545
1	535
0	215

prune733.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0))))
0.2b	(- (hypot re im) re)
0.2b	(* (* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
0.2b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-prod`
44×	`add-sqr-sqrt`
33×	`associate-r`
29×	`pow1`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`pow-prod-down`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-*l/`
10×	`associate-l` `prod-exp` `cbrt-unprod`
9×	`sqrt-pow1` `pow1/2` `prod-diff`
8×	`unswap-sqr`
6×	`sqrt-unprod` `sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`fma-neg` `*-commutative`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log`

Counts

4 → 146

Calls

4 calls:

32.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0))))
7.0ms	(- (hypot re im) re)
377.0ms	(* (* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
133.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

616.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0))))
79.0ms	(- (hypot re im) re)
245.0ms	(* (* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
312.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))

simplify2.1s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2212
1	671
0	255

prune707.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.3b

regimes201.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	6052×	body	80	valid
389.0ms	651×	body	2560	valid
203.0ms	495×	body	1280	valid
149.0ms	313×	body	5120	valid
70.0ms	289×	body	640	valid
26.0ms	134×	body	320	valid
8.0ms	66×	body	160	valid