Details

sample214.0ms

Algorithm

intervals

Results

31.0ms	190×	body	80	valid
20.0ms	21×	body	2560	valid
14.0ms	19×	body	1280	valid
10.0ms	8×	body	5120	valid
5.0ms	9×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.9b	(- (hypot re im) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 45

Calls

2 calls:

8.0ms	(sqrt (* (- (hypot re im) re) 2.0))
7.0ms	(- (hypot re im) re)

series417.0ms

Counts

2 → 6

Calls

2 calls:

318.0ms	(sqrt (* (- (hypot re im) re) 2.0))
98.0ms	(- (hypot re im) re)

simplify2.9s

Counts

51 → 51

Iterations

Iter	Nodes
4	5125
3	1674
2	513
1	223
0	109

prune464.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.9b	(- (hypot re im) re)
0.9b	(- (hypot re im) re)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`sqrt-prod`
27×	`add-cube-cbrt`
20×	`pow1`
18×	`prod-diff`
14×	`sqrt-div`
12×	`swap-sqr`
9×	`sqrt-pow1` `flip3--` `pow1/2` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l` `add-log-exp`
7×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 146

Calls

4 calls:

11.0ms	(sqrt (- (hypot re im) re))
33.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
8.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series455.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (- (hypot re im) re))
91.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
85.0ms	(- (hypot re im) re)
100.0ms	(- (hypot re im) re)

simplify2.1s

Counts

158 → 158

Iterations

Iter	Nodes
4	3925
3	1429
2	618
1	306
0	155

prune2.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
16.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 57

Calls

4 calls:

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series775.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
121.0ms	(sqrt (hypot re im))
116.0ms	(sqrt (hypot re im))
180.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.4s

Counts

69 → 69

Iterations

Iter	Nodes
4	5105
3	1562
2	504
1	207
0	97

prune870.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.0b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

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

series616.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(sqrt (sqrt (hypot re im)))
123.0ms	(sqrt (sqrt (hypot re im)))
108.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
228.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify2.1s

Counts

145 → 145

Iterations

Iter	Nodes
4	3969
3	1440
2	555
1	277
0	136

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

regimes180.0ms

Accuracy

0% (0.2b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

999.0ms	694×	body	2560	valid
920.0ms	5996×	body	80	valid
382.0ms	498×	body	1280	valid
281.0ms	290×	body	5120	valid
161.0ms	285×	body	640	valid
84.0ms	162×	body	320	valid
17.0ms	75×	body	160	valid