Details

sample220.0ms

Algorithm

intervals

Results

27.0ms	190×	body	80	valid
19.0ms	17×	body	2560	valid
12.0ms	17×	body	1280	valid
11.0ms	10×	body	5120	valid
8.0ms	13×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify461.0ms

Counts: 1 → 1

prune74.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize79.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite96.0ms

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:

Slowest

60.0ms	(sqrt (* (- (hypot re im) re) 2.0))
16.0ms	(- (hypot re im) re)

series508.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

319.0ms	(sqrt (* (- (hypot re im) re) 2.0))
189.0ms	(- (hypot re im) re)

simplify584.0ms

Counts: 65 → 51

prune577.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.1b

localize48.0ms

Local error

Found 4 expressions with local error:

9.9b	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

Slowest

31.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series571.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(cbrt (hypot re im))
164.0ms	(cbrt (hypot re im))
163.0ms	(cbrt (hypot re im))
71.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

simplify394.0ms

Counts: 84 → 73

prune905.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.0b

localize54.0ms

Local error

Found 4 expressions with local error:

9.9b	(+ (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (- re))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `associate-+r-` `fma-def` `flip3-+` `unsub-neg` `neg-log` `flip-+`

Counts

4 → 61

Calls

4 calls:

Slowest

36.0ms	(+ (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (- re))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series552.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(cbrt (hypot re im))
145.0ms	(cbrt (hypot re im))
142.0ms	(cbrt (hypot re im))
89.0ms	(+ (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (- re))

simplify721.0ms

Counts: 77 → 73

prune948.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 14.0b

localize35.0ms

Local error

Found 4 expressions with local error:

16.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
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))

rewrite12.0ms

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:

Slowest

7.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series881.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

355.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
231.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
149.0ms	(sqrt (hypot re im))
145.0ms	(sqrt (hypot re im))

simplify544.0ms

Counts: 71 → 69

prune709.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.0b

regimes198.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	6007×	body	80	valid
540.0ms	709×	body	2560	valid
411.0ms	498×	body	1280	valid
265.0ms	272×	body	5120	valid
141.0ms	311×	body	640	valid
47.0ms	145×	body	320	valid
15.0ms	58×	body	160	valid