Details

sample310.0ms

Algorithm

intervals

Results

102.0ms	11×	body	1280	valid
55.0ms	200×	body	80	valid
23.0ms	26×	body	2560	valid
12.0ms	10×	body	5120	valid
3.0ms	4×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	2×	body	320	valid

simplify100.0ms

Counts: 1 → 1

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.9b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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

16.0ms	(sqrt (* (- (hypot re im) re) 2.0))
13.0ms	(- (hypot re im) re)

series428.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

292.0ms	(sqrt (* (- (hypot re im) re) 2.0))
135.0ms	(- (hypot re im) re)

simplify1.9s

Counts: 51 → 51

prune456.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.0b	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

Slowest

44.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
39.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
9.0ms	(- (hypot re im) re)
6.0ms	(- (hypot re im) re)

series465.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

231.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
83.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
79.0ms	(- (hypot re im) re)
72.0ms	(- (hypot re im) re)

simplify968.0ms

Counts: 161 → 161

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

Slowest

5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series343.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(- (hypot re im) re)
89.0ms	(- (hypot re im) re)
78.0ms	(- (hypot re im) re)
69.0ms	(- (hypot re im) re)

simplify1.3s

Counts: 128 → 128

prune1.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.8b

localize24.0ms

Local error

Found 4 expressions with local error:

13.8b	(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))

rewrite7.0ms

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

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series831.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

351.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
219.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
136.0ms	(sqrt (hypot re im))
124.0ms	(sqrt (hypot re im))

simplify2.7s

Counts: 69 → 69

prune785.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.7b

regimes185.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch4.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

845.0ms	6009×	body	80	valid
721.0ms	301×	body	5120	valid
698.0ms	687×	body	2560	valid
344.0ms	526×	body	1280	valid
111.0ms	250×	body	640	valid
50.0ms	149×	body	320	valid
17.0ms	78×	body	160	valid