Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	193×	body	80	valid
18.0ms	15×	body	1280	valid
12.0ms	20×	body	2560	valid
8.0ms	10×	body	5120	valid
4.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify29.0ms

Counts: 1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize27.0ms

Local error

Found 2 expressions with local error:

0.6b	(+ (hypot re im) re)
0.2b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

Slowest

11.0ms	(+ (hypot re im) re)
6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series307.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

236.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
70.0ms	(+ (hypot re im) re)

simplify1.5s

Counts: 40 → 40

prune358.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (hypot re im) re)
0.6b	(+ (hypot re im) re)
0.6b	(+ (hypot re im) re)
0.4b	(cbrt (sqrt (* (+ (hypot re im) re) 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`cbrt-prod` `expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative` `sum-log` `distribute-lft-out`
2×	`cbrt-div` `sqrt-div` `associate-*l/`
1×	`pow1/3` `sqrt-prod`

Counts

4 → 71

Calls

4 calls:

Slowest

12.0ms	(cbrt (sqrt (* (+ (hypot re im) re) 2.0)))
9.0ms	(+ (hypot re im) re)
9.0ms	(+ (hypot re im) re)
9.0ms	(+ (hypot re im) re)

series709.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

436.0ms	(cbrt (sqrt (* (+ (hypot re im) re) 2.0)))
98.0ms	(+ (hypot re im) re)
89.0ms	(+ (hypot re im) re)
86.0ms	(+ (hypot re im) re)

simplify715.0ms

Counts: 83 → 83

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.0b

localize59.0ms

Local error

Found 4 expressions with local error:

15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.6b	(+ (hypot re im) re)
0.6b	(+ (hypot re im) re)
0.5b	(cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`fma-def`
4×	`cbrt-prod` `expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`
1×	`pow1/3` `sqrt-prod` `fma-udef`

Counts

4 → 62

Calls

4 calls:

Slowest

4.0ms	(+ (hypot re im) re)
4.0ms	(+ (hypot re im) re)
3.0ms	(cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series777.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

477.0ms	(cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
158.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
73.0ms	(+ (hypot re im) re)
69.0ms	(+ (hypot re im) re)

simplify1.0s

Counts: 74 → 74

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.2b	(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)

series771.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

345.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
201.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
112.0ms	(sqrt (hypot re im))
112.0ms	(sqrt (hypot re im))

simplify1.8s

Counts: 69 → 69

prune674.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.0b

regimes228.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

865.0ms	6003×	body	80	valid
645.0ms	315×	body	5120	valid
490.0ms	663×	body	2560	valid
334.0ms	492×	body	1280	valid
128.0ms	294×	body	640	valid
48.0ms	154×	body	320	valid
41.0ms	79×	body	160	valid