Details

sample65.0ms

Algorithm

intervals

Results

22.0ms	200×	body	80	valid
15.0ms	22×	body	2560	valid
7.0ms	13×	body	1280	valid
6.0ms	9×	body	5120	valid
4.0ms	9×	body	640	valid
1.0ms	3×	body	320	valid

simplify46.0ms

Counts: 1 → 1

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite11.0ms

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

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
4.0ms	(+ (hypot re im) re)

series332.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

250.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
82.0ms	(+ (hypot re im) re)

simplify429.0ms

Counts: 40 → 40

prune407.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.0b

localize21.0ms

Local error

Found 4 expressions with local error:

13.7b	(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))

rewrite13.0ms

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))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series792.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

336.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
197.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
134.0ms	(sqrt (hypot re im))
125.0ms	(sqrt (hypot re im))

simplify585.0ms

Counts: 71 → 69

prune714.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.9b

localize31.0ms

Local error

Found 4 expressions with local error:

13.7b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))

rewrite24.0ms

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:

Slowest

18.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
2.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
0.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

series605.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

188.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
162.0ms	(sqrt (sqrt (hypot re im)))
154.0ms	(sqrt (sqrt (hypot re im)))
101.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify726.0ms

Counts: 172 → 145

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.9b

localize49.0ms

Local error

Found 4 expressions with local error:

13.7b	(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`add-sqr-sqrt` `-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow-prod-down`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
2×	`pow1/3` `sqrt-unprod`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

4 → 69

Calls

4 calls:

Slowest

63.0ms	(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)

series688.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

200.0ms	(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)
169.0ms	(cbrt (hypot re im))
163.0ms	(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))
156.0ms	(cbrt (hypot re im))

simplify641.0ms

Counts: 84 → 81

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.9b

regimes172.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

722.0ms	5969×	body	80	valid
681.0ms	301×	body	5120	valid
553.0ms	706×	body	2560	valid
405.0ms	517×	body	1280	valid
128.0ms	281×	body	640	valid
77.0ms	152×	body	320	valid
35.0ms	74×	body	160	valid