Details

sample142.0ms

Algorithm

intervals

Results

44.0ms	21×	body	2560	valid
17.0ms	191×	body	80	valid
7.0ms	13×	body	5120	valid
7.0ms	15×	body	1280	valid
3.0ms	9×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	valid

simplify73.0ms

Counts: 1 → 1

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize28.0ms

Local error

Found 3 expressions with local error:

1.1b	(- (hypot re im) re)
0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

Slowest

13.0ms	(sqrt (* (- (hypot re im) re) 2.0))
11.0ms	(- (hypot re im) re)
0.0ms	(hypot re im)

series392.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

226.0ms	(sqrt (* (- (hypot re im) re) 2.0))
99.0ms	(- (hypot re im) re)
67.0ms	(hypot re im)

simplify1.9s

Counts: 65 → 65

prune737.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)
0.4b	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

Slowest

40.0ms	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))
10.0ms	(- (hypot re im) re)
6.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

945.0ms	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))
89.0ms	(- (hypot re im) re)
83.0ms	(- (hypot re im) re)
66.0ms	(- (hypot re im) re)

simplify1.0s

Counts: 153 → 153

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)
0.4b	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

Slowest

41.0ms	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))
6.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series848.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

563.0ms	(* (cbrt (sqrt (* (- (hypot re im) re) 2.0))) (cbrt (sqrt (* (- (hypot re im) re) 2.0))))
105.0ms	(- (hypot re im) re)
98.0ms	(- (hypot re im) re)
82.0ms	(- (hypot re im) re)

simplify1.1s

Counts: 153 → 153

prune2.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.9b	(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	(hypot re im)
0.0b	(hypot re im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

Slowest

8.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(hypot re im)
0.0ms	(hypot re im)

series749.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

362.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
224.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
98.0ms	(hypot re im)
64.0ms	(hypot re im)

simplify1.8s

Counts: 59 → 59

prune706.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.0b

regimes214.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	6003×	body	80	valid
588.0ms	685×	body	2560	valid
296.0ms	299×	body	5120	valid
281.0ms	489×	body	1280	valid
210.0ms	290×	body	640	valid
51.0ms	153×	body	320	valid
20.0ms	81×	body	160	valid