Details

sample126.0ms

Algorithm

intervals

Results

18.0ms	196×	body	80	valid
9.0ms	21×	body	2560	valid
7.0ms	18×	body	1280	valid
4.0ms	8×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify79.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

78.0ms

(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.2b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`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

1 → 29

Calls

1 calls:

Slowest

6.0ms

(- (hypot re im) re)

series82.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

81.0ms

(- (hypot re im) re)

simplify488.0ms

Counts

27 → 32

Calls

27 calls:

Slowest

70.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
53.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
40.0ms	(fma 1 (hypot re im) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
33.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
26.0ms	(/ (exp (hypot re im)) (exp re))

prune238.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 11.9b

localize23.0ms

Local error

Found 3 expressions with local error:

14.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

3 → 43

Calls

3 calls:

Slowest

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series401.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

180.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
115.0ms	(sqrt (hypot re im))
105.0ms	(sqrt (hypot re im))

simplify73.0ms

Counts

19 → 52

Calls

19 calls:

Slowest

9.0ms	(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
9.0ms	(sqrt 1)
9.0ms	(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
7.0ms	(sqrt (sqrt (hypot re im)))
6.0ms	(sqrt (sqrt (hypot re im)))

prune591.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.8b

localize53.0ms

Local error

Found 4 expressions with local error:

14.5b	(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)))

rewrite34.0ms

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

23.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
4.0ms	(sqrt (sqrt (hypot re im)))
3.0ms	(sqrt (sqrt (hypot re im)))
1.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series699.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

211.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))
180.0ms	(sqrt (sqrt (hypot re im)))
179.0ms	(sqrt (sqrt (hypot re im)))
128.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify1.9s

Counts

140 → 145

Calls

140 calls:

Slowest

229.0ms	(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
224.0ms	(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
183.0ms	(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
83.0ms	(* (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))) (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))
31.0ms	(pow (/ -1 re) -1/4)

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.8b

localize97.0ms

Local error

Found 4 expressions with local error:

14.5b	(fma (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (hypot re im)) (- re))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
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` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

Slowest

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(fma (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (hypot re im)) (- re))

series726.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(cbrt (hypot re im))
184.0ms	(fma (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (hypot re im)) (- re))
182.0ms	(cbrt (hypot re im))
171.0ms	(cbrt (hypot re im))

simplify841.0ms

Counts

21 → 65

Calls

21 calls:

Slowest

210.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
207.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
196.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
32.0ms	(pow (/ 1 re) -1/3)
32.0ms	(pow (/ 1 re) -1/3)

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.8b

regimes230.0ms

Accuracy

0% (0.3b remaining)

Error of 13.8b against oracle of 13.5b and baseline of 13.8b

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	5962×	body	80	valid
587.0ms	688×	body	2560	valid
358.0ms	535×	body	1280	valid
350.0ms	295×	body	5120	valid
137.0ms	291×	body	640	valid
53.0ms	151×	body	320	valid
17.0ms	78×	body	160	valid