Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	193×	body	80	valid
19.0ms	22×	body	2560	valid
8.0ms	15×	body	1280	valid
6.0ms	13×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	3×	body	5120	valid
2.0ms	5×	body	160	valid

simplify30.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

30.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize14.0ms

Local error

Found 2 expressions with local error:

1.5b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite12.0ms

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))
5.0ms	(+ (hypot re im) re)

series345.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

242.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
103.0ms	(+ (hypot re im) re)

simplify568.0ms

Counts

15 → 40

Calls

15 calls:

Slowest

269.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
210.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
29.0ms	(* (+ (hypot re im) re) 2.0)
17.0ms	(* (+ (hypot re im) re) 2.0)
13.0ms	(* (exp (hypot re im)) (exp re))

prune400.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.0b

localize19.0ms

Local error

Found 2 expressions with local error:

15.4b	(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))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 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)

series523.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

325.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
198.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify111.0ms

Counts

9 → 31

Calls

9 calls:

Slowest

57.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
42.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
7.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
2.0ms	(+ re im)
0.0ms	(- re (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))

prune354.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.0b

localize20.0ms

Local error

Found 4 expressions with local error:

15.3b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite4.0ms

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))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series746.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

239.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)
180.0ms	(cbrt (hypot re im))
168.0ms	(cbrt (hypot re im))
158.0ms	(cbrt (hypot re im))

simplify853.0ms

Counts

21 → 65

Calls

21 calls:

Slowest

248.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
236.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
179.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
31.0ms	(pow (/ 1 re) -1/3)
29.0ms	(pow (/ 1 re) -1/3)

prune922.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 13.8b

localize26.0ms

Local error

Found 4 expressions with local error:

15.3b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
0.5b	(cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`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×	`pow3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 52

Calls

4 calls:

Slowest

15.0ms	(cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

series706.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))
187.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
172.0ms	(cbrt (hypot re im))
156.0ms	(cbrt (hypot re im))

simplify823.0ms

Counts

20 → 64

Calls

20 calls:

Slowest

243.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
214.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
184.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
31.0ms	(pow (/ 1 re) -1/3)
31.0ms	(pow (/ -1 re) -1/3)

prune944.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.8b

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch1.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	6087×	body	80	valid
515.0ms	624×	body	2560	valid
301.0ms	505×	body	1280	valid
285.0ms	289×	body	5120	valid
131.0ms	280×	body	640	valid
46.0ms	145×	body	320	valid
15.0ms	70×	body	160	valid