Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	187×	body	80	valid
12.0ms	22×	body	2560	valid
10.0ms	19×	body	1280	valid
5.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify56.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

56.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ (hypot re im) re)
0.3b	(sqrt (* (+ (hypot re im) re) 2.0))
0.0b	(hypot re im)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

Slowest

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
4.0ms	(+ (hypot re im) re)
0.0ms	(hypot re im)

series418.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

253.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
83.0ms	(hypot re im)
81.0ms	(+ (hypot re im) re)

simplify517.0ms

Counts

18 → 54

Calls

18 calls:

Slowest

230.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
163.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
30.0ms	(* (+ (hypot re im) re) 2.0)
28.0ms	(* (+ (hypot re im) re) 2.0)
16.0ms	(* (exp (hypot re im)) (exp re))

prune569.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.0b	(hypot re im)
0.0b	(sqrt (+ (hypot re im) re))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 85

Calls

4 calls:

Slowest

22.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
10.0ms	(sqrt (+ (hypot re im) re))
4.0ms	(+ (hypot re im) re)
0.0ms	(hypot re im)

series628.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

271.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
191.0ms	(sqrt (+ (hypot re im) re))
106.0ms	(+ (hypot re im) re)
60.0ms	(hypot re im)

simplify1.5s

Counts

54 → 97

Calls

54 calls:

Slowest

432.0ms	(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
310.0ms	(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
149.0ms	(sqrt (+ (pow (hypot re im) 3) (pow re 3)))
125.0ms	(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
124.0ms	(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.9b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.6b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.3b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b	(hypot re im)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`pow2` `+-commutative` `hypot-udef` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

Slowest

23.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.0ms	(hypot re im)

series455.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

253.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
88.0ms	(hypot re im)
61.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
53.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.6s

Counts

78 → 106

Calls

78 calls:

Slowest

387.0ms	(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
325.0ms	(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
163.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
144.0ms	(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
69.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 14.8b

localize17.0ms

Local error

Found 4 expressions with local error:

17.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.3b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)

rewrite6.0ms

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

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

series667.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

315.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
231.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
67.0ms	(hypot re im)
54.0ms	(hypot re im)

simplify98.0ms

Counts

15 → 59

Calls

15 calls:

Slowest

46.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
34.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
4.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
3.0ms	(* -1 re)
3.0ms	(* -1 re)

prune625.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 14.8b

regimes235.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch1.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	6003×	body	80	valid
592.0ms	667×	body	2560	valid
394.0ms	304×	body	5120	valid
316.0ms	517×	body	1280	valid
166.0ms	295×	body	640	valid
46.0ms	134×	body	320	valid
17.0ms	80×	body	160	valid