Details

sample72.0ms

Algorithm

intervals

Results

22.0ms	193×	body	80	valid
15.0ms	23×	body	2560	valid
7.0ms	8×	body	5120	valid
6.0ms	11×	body	1280	valid
5.0ms	12×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify54.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

54.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 1 expressions with local error:

1.2b	(+ (hypot re im) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

Slowest

9.0ms

(+ (hypot re im) re)

series101.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

101.0ms

(+ (hypot re im) re)

simplify46.0ms

Counts

7 → 21

Calls

7 calls:

Slowest

15.0ms	(* (exp (hypot re im)) (exp re))
7.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
6.0ms	(* 2 re)
5.0ms	(+ (hypot re im) re)
5.0ms	(sqrt (hypot re im))

prune256.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 1 expressions with local error:

15.5b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series195.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

195.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify6.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

4.0ms	(+ re im)
0.0ms	(- re (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))
0.0ms	(- re (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))

prune167.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 2 expressions with local error:

7.8b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

Slowest

9.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

77.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
48.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify751.0ms

Counts

67 → 73

Calls

67 calls:

Slowest

141.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
137.0ms	(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
84.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
19.0ms	(+ 1/2 (/ 1 2))
19.0ms	(* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))

prune777.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.5b

localize42.0ms

Local error

Found 4 expressions with local error:

8.3b	(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
0.3b	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
0.3b	(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.1b	(sqrt (sqrt (hypot re im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

55×	`sqrt-pow1`
52×	`pow1`
42×	`sqrt-prod`
36×	`pow-prod-up`
33×	`pow1/2`
32×	`add-sqr-sqrt`
18×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
7×	`associate-r`
6×	`pow-plus` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cube-unmult` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 133

Calls

4 calls:

Slowest

51.0ms	(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
35.0ms	(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
21.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

184.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
163.0ms	(sqrt (sqrt (hypot re im)))
80.0ms	(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
78.0ms	(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)

simplify3.1s

Counts

127 → 145

Calls

127 calls:

Slowest

430.0ms	(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
386.0ms	(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
355.0ms	(* (exp (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (exp re))
350.0ms	(* (* (* (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)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im)))))
241.0ms	(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.5b

regimes253.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

852.0ms	6028×	body	80	valid
830.0ms	688×	body	2560	valid
316.0ms	481×	body	1280	valid
299.0ms	292×	body	5120	valid
194.0ms	303×	body	640	valid
51.0ms	143×	body	320	valid
50.0ms	65×	body	160	valid