Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	186×	body	80	valid
12.0ms	20×	body	2560	valid
8.0ms	19×	body	1280	valid
6.0ms	10×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

(* 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: 14.9b

localize28.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite22.0ms

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

12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series413.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

303.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
110.0ms	(+ (hypot re im) re)

simplify606.0ms

Counts

15 → 40

Calls

15 calls:

Slowest

277.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
207.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
30.0ms	(* (+ (hypot re im) re) 2.0)
30.0ms	(* (+ (hypot re im) re) 2.0)
17.0ms	(* (exp (hypot re im)) (exp re))

prune366.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.6b

localize16.0ms

Local error

Found 3 expressions with local error:

1.2b	(+ (hypot re im) re)
0.3b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.0b	(sqrt (+ (hypot re im) re))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

Slowest

16.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
8.0ms	(sqrt (+ (hypot re im) re))
5.0ms	(+ (hypot re im) re)

series534.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

284.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
157.0ms	(sqrt (+ (hypot re im) re))
93.0ms	(+ (hypot re im) re)

simplify1.6s

Counts

51 → 83

Calls

51 calls:

Slowest

445.0ms	(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
286.0ms	(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
196.0ms	(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
166.0ms	(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
129.0ms	(sqrt (+ (pow (hypot re im) 3) (pow re 3)))

prune894.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.6b

localize38.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (hypot re im) re)
1.2b	(+ (hypot re im) re)
1.2b	(+ (hypot re im) re)
0.4b	(* (cbrt (sqrt (* (+ (hypot re im) re) 2.0))) (cbrt (sqrt (* (+ (hypot re im) re) 2.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`cbrt-prod`
15×	`add-cube-cbrt`
14×	`associate-*l/`
12×	`cbrt-div` `sqrt-div`
11×	`pow1`
10×	`add-log-exp`
9×	`fma-def` `flip3-+` `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×	`+-commutative` `sum-log` `distribute-lft-out`
2×	`pow-prod-down` `associate-*r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

Slowest

27.0ms	(* (cbrt (sqrt (* (+ (hypot re im) re) 2.0))) (cbrt (sqrt (* (+ (hypot re im) re) 2.0))))
5.0ms	(+ (hypot re im) re)
4.0ms	(+ (hypot re im) re)
4.0ms	(+ (hypot re im) re)

series803.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

549.0ms	(* (cbrt (sqrt (* (+ (hypot re im) re) 2.0))) (cbrt (sqrt (* (+ (hypot re im) re) 2.0))))
97.0ms	(+ (hypot re im) re)
83.0ms	(+ (hypot re im) re)
74.0ms	(+ (hypot re im) re)

simplify4.0s

Counts

84 → 120

Calls

84 calls:

Slowest

430.0ms	(exp (* 1/3 (- (+ (log (/ -1 re)) (log (* 1/2 (pow (sqrt 2.0) 2)))) (* 2 (log (/ -1 im))))))
335.0ms	(* (cbrt (sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))) (cbrt (sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))))
300.0ms	(* (cbrt (sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))) (cbrt (sqrt (* (+ (hypot re im) re) 2.0))))
211.0ms	(* (cbrt (sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))) (cbrt (sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))))
201.0ms	(* (cbrt (sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))) (cbrt (sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))))

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.6b

localize23.0ms

Local error

Found 4 expressions with local error:

17.2b	(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	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

Slowest

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

series788.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

351.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
192.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
122.0ms	(sqrt (hypot re im))
122.0ms	(sqrt (hypot re im))

simplify126.0ms

Counts

25 → 69

Calls

25 calls:

Slowest

41.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
27.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
9.0ms	(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
9.0ms	(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
7.0ms	(sqrt (sqrt (hypot re im)))

prune704.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 14.5b

regimes232.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch1.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	6044×	body	80	valid
574.0ms	655×	body	2560	valid
404.0ms	300×	body	5120	valid
343.0ms	467×	body	1280	valid
194.0ms	311×	body	640	valid
48.0ms	136×	body	320	valid
20.0ms	87×	body	160	valid