Details

sample4.0s

Algorithm

intervals

Results

3.7s	988×	body	10240	exit
66.0ms	256×	body	80	valid

simplify486.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

485.0ms

(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize76.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `associate-l` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `associate-r` `log-pow`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

Slowest

32.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

221.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
138.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
84.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts

37 → 75

Calls

37 calls:

Slowest

451.0ms	(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.im y.im) y.im))
379.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
297.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
295.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
256.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize35.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.2b	(* (atan2 x.im x.re) y.im)
0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
3×	`log-pow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 70

Calls

4 calls:

Slowest

23.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

201.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
129.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(* (atan2 x.im x.re) y.im)

simplify2.6s

Counts

39 → 82

Calls

39 calls:

Slowest

637.0ms	(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))
426.0ms	(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
310.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
309.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
236.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (log (- x.re)) y.re)
0.2b	(* (atan2 x.im x.re) y.im)
0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 52

Calls

3 calls:

Slowest

19.0ms	(* (log (- x.re)) y.re)
15.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms	(* (atan2 x.im x.re) y.im)

series306.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

186.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
99.0ms	(* (log (- x.re)) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)

simplify1.7s

Counts

28 → 61

Calls

28 calls:

Slowest

366.0ms	(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
338.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
220.0ms	(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
165.0ms	(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
151.0ms	(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))

prune896.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(* y.im (atan2 x.im x.re))
0.1b	(* y.re (log x.im))
0.0b	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`log-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate--l+`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 64

Calls

3 calls:

Slowest

15.0ms	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))
8.0ms	(* y.re (log x.im))
6.0ms	(* y.im (atan2 x.im x.re))

series179.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

86.0ms	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))
74.0ms	(* y.re (log x.im))
19.0ms	(* y.im (atan2 x.im x.re))

simplify1.7s

Counts

43 → 73

Calls

43 calls:

Slowest

364.0ms	(* (* (* y.im y.im) y.im) (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)))
337.0ms	(- (* y.re (log -1)) (+ (* y.re (log (/ -1 x.im))) (* y.im (atan2 x.im x.re))))
312.0ms	(* (* (* y.re y.re) y.re) (* (* (log x.im) (log x.im)) (log x.im)))
177.0ms	(/ (exp (* y.re (log x.im))) (exp (* y.im (atan2 x.im x.re))))
138.0ms	(* y.re (- (log -1) (log (/ -1 x.im))))

prune889.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

Details

sample4.0s

simplify486.0ms

prune16.0ms

localize76.0ms

rewrite93.0ms

series517.0ms

simplify2.3s

prune1.4s

localize35.0ms

rewrite66.0ms

series390.0ms

simplify2.6s

prune1.2s

localize26.0ms

rewrite47.0ms

series306.0ms

simplify1.7s

prune896.0ms

localize22.0ms

rewrite30.0ms

series179.0ms

simplify1.7s

prune889.0ms

regimes244.0ms