Details

sample5.0s

Algorithm

intervals

Results

4.7s	1086×	body	10240	exit
166.0ms	256×	body	80	valid

simplify150.0ms

Calls

1 calls:

Slowest

149.0ms

(* (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))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize46.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.8b	(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.re)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
5×	`pow1` `associate-l`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `flip3-+` `log-pow` `flip-+`
1×	`cos-sum` `*-commutative`

Calls

4 calls:

Slowest

10.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series292.0ms

Calls

4 calls:

Slowest

140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
96.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Calls

27 calls:

Slowest

244.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
217.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
109.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
91.0ms	(* -1 (* y.re (log (/ -1 x.re))))
89.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize3.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b	(* (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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

7.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series210.0ms

Calls

4 calls:

Slowest

101.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
74.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
23.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(* (atan2 x.im x.re) y.im)

simplify967.0ms

Calls

23 calls:

Slowest

224.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
130.0ms	(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
122.0ms	(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))
112.0ms	(* -1 (* y.re (log (/ 1 x.re))))
99.0ms	(* -1 (* y.re (log (/ -1 x.re))))

prune978.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-l`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`pow1`
3×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Calls

3 calls:

Slowest

11.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
9.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(* (log (- x.re)) y.re)

series255.0ms

Calls

3 calls:

Slowest

150.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
92.0ms	(* (log (- x.re)) y.re)
13.0ms	(* (atan2 x.im x.re) y.im)

simplify671.0ms

Calls

14 calls:

Slowest

147.0ms	(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
129.0ms	(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
98.0ms	(- (+ (* y.re (log -1)) (* y.re (log x.re))) (* y.im (atan2 x.im x.re)))
93.0ms	(* -1 (* y.re (log (/ -1 x.re))))
74.0ms	(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune565.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (atan2 x.im x.re) y.im)
0.1b	(* (log x.im) y.re)
0.0b	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-l`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

3 calls:

Slowest

5.0ms	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
3.0ms	(* (log x.im) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series210.0ms

Calls

3 calls:

Slowest

123.0ms	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
74.0ms	(* (log x.im) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)

simplify684.0ms

Calls

14 calls:

Slowest

284.0ms	(- (* y.re (log -1)) (+ (* y.re (log (/ -1 x.im))) (* y.im (atan2 x.im x.re))))
117.0ms	(* y.re (- (log -1) (log (/ -1 x.im))))
81.0ms	(/ (exp (* (log x.im) y.re)) (exp (* (atan2 x.im x.re) y.im)))
78.0ms	(* -1 (* y.re (log (/ 1 x.im))))
46.0ms	(- (+ (* y.re (log (/ 1 x.im))) (* y.im (atan2 x.im x.re))))

prune496.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.1b

Details

sample5.0s

simplify150.0ms

prune23.0ms

localize46.0ms

rewrite23.0ms

series292.0ms

simplify1.1s

prune1.2s

localize3.0ms

rewrite17.0ms

series210.0ms

simplify967.0ms

prune978.0ms

localize25.0ms

rewrite28.0ms

series255.0ms

simplify671.0ms

prune565.0ms

localize18.0ms

rewrite12.0ms

series210.0ms

simplify684.0ms

prune496.0ms

regimes261.0ms