Details

sample7.7s

Algorithm

intervals

Results

7.4s	1707×	body	10240	exit
78.0ms	256×	body	80	valid

simplify556.0ms

Calls

1 calls:

Slowest

555.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize52.0ms

Local error

Found 4 expressions with local error:

37.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite51.0ms

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×	`sin-sum` `*-commutative`

Calls

4 calls:

Slowest

21.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series288.0ms

Calls

4 calls:

Slowest

172.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
73.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
24.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify969.0ms

Calls

27 calls:

Slowest

201.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
199.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
97.0ms	(* -1 (* y.re (log (/ -1 x.re))))
95.0ms	(* -1 (* y.re (log (/ 1 x.re))))
82.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.7b

localize26.0ms

Local error

Found 4 expressions with local error:

37.3b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.5b	(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)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

15.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
5.0ms	(* (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)))

series242.0ms

Calls

4 calls:

Slowest

123.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
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)))
22.0ms	(* (atan2 x.im x.re) y.im)

simplify943.0ms

Calls

23 calls:

Slowest

199.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
146.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
120.0ms	(* -1 (* y.re (log (/ -1 x.re))))
120.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
97.0ms	(* -1 (* y.re (log (/ 1 x.re))))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.5b

localize12.0ms

Local error

Found 4 expressions with local error:

37.3b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
0.3b	(* (log (- x.re)) y.re)
0.3b	(* (atan2 x.im x.re) y.im)
0.2b	(* (log (- x.re)) y.im)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-l`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`log-pow`
1×	`sin-sum`

Calls

4 calls:

Slowest

21.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(* (log (- x.re)) y.re)
7.0ms	(* (log (- x.re)) y.im)
6.0ms	(* (atan2 x.im x.re) y.im)

series401.0ms

Calls

4 calls:

Slowest

178.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
108.0ms	(* (log (- x.re)) y.re)
92.0ms	(* (log (- x.re)) y.im)
22.0ms	(* (atan2 x.im x.re) y.im)

simplify727.0ms

Calls

19 calls:

Slowest

125.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
113.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
103.0ms	(* -1 (* y.re (log (/ -1 x.re))))
79.0ms	(* -1 (* y.im (log (/ -1 x.re))))
71.0ms	(* y.re (- (log -1) (log (/ 1 x.re))))

prune1.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

localize22.0ms

Local error

Found 4 expressions with local error:

37.3b	(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
0.7b	(cbrt (* (log (- x.re)) y.im))
0.7b	(cbrt (* (log (- x.re)) y.im))
0.7b	(cbrt (* (log (- x.re)) y.im))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum`

Calls

4 calls:

Slowest

97.0ms	(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
6.0ms	(cbrt (* (log (- x.re)) y.im))
4.0ms	(cbrt (* (log (- x.re)) y.im))
4.0ms	(cbrt (* (log (- x.re)) y.im))

series678.0ms

Calls

4 calls:

Slowest

189.0ms	(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
171.0ms	(cbrt (* (log (- x.re)) y.im))
168.0ms	(cbrt (* (log (- x.re)) y.im))
149.0ms	(cbrt (* (log (- x.re)) y.im))

simplify2.0s

Calls

16 calls:

Slowest

309.0ms	(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
272.0ms	(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
233.0ms	(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
168.0ms	(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))
162.0ms	(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))

prune968.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

Details

sample7.7s

simplify556.0ms

prune18.0ms

localize52.0ms

rewrite51.0ms

series288.0ms

simplify969.0ms

prune1.3s

localize26.0ms

rewrite26.0ms

series242.0ms

simplify943.0ms

prune1.2s

localize12.0ms

rewrite41.0ms

series401.0ms

simplify727.0ms

prune1.0s

localize22.0ms

rewrite112.0ms

series678.0ms

simplify2.0s

prune968.0ms

regimes765.0ms