Details

sample6.0s

Algorithm

intervals

Results

5.8s	1354×	body	10240	exit
70.0ms	256×	body	80	valid

simplify228.0ms

Calls

1 calls:

Slowest

227.0ms

(* (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))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize56.0ms

Local error

Found 4 expressions with local error:

36.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series365.0ms

Calls

4 calls:

Slowest

213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(* (atan2 x.im x.re) y.im)

simplify952.0ms

Calls

27 calls:

Slowest

221.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
194.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
126.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
90.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
82.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.5b

localize18.0ms

Local error

Found 4 expressions with local error:

36.5b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (log (- x.re)) y.im)
0.3b	(* (atan2 x.im x.re) y.im)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

20.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms	(* (log (- x.re)) y.im)
6.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series380.0ms

Calls

4 calls:

Slowest

207.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
110.0ms	(* (log (- x.re)) y.im)
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(* (atan2 x.im x.re) y.im)

simplify955.0ms

Calls

23 calls:

Slowest

199.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
159.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
134.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
131.0ms	(* -1 (* y.im (log (/ -1 x.re))))
115.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize30.0ms

Local error

Found 4 expressions with local error:

36.5b	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.5b	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
0.5b	(cbrt (log (- x.re)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `pow1`
11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
5×	`pow1/3`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-pow` `sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `flip3-+` `pow-plus` `pow1/2` `sin-sum` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

57.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
6.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(cbrt (log (- x.re)))

series1.3s

Calls

4 calls:

Slowest

507.0ms	(cbrt (log (- x.re)))
493.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
199.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Calls

45 calls:

Slowest

213.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
142.0ms	(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
107.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
105.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
64.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

36.5b	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.6b	(* (log (- x.re)) (log (- x.re)))
0.5b	(cbrt (* (log (- x.re)) (log (- x.re))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`log-prod`
6×	`add-cbrt-cube` `add-exp-log`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`neg-mul-1` `sqrt-div` `log-pow`
1×	`cbrt-prod` `pow2` `rem-sqrt-square` `flip3-+` `pow-plus` `pow1/2` `sin-sum` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

32.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
6.0ms	(* (log (- x.re)) (log (- x.re)))
3.0ms	(cbrt (* (log (- x.re)) (log (- x.re))))
2.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series1.0s

Calls

4 calls:

Slowest

471.0ms	(cbrt (* (log (- x.re)) (log (- x.re))))
317.0ms	(* (log (- x.re)) (log (- x.re)))
194.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Calls

40 calls:

Slowest

188.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
156.0ms	(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
136.0ms	(pow (- (log -1) (log (/ 1 x.re))) 2)
126.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))
103.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

Details

sample6.0s

simplify228.0ms

prune11.0ms

localize56.0ms

rewrite28.0ms

series365.0ms

simplify952.0ms

prune1.1s

localize18.0ms

rewrite43.0ms

series380.0ms

simplify955.0ms

prune1.1s

localize30.0ms

rewrite67.0ms

series1.3s

simplify1.1s

prune1.7s

localize34.0ms

rewrite43.0ms

series1.0s

simplify1.2s

prune1.6s

regimes801.0ms