Details

sample7.0s

Algorithm

intervals

Results

6.7s	1562×	body	10240	exit
97.0ms	256×	body	80	valid

simplify478.0ms

Calls

1 calls:

Slowest

477.0ms

(* (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))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize76.0ms

Local error

Found 4 expressions with local error:

41.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

104.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(* (atan2 x.im x.re) y.im)

series340.0ms

Calls

4 calls:

Slowest

212.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls

47 calls:

Slowest

369.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
269.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
261.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
231.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
227.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize72.0ms

Local error

Found 4 expressions with local error:

41.0b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)
0.2b	(* (log (- x.re)) y.im)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
11×	`associate-l`
10×	`pow1`
9×	`add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
6×	`associate-r`
5×	`distribute-lft-out`
4×	`insert-posit16` `add-log-exp`
2×	`sin-sum` `sqrt-div` `swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `log-pow` `flip-+`

Calls

4 calls:

Slowest

77.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
33.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(* (log (- x.re)) y.im)

series357.0ms

Calls

4 calls:

Slowest

173.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
102.0ms	(* (log (- x.re)) y.im)
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(* (atan2 x.im x.re) y.im)

simplify1.9s

Calls

44 calls:

Slowest

321.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
282.0ms	(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.im y.im) y.im))
276.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
234.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
147.0ms	(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize118.0ms

Local error

Found 4 expressions with local error:

41.0b	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
29.3b	(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)))

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

422.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
1.0ms	(cbrt (log (- x.re)))

series1.3s

Calls

4 calls:

Slowest

521.0ms	(cbrt (log (- x.re)))
443.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
228.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.8s

Calls

85 calls:

Slowest

772.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
276.0ms	(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
260.0ms	(pow (- (log (/ -1 x.re))) 1/3)
250.0ms	(pow (- (log -1) (log (/ 1 x.re))) 1/3)
232.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize92.0ms

Local error

Found 4 expressions with local error:

41.0b	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.5b	(* (log (- x.re)) (log (- x.re)))
0.5b	(cbrt (log (- x.re)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

332.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(* (log (- x.re)) (log (- x.re)))
1.0ms	(cbrt (log (- x.re)))

series982.0ms

Calls

4 calls:

Slowest

491.0ms	(cbrt (log (- x.re)))
269.0ms	(* (log (- x.re)) (log (- x.re)))
163.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.7s

Calls

78 calls:

Slowest

484.0ms	(pow (- (log -1) (log (/ 1 x.re))) 2)
318.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
312.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
259.0ms	(pow (- (log (/ -1 x.re))) 1/3)
245.0ms	(pow (- (log -1) (log (/ 1 x.re))) 1/3)

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

Details

sample7.0s

simplify478.0ms

prune16.0ms

localize76.0ms

rewrite172.0ms

series340.0ms

simplify1.8s

prune1.6s

localize72.0ms

rewrite127.0ms

series357.0ms

simplify1.9s

prune1.4s

localize118.0ms

rewrite467.0ms

series1.3s

simplify3.8s

prune2.1s

localize92.0ms

rewrite379.0ms

series982.0ms

simplify2.7s

prune2.3s

regimes645.0ms