Details

sample6.2s

Algorithm

intervals

Results

5.6s	1354×	body	10240	exit
77.0ms	256×	body	80	valid

simplify418.0ms

Calls

1 calls:

Slowest

417.0ms

(* (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))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize67.0ms

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)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

29.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(* (atan2 x.im x.re) y.im)

series377.0ms

Calls

4 calls:

Slowest

225.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls

36 calls:

Slowest

621.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
289.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
207.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
205.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
200.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.5b

localize62.0ms

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)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

14.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(* (log (- x.re)) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series337.0ms

Calls

4 calls:

Slowest

163.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
104.0ms	(* (log (- x.re)) y.im)
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls

38 calls:

Slowest

375.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
302.0ms	(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.im y.im) y.im))
263.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
208.0ms	(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)))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize109.0ms

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)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

133.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
18.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(cbrt (log (- x.re)))

series1.2s

Calls

4 calls:

Slowest

469.0ms	(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
457.0ms	(cbrt (log (- x.re)))
188.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Calls

76 calls:

Slowest

259.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
228.0ms	(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
208.0ms	(pow (- (log (/ -1 x.re))) 1/3)
208.0ms	(pow (pow (+ (log -1) (log x.re)) 2) 1/3)
201.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize88.0ms

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))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

42.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
15.0ms	(* (log (- x.re)) (log (- x.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(cbrt (* (log (- x.re)) (log (- x.re))))

series959.0ms

Calls

4 calls:

Slowest

432.0ms	(cbrt (* (log (- x.re)) (log (- x.re))))
308.0ms	(* (log (- x.re)) (log (- x.re)))
168.0ms	(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.6s

Calls

69 calls:

Slowest

445.0ms	(pow (- (log -1) (log (/ 1 x.re))) 2)
273.0ms	(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
259.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
230.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
207.0ms	(pow (pow (+ (log -1) (log x.re)) 2) 1/3)

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

Details

sample6.2s

simplify418.0ms

prune12.0ms

localize67.0ms

rewrite61.0ms

series377.0ms

simplify1.8s

prune1.3s

localize62.0ms

rewrite35.0ms

series337.0ms

simplify1.8s

prune1.3s

localize109.0ms

rewrite165.0ms

series1.2s

simplify2.4s

prune2.0s

localize88.0ms

rewrite67.0ms

series959.0ms

simplify2.6s

prune2.0s

regimes832.0ms