Details

sample4.6s

Algorithm

intervals

Results

4.4s	1094×	body	10240	exit
103.0ms	256×	body	80	valid

simplify746.0ms

Calls

1 calls:

Slowest

746.0ms

(* (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))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize69.0ms

Local error

Found 4 expressions with local error:

30.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)

rewrite160.0ms

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` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Calls

4 calls:

Slowest

103.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
26.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(* (atan2 x.im x.re) y.im)

series331.0ms

Calls

4 calls:

Slowest

195.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls

47 calls:

Slowest

295.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
295.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
294.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
279.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
222.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize58.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`associate-l`
13×	`pow1`
9×	`add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
6×	`associate-r` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
5×	`log-pow` `distribute-lft-out`
4×	`insert-posit16` `difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Calls

4 calls:

Slowest

52.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
22.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms	(* (atan2 x.im x.re) y.im)

series343.0ms

Calls

4 calls:

Slowest

170.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
101.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)

simplify2.6s

Calls

58 calls:

Slowest

405.0ms	(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
351.0ms	(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
334.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
271.0ms	(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
207.0ms	(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`associate-l`
10×	`pow1`
7×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `distribute-lft-out--` `unswap-sqr`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`log-pow` `insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

3 calls:

Slowest

49.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
6.0ms	(* (log (- x.re)) y.re)
5.0ms	(* (atan2 x.im x.re) y.im)

series260.0ms

Calls

3 calls:

Slowest

148.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
91.0ms	(* (log (- x.re)) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Calls

42 calls:

Slowest

299.0ms	(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
263.0ms	(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
185.0ms	(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
143.0ms	(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
134.0ms	(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))

prune965.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

95.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.2b

bsearch1.8s

end0.0ms

sample2.0m

Algorithm

intervals

Results

2.0m	29603×	body	10240	exit
3.1s	8000×	body	80	valid