Details

sample351.0ms

Algorithm

intervals

Results

112.0ms	47×	body	1280	valid
46.0ms	258×	body	80	valid
35.0ms	39×	body	640	valid
9.0ms	17×	body	320	valid
4.0ms	10×	body	160	valid

simplify595.0ms

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

14.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.im)
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
261.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts: 68 → 68

prune487.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

51.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
144.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
32.0ms	(* (atan2 x.im x.re) y.im)
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts: 81 → 81

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.9b	(* (atan2 x.im x.re) y.im)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/r*`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`exp-prod`
5×	`pow1` `div-exp` `div-inv` `add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `exp-diff` `pow-exp` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `frac-2neg` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

43.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
11.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
12.0ms	(* (atan2 x.im x.re) y.im)

series172.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
40.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
25.0ms	(* (atan2 x.im x.re) y.im)

simplify768.0ms

Counts: 132 → 132

prune639.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))
3.7b	(cbrt (atan2 x.im x.re))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
2.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
12.0ms	(cbrt (atan2 x.im x.re))

series246.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
55.0ms	(cbrt (atan2 x.im x.re))
62.0ms	(cbrt (atan2 x.im x.re))
56.0ms	(cbrt (atan2 x.im x.re))

simplify777.0ms

Counts: 85 → 85

prune411.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes319.0ms

bsearch816.0ms

Steps

Iters	Range		Point
11	-1.8064072260362412e-290	5.147296625674691e-303	2.9106186824831246e-307
8	-9.07075452395602e-152	-2.051209900968979e-156	-8.840626789860417e-152
8	-1.4044621988311022e-69	-8.006417948394775e-74	-1.085931852353555e-71
8	-1163.8105601768866	-1.1154561922801245	-1.448187283069528

Details

sample351.0ms

simplify595.0ms

prune22.0ms

localize44.0ms

rewrite108.0ms

series398.0ms

simplify1.2s

prune487.0ms

localize30.0ms

rewrite90.0ms

series372.0ms

simplify1.1s

prune437.0ms

localize19.0ms

rewrite77.0ms

series172.0ms

simplify768.0ms

prune639.0ms

localize41.0ms

rewrite35.0ms

series246.0ms

simplify777.0ms

prune411.0ms

regimes319.0ms

bsearch816.0ms

simplify1.8s