Details

sample201.0ms

Algorithm

intervals

Results

37.0ms	47×	body	1280	valid
32.0ms	252×	body	80	valid
19.0ms	35×	body	640	valid
7.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.7b	(* (atan2 x.im x.re) y.re)
1.7b	(pow (exp y.im) (atan2 x.im x.re))
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

343×	`times-frac`
175×	`add-sqr-sqrt`
173×	`*-un-lft-identity` `add-cube-cbrt`
153×	`unpow-prod-down`
51×	`sqr-pow`
29×	`add-exp-log`
25×	`associate-/r*`
21×	`div-exp`
11×	`add-cbrt-cube`
9×	`div-inv`
8×	`pow-to-exp` `pow-exp`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `exp-prod` `associate-r` `associate-l`
1×	`clear-num` `frac-2neg` `sin-sum` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 286

Calls

4 calls:

24.0ms	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
11.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(pow (exp y.im) (atan2 x.im x.re))
8.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series945.0ms

Counts

4 → 12

Calls

4 calls:

660.0ms	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
22.0ms	(* (atan2 x.im x.re) y.re)
36.0ms	(pow (exp y.im) (atan2 x.im x.re))
226.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify858.0ms

Counts

298 → 298

Iterations

Iter	Nodes
done	5000
1	1403
0	526

prune2.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (exp (- (* (atan2 x.im x.re) y.im))) (* (pow (hypot x.re x.im) y.re) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.1b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.re)
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
13×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`pow1`
9×	`-un-lft-identity` `associate-l*` `prod-exp` `add-cube-cbrt`
7×	`associate-r`
5×	`sin-sum` `cbrt-unprod` `fma-udef`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`associate-*l/` `unswap-sqr`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `exp-diff` `pow-exp`

Counts

4 → 77

Calls

4 calls:

41.0ms	(* (exp (- (* (atan2 x.im x.re) y.im))) (* (pow (hypot x.re x.im) y.re) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
11.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

609.0ms	(* (exp (- (* (atan2 x.im x.re) y.im))) (* (pow (hypot x.re x.im) y.re) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
26.0ms	(* (atan2 x.im x.re) y.im)
24.0ms	(* (atan2 x.im x.re) y.re)
201.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1907
1	414
0	177

prune934.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))
1.0b	(* (cbrt y.re) (atan2 x.im x.re))
1.1b	(* (atan2 x.im x.re) y.im)
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `pow1` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `associate-l`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
1×	`sin-sum` `fma-udef`

Counts

4 → 80

Calls

4 calls:

84.0ms	(* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))
21.0ms	(* (cbrt y.re) (atan2 x.im x.re))
10.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))
114.0ms	(* (cbrt y.re) (atan2 x.im x.re))
32.0ms	(* (atan2 x.im x.re) y.im)
221.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt y.re) (atan2 x.im x.re)) (cbrt y.re)) (cbrt y.re))))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1869
1	315
0	140

prune1.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.2b

localize63.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
6.1b	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
6.1b	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
31.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (* (cbrt y.re) (atan2 x.im x.re))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt y.re)) (cbrt y.re))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

4.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
4.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
4.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (* (cbrt y.re) (atan2 x.im x.re))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt y.re)) (cbrt y.re))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
143.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
184.0ms	(cbrt (* (cbrt y.re) (atan2 x.im x.re)))
207.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (* (cbrt y.re) (atan2 x.im x.re))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt (* (cbrt y.re) (atan2 x.im x.re)))) (cbrt y.re)) (cbrt y.re))))

simplify1.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
4	1608
3	529
2	219
1	119
0	68

prune708.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 3.2b

regimes1.3s

Accuracy

21.6% (4.3b remaining)

Error of 7.6b against oracle of 3.3b and baseline of 8.8b

bsearch746.0ms

Steps

Iters	Range		Point
8	9.021466124990589e+156	4.322308559229635e+159	6.712004652234251e+157
4	3.884319661785569e-06	7.46228068957284e-06	7.350469407454487e-06
8	-0.00018459959308109883	-6.590418748316962e-09	-1.060367367938335e-06

simplify19.0ms

Iterations

Iter	Nodes
done	80
2	80
1	78
0	59

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.8s	2173×	body	1280	valid
1.7s	7959×	body	80	valid
1.3s	1386×	body	640	valid
767.0ms	583×	body	320	valid
147.0ms	45×	body	2560	valid
138.0ms	223×	body	160	valid