Details

sample368.0ms

Algorithm

intervals

Results

42.0ms	66×	body	1280	valid
21.0ms	250×	body	80	valid
20.0ms	43×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	10×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize33.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sin-sum`

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
95.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
266.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	226	599
1	690	543
2	2010	539
3	5002	538

prune438.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.0b

localize38.0ms

Local error

Found 4 expressions with local error:

30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sin-sum`

Counts

4 → 47

Calls

4 calls:

4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
95.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
269.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	214	777
1	648	689
2	1928	683
3	5001	683

prune511.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.0b

localize41.0ms

Local error

Found 4 expressions with local error:

30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sin-sum`

Counts

4 → 47

Calls

4 calls:

4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
266.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	216	801
1	657	709
2	1960	703
3	5001	703

prune511.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.0b

regimes413.0ms

Accuracy

77.5% (3.1b remaining)

Error of 22.2b against oracle of 19.1b and baseline of 32.9b

bsearch388.0ms

Steps

Iters	Range		Point
9	8.211979739506963e-78	2.318953502136414e-69	1.3997201639137561e-73
8	5.668963595959583e-174	4.614711203633007e-170	3.081011543928129e-170
9	-8.557077847409789e-308	3.482262805343108e-300	-4.91324257936214e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	80
1	61	80

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2270×	body	1280	valid
694.0ms	8006×	body	80	valid
558.0ms	1366×	body	640	valid
165.0ms	585×	body	320	valid
74.0ms	47×	body	2560	valid
42.0ms	226×	body	160	valid