Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	19×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	10×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
53.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune239.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
0.3b	(- (hypot re im) re)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1` `prod-diff`
5×	`add-log-exp`
4×	`associate-*r/`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `fma-neg` `pow-prod-down` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 54

Calls

3 calls:

0.0ms	(hypot re im)
43.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
6.0ms	(- (hypot re im) re)

series300.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(hypot re im)
186.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
62.0ms	(- (hypot re im) re)

simplify32.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	242	349
1	892	254
2	5002	241

prune158.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* 2.0 (* 1 (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.1b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`pow1`
22×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-pow1`
10×	`pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `pow-prod-down` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-sqr`
2×	`flip3--` `sqrt-div` `flip--`
1×	`pow2` `sub-neg` `rem-sqrt-square` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
62.0ms	(sqrt (* 2.0 (* 1 (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))))
12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
13.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series389.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (hypot re im))
190.0ms	(sqrt (* 2.0 (* 1 (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))))
48.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
62.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	353	629
1	1523	514
2	5002	498

prune253.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
6.9b	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `associate-r` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`associate-l` `prod-diff`
2×	`pow1/3` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 68

Calls

4 calls:

12.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
28.0ms	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

series435.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
110.0ms	(cbrt (hypot re im))
115.0ms	(cbrt (hypot re im))
112.0ms	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	342	719
1	1404	611
2	5001	588

prune298.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

regimes99.0ms

Accuracy

20% (4.3b remaining)

Error of 11.9b against oracle of 7.6b and baseline of 13.0b

bsearch48.0ms

Steps

Iters	Range		Point
7	5.834639018555973e+189	1.1171867974082764e+192	6.234036773388663e+189

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	35	14
2	35	14

end0.0ms

sample711.0ms

Algorithm

intervals

Results

199.0ms	6064×	body	80	valid
137.0ms	674×	body	2560	valid
77.0ms	486×	body	1280	valid
66.0ms	286×	body	5120	valid
33.0ms	273×	body	640	valid
13.0ms	139×	body	320	valid
5.0ms	78×	body	160	valid