Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	22×	body	2560	valid
6.0ms	194×	body	80	valid
3.0ms	13×	body	5120	valid
2.0ms	14×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	5×	body	320	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: 38.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.0b	(- (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:

15.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(+ (* re re) (* im im))
9.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
29.0ms	(+ (* re re) (* im im))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

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

prune238.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

7.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
1.0ms	(hypot re im)
5.0ms	(- (* 1 (hypot re im)) re)

series284.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
43.0ms	(hypot re im)
59.0ms	(- (* 1 (hypot re im)) re)

simplify33.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	235	265
1	803	220
2	5002	213

prune153.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.8b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
14×	`*-un-lft-identity`
13×	`add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

1.0ms	(hypot re im)
1.0ms	(hypot re im)
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series192.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
46.0ms	(hypot re im)
47.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
55.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify43.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	211	391
1	869	298
2	5001	281

prune243.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (hypot re im)))
0.2b	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
10.3b	(- (* 1 (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-r` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-l`
8×	`sqrt-pow1`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `flip--` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 154

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
15.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
12.0ms	(- (* 1 (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

series344.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (sqrt (hypot re im)))
47.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
129.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
60.0ms	(- (* 1 (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

simplify73.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	398	1484
1	1865	977
2	5002	850

prune369.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

regimes132.0ms

Accuracy

23% (4.4b remaining)

Error of 11.5b against oracle of 7.1b and baseline of 12.8b

bsearch51.0ms

Steps

Iters	Range		Point
7	3.3765927396946256e+151	1.3584121836592172e+153	4.412835503564449e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	37	14
2	37	14

end0.0ms

sample670.0ms

Algorithm

intervals

Results

207.0ms	6089×	body	80	valid
127.0ms	656×	body	2560	valid
71.0ms	460×	body	1280	valid
67.0ms	287×	body	5120	valid
32.0ms	266×	body	640	valid
15.0ms	159×	body	320	valid
10.0ms	83×	body	160	valid