Details

sample44.0ms

Algorithm

intervals

Results

16.0ms	195×	body	80	valid
7.0ms	21×	body	2560	valid
4.0ms	11×	body	5120	valid
4.0ms	13×	body	1280	valid
3.0ms	11×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

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)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

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:

3.0ms	(+ (* re re) (* im im))
31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

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

prune228.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.8b	(- (* 1 (hypot re im)) re)

rewrite12.0ms

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:

0.0ms	(hypot re im)
8.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
3.0ms	(- (* 1 (hypot re im)) re)

series287.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(hypot re im)
181.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
59.0ms	(- (* 1 (hypot re im)) re)

simplify33.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

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

prune148.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* 1 (hypot re im)) re))
0.0b	(hypot re im)
0.3b	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
0.8b	(- (* 1 (hypot re im)) re)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-r`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `prod-diff` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `hypot-udef` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

5.0ms	(sqrt (- (* 1 (hypot re im)) re))
0.0ms	(hypot re im)
14.0ms	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
3.0ms	(- (* 1 (hypot re im)) re)

series407.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (- (* 1 (hypot re im)) re))
47.0ms	(hypot re im)
182.0ms	(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))
58.0ms	(- (* 1 (hypot re im)) re)

simplify44.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	350	567
1	1333	489
2	5001	478

prune253.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (hypot re im) re)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

3.0ms	(- (hypot re im) re)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series58.0ms

Counts

4 → 6

Calls

4 calls:

58.0ms	(- (hypot re im) re)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	148	337
1	385	254
2	1579	236
3	5001	205

prune197.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes125.0ms

Accuracy

20.3% (4.6b remaining)

Error of 11.9b against oracle of 7.3b and baseline of 13.0b

bsearch75.0ms

Steps

Iters	Range		Point
8	4.8763098562687214e+173	1.5173481456430677e+178	3.3204403376095907e+174

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

424.0ms	6066×	body	80	valid
231.0ms	663×	body	2560	valid
138.0ms	491×	body	1280	valid
120.0ms	288×	body	5120	valid
67.0ms	291×	body	640	valid
24.0ms	135×	body	320	valid
8.0ms	66×	body	160	valid