Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
4.0ms	22×	body	2560	valid
2.0ms	16×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `fma-def` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `hypot-def` `distribute-lft-out`

Counts

4 → 67

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* re re) (* im im))
157.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune215.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.7b	(+ (hypot re im) re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

8.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
8.0ms	(+ (hypot re im) re)

series217.0ms

Counts

2 → 6

Calls

2 calls:

168.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
49.0ms	(+ (hypot re im) re)

simplify51.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	183	173
1	519	156
2	1741	150
3	5001	148

prune106.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.4b	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
0.7b	(+ (hypot re im) re)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`associate-r`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

3 → 71

Calls

3 calls:

8.0ms	(sqrt (+ (hypot re im) re))
28.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
6.0ms	(+ (hypot re im) re)

series332.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(sqrt (+ (hypot re im) re))
168.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
52.0ms	(+ (hypot re im) re)

simplify108.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	287	433
1	995	403
2	4338	388
3	5001	387

prune190.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series342.0ms

Counts

2 → 6

Calls

2 calls:

217.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
125.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	129	225
1	378	193
2	1445	178
3	5002	174

prune74.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

regimes164.0ms

Accuracy

-16.7% (6.7b remaining)

Error of 14.0b against oracle of 7.3b and baseline of 13.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	51
1	51	51
2	51	51

end0.0ms

sample689.0ms

Algorithm

intervals

Results

191.0ms	6053×	body	80	valid
129.0ms	655×	body	2560	valid
78.0ms	477×	body	1280	valid
64.0ms	283×	body	5120	valid
33.0ms	282×	body	640	valid
15.0ms	164×	body	320	valid
5.0ms	86×	body	160	valid