Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
5.0ms	23×	body	2560	valid
3.0ms	13×	body	5120	valid
2.0ms	14×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize9.0ms

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))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

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:

14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
3.0ms	(+ (* re re) (* im im))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
26.0ms	(+ (* re re) (* im im))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (87.0ms)

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

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.6b	(+ (hypot re im) re)

rewrite7.0ms

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:

4.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series244.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
58.0ms	(+ (hypot re im) re)

simplify51.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (48.0ms)

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

prune107.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

2.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series544.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
85.0ms	(sqrt (hypot re im))
85.0ms	(sqrt (hypot re im))
139.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify76.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	194	379
1	555	327
2	2599	302
3	5002	300

prune195.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

2.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series549.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
85.0ms	(sqrt (hypot re im))
84.0ms	(sqrt (hypot re im))
139.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify80.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	194	379
1	555	327
2	2599	302
3	5002	300

prune184.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

regimes167.0ms

Accuracy

26.2% (4.3b remaining)

Error of 11.8b against oracle of 7.5b and baseline of 13.3b

bsearch43.0ms

Steps

Iters	Range		Point
8	-1.9024895209928806e-29	-1.5787481178162737e-32	-2.6679783667570792e-30

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample675.0ms

Algorithm

intervals

Results

199.0ms	5999×	body	80	valid
139.0ms	699×	body	2560	valid
78.0ms	478×	body	1280	valid
76.0ms	310×	body	5120	valid
36.0ms	288×	body	640	valid
19.0ms	151×	body	320	valid
5.0ms	75×	body	160	valid