Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	181×	body	80	valid
5.0ms	26×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	17×	body	640	valid
2.0ms	8×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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: 39.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune192.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
0.9b	(+ (* 1 (hypot re im)) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
3.0ms	(+ (* 1 (hypot re im)) re)

series245.0ms

Counts

2 → 6

Calls

2 calls:

187.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
58.0ms	(+ (* 1 (hypot re im)) re)

simplify75.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	203	208
1	623	184
2	2642	176
3	5001	175

prune116.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ (* 1 (hypot re im)) re))
0.9b	(+ (* 1 (hypot re im)) re)
0.9b	(+ (* 1 (hypot re im)) re)
0.9b	(+ (* 1 (hypot re im)) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (+ (* 1 (hypot re im)) re))
3.0ms	(+ (* 1 (hypot re im)) re)
3.0ms	(+ (* 1 (hypot re im)) re)
3.0ms	(+ (* 1 (hypot re im)) re)

series320.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (+ (* 1 (hypot re im)) re))
54.0ms	(+ (* 1 (hypot re im)) re)
58.0ms	(+ (* 1 (hypot re im)) re)
58.0ms	(+ (* 1 (hypot re im)) re)

simplify68.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	201	380
1	558	326
2	2452	317
3	5001	309

prune298.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* 1 (hypot re im)) re)
0.9b	(+ (* 1 (hypot re im)) re)
0.9b	(+ (* 1 (hypot re im)) re)
2.4b	(expm1 (log1p (cbrt (+ (* 1 (hypot re im)) re))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 56

Calls

4 calls:

3.0ms	(+ (* 1 (hypot re im)) re)
3.0ms	(+ (* 1 (hypot re im)) re)
3.0ms	(+ (* 1 (hypot re im)) re)
0.0ms	(expm1 (log1p (cbrt (+ (* 1 (hypot re im)) re))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* 1 (hypot re im)) re)
60.0ms	(+ (* 1 (hypot re im)) re)
60.0ms	(+ (* 1 (hypot re im)) re)
188.0ms	(expm1 (log1p (cbrt (+ (* 1 (hypot re im)) re))))

simplify69.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	197	346
1	551	297
2	2445	287
3	5001	281

prune312.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

regimes133.0ms

Accuracy

3.3% (5.5b remaining)

Error of 13.4b against oracle of 7.9b and baseline of 13.6b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	40	36
1	45	36
2	51	17
3	54	17
4	60	17
5	71	17
6	78	17
7	79	17
8	79	17

end0.0ms

sample695.0ms

Algorithm

intervals

Results

207.0ms	6015×	body	80	valid
139.0ms	695×	body	2560	valid
83.0ms	500×	body	1280	valid
72.0ms	285×	body	5120	valid
40.0ms	292×	body	640	valid
13.0ms	137×	body	320	valid
5.0ms	76×	body	160	valid