Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	190×	body	80	valid
8.0ms	19×	body	2560	valid
6.0ms	18×	body	1280	valid
4.0ms	8×	body	5120	valid
4.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 36.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
26.4b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* re re) (* im im))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	194	279
1	769	246
2	2332	233
3	5002	230

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
1.1b	(+ (hypot re im) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series107.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(hypot re im)
61.0ms	(+ (hypot re im) re)

simplify74.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	87	85
1	176	79
2	380	79
3	1030	78
4	3143	78
5	5001	78

prune103.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
16.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef`
1×	`fma-udef`

Counts

3 → 30

Calls

3 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series288.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(hypot re im)
46.0ms	(hypot re im)
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify49.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	61	142
1	158	121
2	456	117
3	1647	114
4	5002	114

prune144.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
16.1b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series490.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (hypot re im))
115.0ms	(cbrt (hypot re im))
120.0ms	(cbrt (hypot re im))
143.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

simplify138.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (133.0ms)

Iter	Nodes	Cost
0	100	381
1	249	336
2	841	330
3	4138	294
4	5001	282

prune225.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.4b

regimes112.0ms

Accuracy

34.9% (4.2b remaining)

Error of 11.6b against oracle of 7.5b and baseline of 13.9b

bsearch57.0ms

Steps

Iters	Range		Point
8	-3.758434163976895e-83	-9.752254444540214e-88	-2.6992662708432965e-84

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample1.4s

Algorithm

intervals

Results

541.0ms	5951×	body	80	valid
298.0ms	722×	body	2560	valid
168.0ms	482×	body	1280	valid
141.0ms	294×	body	5120	valid
82.0ms	304×	body	640	valid
34.0ms	165×	body	320	valid
14.0ms	82×	body	160	valid