Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
4.0ms	19×	body	2560	valid
3.0ms	22×	body	1280	valid
3.0ms	14×	body	5120	valid
1.0ms	11×	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 (1.0ms)

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: 43.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (82.0ms)

Iter	Nodes	Cost
0	155	205
1	421	183
2	1067	180
3	3190	179
4	5001	178

prune138.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.7b

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

4.0ms

(+ (* (sqrt 1) (hypot re im)) re)

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(+ (* (sqrt 1) (hypot re im)) re)

simplify91.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 4 (88.0ms)

Iter	Nodes	Cost
0	95	97
1	268	85
2	754	82
3	3049	80
4	5001	79

prune71.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* (sqrt 1) (hypot re im)) re)
3.6b	(expm1 (log1p (+ (* (sqrt 1) (hypot re im)) re)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

8.0ms	(+ (* (sqrt 1) (hypot re im)) re)
0.0ms	(expm1 (log1p (+ (* (sqrt 1) (hypot re im)) re)))

series185.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ (* (sqrt 1) (hypot re im)) re)
126.0ms	(expm1 (log1p (+ (* (sqrt 1) (hypot re im)) re)))

simplify37.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	135	177
1	357	154
2	964	146
3	5001	139

prune112.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(fma -1 re (hypot re im))
5.9b	(sqrt (* 2.0 (/ (* im im) (fma -1 re (hypot re im)))))
23.5b	(/ (* im im) (fma -1 re (hypot re im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`expm1-log1p-u` `times-frac` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp`
1×	`frac-2neg` `pow1/2` `sqrt-div` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `sqrt-prod` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l`

Counts

3 → 47

Calls

3 calls:

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

series358.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma -1 re (hypot re im))
205.0ms	(sqrt (* 2.0 (/ (* im im) (fma -1 re (hypot re im)))))
88.0ms	(/ (* im im) (fma -1 re (hypot re im)))

simplify135.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	264	332
1	999	284
2	4612	275
3	5001	275

prune161.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

regimes148.0ms

Accuracy

78.9% (2.0b remaining)

Error of 5.7b against oracle of 3.7b and baseline of 13.2b

bsearch34.0ms

Steps

Iters	Range		Point
7	-4.7884843669465375e-217	-5.039965811152407e-219	-9.19175241240825e-219

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	31	14

end0.0ms

sample671.0ms

Algorithm

intervals

Results

201.0ms	6023×	body	80	valid
125.0ms	653×	body	2560	valid
77.0ms	483×	body	1280	valid
71.0ms	309×	body	5120	valid
41.0ms	302×	body	640	valid
13.0ms	143×	body	320	valid
6.0ms	87×	body	160	valid