Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	177×	body	80	valid
5.0ms	26×	body	2560	valid
3.0ms	20×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	10×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	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: 40.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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

series112.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* re re) (* im im))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

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

prune191.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize8.0ms

Local error

Found 1 expressions with local error:

1.8b	(+ (* 1 (hypot re im)) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

3.0ms

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

series59.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

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

simplify58.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	96	77
1	240	67
2	714	66
3	2180	63
4	5001	62

prune61.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ (* 1 (hypot re im)) re))
1.8b	(+ (* 1 (hypot re im)) re)
1.8b	(+ (* 1 (hypot re im)) re)
1.8b	(+ (* 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:

2.0ms	(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)

series328.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (+ (* 1 (hypot re im)) re))
54.0ms	(+ (* 1 (hypot re im)) re)
60.0ms	(+ (* 1 (hypot re im)) re)
59.0ms	(+ (* 1 (hypot re im)) re)

simplify68.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (62.0ms)

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

prune418.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 8.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ (pow im 2) (- (hypot re im) re)))
0.5b	(- (hypot re im) re)
6.3b	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
20.4b	(/ (pow im 2) (- (hypot re im) re))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`times-frac`
52×	`add-cube-cbrt`
46×	`associate-r`
34×	`unpow-prod-down`
19×	`add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`unpow2` `sqr-pow`
11×	`add-cbrt-cube`
9×	`pow1` `prod-diff`
8×	`associate-/l*`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-l` `flip--`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `associate-*r/` `pow-prod-down` `pow-exp` `cbrt-unprod` `div-inv`
1×	`sub-neg` `frac-2neg` `pow1/2` `sqrt-div` `diff-log` `clear-num` `sqrt-prod` `*-commutative`

Counts

4 → 185

Calls

4 calls:

24.0ms	(* 2.0 (/ (pow im 2) (- (hypot re im) re)))
3.0ms	(- (hypot re im) re)
7.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
8.0ms	(/ (pow im 2) (- (hypot re im) re))

series429.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* 2.0 (/ (pow im 2) (- (hypot re im) re)))
59.0ms	(- (hypot re im) re)
197.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
82.0ms	(/ (pow im 2) (- (hypot re im) re))

simplify79.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	638	1437
1	2858	1201
2	5002	1192

prune466.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.0b

regimes97.0ms

Accuracy

80.1% (1.8b remaining)

Error of 5.6b against oracle of 3.7b and baseline of 13.0b

bsearch44.0ms

Steps

Iters	Range		Point
9	-1.94649178438058e-226	-4.169840253672973e-233	-4.3168234763468e-232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	33	14
2	33	14

end0.0ms

sample670.0ms

Algorithm

intervals

Results

208.0ms	6080×	body	80	valid
136.0ms	699×	body	2560	valid
71.0ms	447×	body	1280	valid
65.0ms	262×	body	5120	valid
33.0ms	266×	body	640	valid
14.0ms	154×	body	320	valid
10.0ms	92×	body	160	valid