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 (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: 40.8b

localize16.0ms

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)))

rewrite16.0ms

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:

4.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
49.0ms	(+ (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 (62.0ms)

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

prune188.0ms

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	(+ re (hypot re im))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

3.0ms

(+ re (hypot re im))

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(+ re (hypot re im))

simplify71.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	74	60
1	162	54
2	350	54
3	952	54
4	3051	54
5	5001	54

prune71.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ re (hypot re im)))
1.8b	(+ re (hypot re im))
1.8b	(+ re (hypot re im))
1.8b	(+ re (hypot re im))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
8×	`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` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 67

Calls

4 calls:

3.0ms	(cbrt (+ re (hypot re im)))
7.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))

series330.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (+ re (hypot re im)))
61.0ms	(+ re (hypot re im))
61.0ms	(+ re (hypot re im))
55.0ms	(+ re (hypot re im))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	180	308
1	443	283
2	1525	280
3	5001	277

prune303.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt re)
0.5b	(cbrt re)
0.5b	(cbrt re)
18.7b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite5.0ms

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:

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

series899.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt re)
171.0ms	(cbrt re)
360.0ms	(cbrt re)
193.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify69.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	60	220
1	121	195
2	359	187
3	1734	185
4	5001	185

prune203.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.4b

regimes257.0ms

Accuracy

15.8% (4.9b remaining)

Error of 12.0b against oracle of 7.2b and baseline of 13.0b

bsearch157.0ms

Steps

Iters	Range	Point
5	-3.604041719607414e-89	-1.3548869531543663e-89	-3.3945979597993974e-89
10	-5.991532222681368e+46	-9.78963830731076e+36	-2.8979168285597056e+45
9	-1.5013042432692243e+90	-6.317617841719785e+84	-4.336243762655158e+86

Iters

Range

Point

-3.604041719607414e-89

-1.3548869531543663e-89

-3.3945979597993974e-89

-5.991532222681368e+46

-9.78963830731076e+36

-2.8979168285597056e+45

-1.5013042432692243e+90

-6.317617841719785e+84

-4.336243762655158e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	33
1	58	33
2	58	33

end0.0ms

sample669.0ms

Algorithm

intervals

Results

202.0ms	6080×	body	80	valid
143.0ms	699×	body	2560	valid
73.0ms	447×	body	1280	valid
62.0ms	262×	body	5120	valid
33.0ms	266×	body	640	valid
14.0ms	154×	body	320	valid
6.0ms	92×	body	160	valid