Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	26×	body	2560	valid
6.0ms	177×	body	80	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

Filtered

1 candidates to 0 candidates (0.0%)

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)))

rewrite23.0ms

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)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(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

prune182.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize7.0ms

Local error

Found 1 expressions with local error:

1.8b	(+ (hypot re im) re)

rewrite3.0ms

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

(+ (hypot re im) re)

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(+ (hypot re im) re)

simplify71.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	74	61
1	162	55
2	350	55
3	952	54
4	3051	54
5	5001	54

prune69.0ms

Filtered

20 candidates to 18 candidates (90.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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:

2.0ms	(cbrt (+ (hypot re im) re))
3.0ms	(+ (hypot re im) re)
3.0ms	(+ (hypot re im) re)
3.0ms	(+ (hypot re im) re)

series314.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (+ (hypot re im) re))
56.0ms	(+ (hypot re im) re)
53.0ms	(+ (hypot re im) re)
57.0ms	(+ (hypot re im) re)

simplify43.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	180	311
1	447	286
2	1542	283
3	5002	277

prune271.0ms

Filtered

79 candidates to 71 candidates (89.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 1 expressions with local error:

18.9b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series136.0ms

Counts

1 → 3

Calls

1 calls:

136.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	45	88
1	118	73
2	387	69
3	1530	66
4	5001	66

prune36.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

regimes189.0ms

Accuracy

17.5% (4.7b remaining)

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

bsearch136.0ms

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	-2.1233934513353364e+89

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

-2.1233934513353364e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	33	24
1	36	12
2	39	12
3	39	12

end0.0ms

sample715.0ms

Algorithm

intervals

Results

214.0ms	6080×	body	80	valid
142.0ms	699×	body	2560	valid
82.0ms	447×	body	1280	valid
68.0ms	262×	body	5120	valid
38.0ms	266×	body	640	valid
15.0ms	154×	body	320	valid
6.0ms	92×	body	160	valid