Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
4.0ms	21×	body	2560	valid
3.0ms	12×	body	5120	valid
3.0ms	16×	body	1280	valid
2.0ms	13×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	5×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.5b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series264.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune166.0ms

Filtered

62 candidates to 56 candidates (90.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Merged error: 7.5b

Counts

63 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.0b	(hypot re im)
1.1b	(+ (hypot re im) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
1.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series292.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
49.0ms	(hypot re im)
54.0ms	(+ (hypot re im) re)

simplify53.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	196	197
1	536	180
2	1779	174
3	5002	172

prune131.0ms

Filtered

51 candidates to 47 candidates (92.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Merged error: 7.3b

Counts

54 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(log1p (sqrt (* 2.0 (+ (hypot re im) re))))
1.1b	(+ (hypot re im) re)
2.8b	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(hypot re im)
1.0ms	(log1p (sqrt (* 2.0 (+ (hypot re im) re))))
3.0ms	(+ (hypot re im) re)
1.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot re im)
481.0ms	(log1p (sqrt (* 2.0 (+ (hypot re im) re))))
53.0ms	(+ (hypot re im) re)
533.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	326	377
1	1099	327
2	5002	305

prune190.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	59	9	68

Merged error: 7.3b

Counts

68 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (hypot re im) re)
2.8b	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
2.8b	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
2.8b	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

3.0ms	(+ (hypot re im) re)
1.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
1.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
1.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (hypot re im) re)
545.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
528.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))
529.0ms	(expm1 (log1p (sqrt (* 2.0 (+ (hypot re im) re)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	236	523
1	793	442
2	3867	409
3	5001	405

prune260.0ms

Filtered

62 candidates to 57 candidates (91.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	62	9	71

Merged error: 7.3b

Counts

71 → 9

regimes118.0ms

Accuracy

24.1% (4.5b remaining)

Error of 11.3b against oracle of 6.8b and baseline of 12.7b

bsearch133.0ms

Steps

Iters	Range	Point
10	-1.9003612051606162e-24	-1.0002625202821165e-38	-2.8486185678520585e-26
4	-4.411763548955001e+21	-2.512398608984434e+21	-4.352408394580921e+21
9	-1.0885082802572525e+92	-7.392779700790835e+83	-8.932262358816654e+87

Iters

Range

Point

-1.9003612051606162e-24

-1.0002625202821165e-38

-2.8486185678520585e-26

-4.411763548955001e+21

-2.512398608984434e+21

-4.352408394580921e+21

-1.0885082802572525e+92

-7.392779700790835e+83

-8.932262358816654e+87

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	32	24
1	35	12
2	38	12
3	38	12

end0.0ms

sample834.0ms

Algorithm

intervals

Results

347.0ms	6080×	body	80	valid
132.0ms	657×	body	2560	valid
82.0ms	475×	body	1280	valid
75.0ms	299×	body	5120	valid
35.0ms	277×	body	640	valid
13.0ms	134×	body	320	valid
5.0ms	78×	body	160	valid