Details

sample215.0ms

Algorithm

intervals

Results

120.0ms	97×	body	1280	valid
48.0ms	64×	body	640	valid
12.0ms	23×	body	320	valid
9.0ms	56×	body	80	valid
6.0ms	16×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	74	30
1	193	27
2	704	27
3	2994	27
4	5001	27

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.3b

Counts

2 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.4b	(- (cos x) (cos y))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

184×	`add-sqr-sqrt`
183×	`prod-diff`
172×	`*-un-lft-identity`
164×	`add-cube-cbrt`
110×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `div-inv`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg` `fma-neg`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 291

Calls

4 calls:

21.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series281.0ms

Counts

4 → 10

Calls

4 calls:

135.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
54.0ms	(- (cos x) (cos y))

simplify94.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1730	7731
1	5001	6094

prune960.0ms

Filtered

301 candidates to 127 candidates (42.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	290	11	301
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	12	303

Merged error: 0.1b

Counts

303 → 12

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(* (cbrt 5.0) (cbrt 5.0))
1.4b	(- (cos x) (cos y))
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`cbrt-prod`
11×	`pow1`
9×	`prod-diff`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt 5.0)
6.0ms	(* (cbrt 5.0) (cbrt 5.0))
5.0ms	(- (cos x) (cos y))
1.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

series58.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(* (cbrt 5.0) (cbrt 5.0))
57.0ms	(- (cos x) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	325	834
1	1016	680
2	5001	657

prune749.0ms

Filtered

100 candidates to 67 candidates (67.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 0.1b

Counts

112 → 11

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
1.4b	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`prod-diff`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `fma-udef`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt 5.0)
1.0ms	(cbrt 5.0)
11.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
1.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

series58.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
58.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

simplify145.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	270	730
1	877	577
2	4591	539
3	5001	537

prune651.0ms

Filtered

60 candidates to 49 candidates (81.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
1.4b	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`prod-diff`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `fma-udef`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt 5.0)
1.0ms	(cbrt 5.0)
10.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
1.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

series249.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
249.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

simplify113.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	246	721
1	751	577
2	3650	539
3	5001	536

prune556.0ms

Filtered

60 candidates to 48 candidates (80.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

regimes216.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	55
1	64	55
2	64	55

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.5s	2812×	body	1280	valid
1.4s	1826×	body	640	valid
410.0ms	728×	body	320	valid
384.0ms	2278×	body	80	valid
129.0ms	356×	body	160	valid