Details

sample186.0ms

Algorithm

intervals

Results

94.0ms	93×	body	1280	valid
51.0ms	69×	body	640	valid
10.0ms	72×	body	80	valid
7.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
137×	`add-cube-cbrt`
130×	`times-frac`
105×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
13×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube` `div-inv`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `diff-cos` `associate-/l/`

Counts

4 → 250

Calls

4 calls:

6.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))) 3.0)
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series1.1s

Counts

4 → 10

Calls

4 calls:

944.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))) 3.0)
89.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
57.0ms	(- (cos x) (cos y))

simplify89.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1406	7067
1	5002	5887

prune1.2s

Filtered

260 candidates to 139 candidates (53.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	250	10	260
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	251	11	262

Merged error: 0.0b

Counts

262 → 11

localize52.0ms

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))))))

series50.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(* (cbrt 5.0) (cbrt 5.0))
50.0ms	(- (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))))))

simplify153.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	305	825
1	926	680
2	4824	648
3	5001	639

prune700.0ms

Filtered

100 candidates to 66 candidates (66.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

localize33.0ms

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))

rewrite70.0ms

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:

20.0ms	(* (* (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))
7.0ms	(- (cos x) (cos y))

series275.0ms

Counts

4 → 10

Calls

4 calls:

133.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))

simplify90.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1730	7731
1	5001	6094

prune960.0ms

Filtered

301 candidates to 127 candidates (42.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	299	2	301
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	301	11	312

Merged error: 0.0b

Counts

312 → 11

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))))))

rewrite19.0ms

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))
8.0ms	(- (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))))))

series51.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(* (cbrt 5.0) (cbrt 5.0))
51.0ms	(- (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))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (32.0ms)

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

prune675.0ms

Filtered

100 candidates to 67 candidates (67.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

regimes330.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	51
1	64	51
2	64	51

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.8s	2692×	body	1280	valid
1.3s	1853×	body	640	valid
354.0ms	762×	body	320	valid
337.0ms	2345×	body	80	valid
106.0ms	348×	body	160	valid