Details

sample220.0ms

Algorithm

intervals

Results

114.0ms	97×	body	1280	valid
52.0ms	59×	body	640	valid
14.0ms	63×	body	80	valid
13.0ms	23×	body	320	valid
6.0ms	14×	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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
123×	`prod-diff`
119×	`*-un-lft-identity`
109×	`add-cube-cbrt`
56×	`times-frac`
52×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `associate-l`
9×	`flip3--` `flip--`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
6×	`sub-neg` `fma-neg` `div-inv`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u`
3×	`unswap-sqr`
2×	`diff-log` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 234

Calls

4 calls:

36.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
37.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series243.0ms

Counts

4 → 10

Calls

4 calls:

94.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify122.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1079	4683
1	4343	3463
2	5001	3456

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))
1.6b	(log (exp (- (cos x) (cos y))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
114×	`prod-diff`
111×	`*-un-lft-identity`
103×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`log-prod` `sqrt-prod`
11×	`exp-sum`
8×	`add-log-exp`
7×	`pow1` `log-pow`
6×	`add-exp-log` `exp-prod` `fma-neg` `associate-r` `associate-l` `add-cbrt-cube` `div-inv` `difference-of-squares`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-*r/` `diff-cos` `unswap-sqr`
1×	`log-div` `exp-diff` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 210

Calls

4 calls:

35.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))
9.0ms	(log (exp (- (cos x) (cos y))))

series199.0ms

Counts

4 → 10

Calls

4 calls:

88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
57.0ms	(- (cos x) (cos y))
54.0ms	(log (exp (- (cos x) (cos y))))

simplify102.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	949	3958
1	3329	2838
2	5002	2581

prune776.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.5b	(- (cos x) (cos y))
1.6b	(log (exp (- (cos x) (cos y))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
7×	`log-pow`
6×	`cbrt-prod` `exp-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`sub-neg` `pow1/3` `diff-cos` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 87

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
4.0ms	(- (cos x) (cos y))
9.0ms	(log (exp (- (cos x) (cos y))))

series108.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
50.0ms	(- (cos x) (cos y))
57.0ms	(log (exp (- (cos x) (cos y))))

simplify133.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	321	763
1	877	560
2	4004	458
3	5001	456

prune678.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite64.0ms

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))) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
34.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.1s

Counts

4 → 10

Calls

4 calls:

1.0s	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
92.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
52.0ms	(- (cos x) (cos y))

simplify81.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1405	7108
1	5001	5926

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	52
1	60	52
2	60	52

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.4s	2819×	body	1280	valid
1.5s	1824×	body	640	valid
532.0ms	2270×	body	80	valid
450.0ms	762×	body	320	valid
135.0ms	325×	body	160	valid