Details

sample81.0ms

Algorithm

intervals

Results

33.0ms	285×	body	80	valid
14.0ms	32×	body	1280	valid
11.0ms	30×	body	640	valid
4.0ms	17×	body	320	valid
3.0ms	18×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.0b	(* (* x (pow sin 2.0)) x)
12.0b	(* x (pow sin 2.0))
19.0b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 123

Calls

4 calls:

28.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
26.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series849.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
147.0ms	(* (* x (pow sin 2.0)) x)
138.0ms	(* x (pow sin 2.0))
263.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify59.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	448	971
1	2063	815
2	5002	815

prune309.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.0b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 171

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
92.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
32.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
94.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series742.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cos (* 2.0 x))
302.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
156.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
265.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify81.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	566	2020
1	2548	1394
2	5001	1382

prune294.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.4b	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
4.3b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.3b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-l`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

3.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
103.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
222.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	325	1562
1	1244	1292
2	5001	1217

prune398.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.8b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.3b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.3b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
42×	`prod-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
14×	`pow-to-exp` `associate-l` `pow-exp`
9×	`times-frac`
6×	`unpow-prod-down` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
69.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
218.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	289	1087
1	993	973
2	5001	973

prune331.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

regimes357.0ms

Accuracy

6.6% (2.1b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.4b

bsearch174.0ms

Steps

Iters	Range		Point
6	4.3988303560488366e-111	5.588059564773241e-110	4.88319876901602e-111
9	-1.9592565212578152e-112	-8.46541346263711e-122	-4.65962850443894e-117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	61
1	46	61

end0.0ms

sample2.1s

Algorithm

intervals

Results

924.0ms	9034×	body	80	valid
350.0ms	789×	body	1280	valid
342.0ms	983×	body	640	valid
159.0ms	601×	body	320	valid
59.0ms	312×	body	160	valid