Details

sample74.0ms

Algorithm

intervals

Results

30.0ms	269×	body	80	valid
13.0ms	27×	body	640	valid
11.0ms	23×	body	1280	valid
5.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b	(* (* x (pow sin 2.0)) x)
7.2b	(* x (pow sin 2.0))
16.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite70.0ms

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:

27.0ms	(/ (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))
25.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series843.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
147.0ms	(* (* x (pow sin 2.0)) x)
135.0ms	(* x (pow sin 2.0))
262.0ms	(* (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

prune312.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.9b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 194

Calls

4 calls:

11.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
91.0ms	(/ (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)
92.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series873.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
297.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
155.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
280.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify97.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	603	2216
1	2821	1509
2	5002	1497

prune309.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.9b	(/ (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)))))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite32.0ms

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))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
105.0ms	(/ (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)))))))
216.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

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

prune391.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (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))))))
1.1b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

7.0ms	(/ (/ (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))))))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
14.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (/ (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))))))
71.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
216.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
212.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	519	3377
1	1844	3082
2	5001	2997

prune535.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

regimes275.0ms

Accuracy

0.1% (2.4b remaining)

Error of 2.5b against oracle of 0.1b and baseline of 2.5b

bsearch136.0ms

Steps

Iters	Range		Point
9	1.8694608836957067e-181	4.5123675782240195e-176	1.5373364345653098e-179

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	39
1	38	39

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	9011×	body	80	valid
408.0ms	830×	body	1280	valid
333.0ms	922×	body	640	valid
151.0ms	561×	body	320	valid
52.0ms	272×	body	160	valid