Details

sample52.0ms

Algorithm

intervals

Results

17.0ms	301×	body	80	valid
8.0ms	32×	body	640	valid
8.0ms	24×	body	1280	valid
4.0ms	21×	body	320	valid
0.0ms	2×	body	160	valid

simplify43.0ms

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: 24.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.8b	(* (* x (pow sin 2.0)) x)
6.8b	(* x (pow sin 2.0))
16.9b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite76.0ms

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:

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

series815.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
140.0ms	(* (* x (pow sin 2.0)) x)
131.0ms	(* x (pow sin 2.0))
256.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify63.0ms

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

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.9b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite249.0ms

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:

12.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
93.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
35.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
96.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series878.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
304.0ms	(/ (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)
274.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify91.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (72.0ms)

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

prune313.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize16.0ms

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)))))))
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))))))
4.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite37.0ms

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:

8.0ms	(/ (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)))))))
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))))))
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:

108.0ms	(/ (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)))))))
34.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
215.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
211.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

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

prune393.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
0.2b	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
4.7b	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`prod-exp`
18×	`pow-exp`
16×	`unpow-prod-down`
9×	`pow-to-exp`
8×	`associate-/r*`
7×	`add-cbrt-cube` `sqr-pow`
5×	`associate-l` `unpow2`
4×	`pow1`
3×	`expm1-log1p-u` `pow-unpow` `div-exp` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
1.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
7.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series450.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
34.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
317.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	342	1364
1	1160	1248
2	5002	1239

prune351.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

7.1% (2.4b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.7b

bsearch179.0ms

Steps

Iters	Range		Point
6	2.1285005641463748e+145	1.7958241045161027e+146	7.576854927319505e+145
8	-6.75216425001212e-306	6.311120560139708e-307	4.1989922527869865e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms

sample1.5s

Algorithm

intervals

Results

540.0ms	8953×	body	80	valid
285.0ms	783×	body	1280	valid
234.0ms	970×	body	640	valid
104.0ms	574×	body	320	valid
42.0ms	310×	body	160	valid