Details

sample158.0ms

Algorithm

intervals

Results

55.0ms	48×	body	2560	valid
26.0ms	49×	body	640	valid
25.0ms	35×	body	1280	valid
12.0ms	30×	body	320	valid
10.0ms	81×	body	80	valid
3.0ms	13×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	23
1	15
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize14.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1 (cos x))
14.4b	(/ (- 1 (cos x)) (* x x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
104×	`*-un-lft-identity`
90×	`times-frac`
53×	`add-cube-cbrt`
34×	`difference-of-squares`
21×	`swap-sqr` `associate-r` `associate-l`
17×	`distribute-lft-out--`
15×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `*-commutative` `unswap-sqr`
6×	`associate-/l*`
4×	`add-log-exp`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 145

Calls

2 calls:

12.0ms	(- 1 (cos x))
34.0ms	(/ (- 1 (cos x)) (* x x))

series139.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- 1 (cos x))
96.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5091
2	2331
1	607
0	208

prune436.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
14.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

2010×	`times-frac`
1482×	`*-un-lft-identity`
1242×	`add-sqr-sqrt`
966×	`add-cube-cbrt`
414×	`swap-sqr` `associate-r` `associate-l`
258×	`distribute-lft-out`
138×	`*-commutative` `unswap-sqr`
96×	`associate-/l*`
34×	`associate-/r/`
32×	`add-cbrt-cube` `add-exp-log`
25×	`associate-/l/`
23×	`associate-/r*`
18×	`flip3-+` `flip-+` `div-inv`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg` `div-sub` `sqr-sin` `sin-mult`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up`

Counts

4 → 1257

Calls

4 calls:

45.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
15.0ms	(* (sin x) (sin x))
7.0ms	(+ 1 (cos x))
123.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
33.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))
93.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify3.0s

Counts

1269 → 1269

Iterations

Iter	Nodes
done	5000
1	3271
0	1109

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
0.1b	(/ (tan (/ x 2)) x)
0.1b	(/ (sin x) x)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

90×	`frac-times`
87×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
70×	`associate-/l*`
69×	`associate-/r*`
40×	`times-frac`
24×	`clear-num`
23×	`frac-2neg`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
11×	`tan-quot` `associate-/l/`
10×	`associate-*r/`
9×	`associate-*l/`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`insert-posit16` `add-log-exp`
2×	`un-div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

3 → 216

Calls

3 calls:

83.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
21.0ms	(/ (tan (/ x 2)) x)
17.0ms	(/ (sin x) x)

series267.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
91.0ms	(/ (tan (/ x 2)) x)
56.0ms	(/ (sin x) x)

simplify1.7s

Counts

225 → 225

Iterations

Iter	Nodes
done	5002
2	3162
1	1035
0	305

prune664.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (sin (/ x 2)) (* x (cos (/ x 2)))))
0.1b	(/ (sin x) x)
0.1b	(* x (cos (/ x 2)))
0.2b	(/ (sin (/ x 2)) (* x (cos (/ x 2))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

203×	`add-sqr-sqrt`
192×	`associate-/r*`
162×	`frac-times`
147×	`*-un-lft-identity`
146×	`add-cube-cbrt`
97×	`times-frac`
94×	`associate-r` `associate-/l*`
67×	`associate-l`
34×	`add-cbrt-cube` `add-exp-log`
32×	`clear-num`
31×	`frac-2neg`
26×	`unswap-sqr`
19×	`*-commutative`
18×	`associate-*r/`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`associate-*l/`
8×	`pow1`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`pow-prod-down` `un-div-inv`

Counts

4 → 385

Calls

4 calls:

124.0ms	(* (/ (sin x) x) (/ (sin (/ x 2)) (* x (cos (/ x 2)))))
9.0ms	(/ (sin x) x)
14.0ms	(* x (cos (/ x 2)))
35.0ms	(/ (sin (/ x 2)) (* x (cos (/ x 2))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ (sin x) x) (/ (sin (/ x 2)) (* x (cos (/ x 2)))))
43.0ms	(/ (sin x) x)
56.0ms	(* x (cos (/ x 2)))
68.0ms	(/ (sin (/ x 2)) (* x (cos (/ x 2))))

simplify1.6s

Counts

397 → 397

Iterations

Iter	Nodes
done	5000
1	1864
0	517

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	1607×	body	2560	valid
985.0ms	1473×	body	640	valid
806.0ms	1250×	body	1280	valid
449.0ms	492×	body	160	valid
341.0ms	990×	body	320	valid
198.0ms	2188×	body	80	valid