Details

sample112.0ms

Algorithm

intervals

Results

38.0ms	49×	body	2560	valid
27.0ms	35×	body	1280	valid
18.0ms	46×	body	640	valid
10.0ms	30×	body	320	valid
6.0ms	73×	body	80	valid
4.0ms	23×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	26
2	21
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize12.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1 (cos x))
13.7b	(/ (- 1 (cos x)) (* x x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 63

Calls

2 calls:

6.0ms	(- 1 (cos x))
56.0ms	(/ (- 1 (cos x)) (* x x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(- 1 (cos x))
85.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.8s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune469.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
13.8b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

32.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series230.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))
116.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify8.7s

Counts

138 → 138

Iterations

Iter	Nodes
3	9653
2	1861
1	512
0	190

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 114

Calls

3 calls:

18.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
10.0ms	(/ (tan (/ x 2)) x)

series210.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
43.0ms	(/ (sin x) x)
67.0ms	(/ (tan (/ x 2)) x)

simplify8.5s

Counts

123 → 123

Iterations

Iter	Nodes
3	6069
2	1656
1	449
0	172

prune936.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
0.1b	(/ (sin x) x)
0.1b	(* (cos (* 1/2 x)) x)
0.2b	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
32×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`associate-l`
10×	`cbrt-undiv` `div-exp` `associate-r` `prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 124

Calls

4 calls:

47.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
8.0ms	(/ (sin x) x)
18.0ms	(* (cos (* 1/2 x)) x)
28.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))

series238.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
35.0ms	(/ (sin x) x)
41.0ms	(* (cos (* 1/2 x)) x)
74.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))

simplify57.3s

Counts

136 → 136

Iterations

Iter	Nodes
3	13053
2	1852
1	489
0	192

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	13
1	13
0	10

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	1559×	body	2560	valid
951.0ms	1309×	body	1280	valid
780.0ms	1511×	body	640	valid
678.0ms	934×	body	320	valid
348.0ms	2228×	body	80	valid
106.0ms	459×	body	160	valid