Details

sample175.0ms

Algorithm

intervals

Results

70.0ms	57×	body	2560	valid
44.0ms	43×	body	1280	valid
24.0ms	39×	body	640	valid
11.0ms	27×	body	320	valid
10.0ms	77×	body	80	valid
4.0ms	13×	body	160	valid

simplify27.0ms

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: 32.4b

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1 (cos x))
17.1b	(/ (- 1 (cos x)) (* x x))

rewrite55.0ms

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:

11.0ms	(- 1 (cos x))
42.0ms	(/ (- 1 (cos x)) (* x x))

series126.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- 1 (cos x))
101.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.7s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune520.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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))
16.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite113.0ms

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)))
22.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
46.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series166.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
19.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
89.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify8.1s

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

localize22.0ms

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)

rewrite35.0ms

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))
9.0ms	(/ (sin x) x)
7.0ms	(/ (tan (/ x 2)) x)

series280.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
62.0ms	(/ (sin x) x)
66.0ms	(/ (tan (/ x 2)) x)

simplify9.5s

Counts

123 → 123

Iterations

Iter	Nodes
3	6069
2	1656
1	449
0	172

prune993.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 93

Calls

3 calls:

26.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
12.0ms	(/ (tan (/ x 2)) x)
24.0ms	(* (sin x) (/ (tan (/ x 2)) x))

series305.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
68.0ms	(/ (tan (/ x 2)) x)
131.0ms	(* (sin x) (/ (tan (/ x 2)) x))

simplify6.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	7109
2	1341
1	370
0	154

prune873.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.4s	1585×	body	2560	valid
1.4s	1279×	body	1280	valid
725.0ms	1510×	body	640	valid
363.0ms	925×	body	320	valid
227.0ms	2254×	body	80	valid
92.0ms	447×	body	160	valid