Details

sample147.0ms

Algorithm

intervals

Results

70.0ms	54×	body	2560	valid
23.0ms	36×	body	1280	valid
21.0ms	46×	body	640	valid
11.0ms	30×	body	320	valid
8.0ms	77×	body	80	valid
3.0ms	13×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize11.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1 (cos x))
16.0b	(/ (- 1 (cos x)) (* x x))

rewrite34.0ms

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:

15.0ms	(- 1 (cos x))
18.0ms	(/ (- 1 (cos x)) (* x x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1 (cos x))
81.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.8s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune222.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))
16.3b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite59.0ms

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:

21.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
6.0ms	(+ 1 (cos x))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series185.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))
94.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.7s

Counts

138 → 138

Iterations

Iter	Nodes
3	9653
2	1861
1	512
0	190

prune455.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

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:

22.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
6.0ms	(/ (tan (/ x 2)) x)
8.0ms	(/ (sin x) x)

series282.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
85.0ms	(/ (tan (/ x 2)) x)
56.0ms	(/ (sin x) x)

simplify9.8s

Counts

123 → 123

Iterations

Iter	Nodes
3	6939
2	1694
1	449
0	172

prune526.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
139×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
106×	`add-cube-cbrt`
64×	`add-exp-log`
47×	`associate-r`
34×	`add-cbrt-cube`
30×	`div-exp`
20×	`associate-/r*`
14×	`cbrt-undiv` `prod-exp`
13×	`associate-l`
12×	`div-inv`
10×	`associate-/r/` `unswap-sqr`
9×	`associate-/l*`
8×	`tan-quot`
7×	`pow1`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 250

Calls

4 calls:

29.0ms	(* (/ (sin x) x) (/ 1 (/ x (tan (/ x 2)))))
16.0ms	(/ 1 (/ x (tan (/ x 2))))
11.0ms	(/ x (tan (/ x 2)))
11.0ms	(/ (sin x) x)

series344.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (/ (sin x) x) (/ 1 (/ x (tan (/ x 2)))))
76.0ms	(/ 1 (/ x (tan (/ x 2))))
61.0ms	(/ x (tan (/ x 2)))
45.0ms	(/ (sin x) x)

simplify14.2s

Counts

262 → 262

Iterations

Iter	Nodes
2	3037
1	983
0	337

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes46.0ms

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	11
1	11
0	10

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	1531×	body	2560	valid
940.0ms	1265×	body	1280	valid
802.0ms	1502×	body	640	valid
569.0ms	453×	body	160	valid
328.0ms	950×	body	320	valid
301.0ms	2299×	body	80	valid