Details

sample175.0ms

Algorithm

intervals

Results

86.0ms	56×	body	2560	valid
32.0ms	54×	body	640	valid
23.0ms	32×	body	1280	valid
11.0ms	29×	body	320	valid
9.0ms	70×	body	80	valid
4.0ms	15×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize23.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1 (cos x))
16.3b	(/ (- 1 (cos x)) (* x x))

rewrite42.0ms

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

series101.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- 1 (cos x))
77.0ms	(/ (- 1 (cos x)) (* x x))

simplify995.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2048
3	2048
2	867
1	295
0	121

prune220.0ms

Pruning

8 alts after pruning (8 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)))
0.2b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
16.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite85.0ms

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:

16.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
13.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))
44.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
36.0ms	(* (sin x) (sin x))
20.0ms	(+ 1 (cos x))
94.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	2000
3	2000
2	1777
1	525
0	190

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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:

26.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
14.0ms	(/ (sin x) x)
11.0ms	(/ (tan (/ x 2)) x)

series243.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
42.0ms	(/ (sin x) x)
91.0ms	(/ (tan (/ x 2)) x)

simplify1.0s

Counts

123 → 123

Iterations

Iter	Nodes
done	2004
3	2004
2	1627
1	453
0	172

prune475.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
43×	`associate-r`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`pow-prod-down` `tan-quot` `associate-r/` `-commutative`

Counts

3 → 172

Calls

3 calls:

18.0ms	(/ (/ (tan (/ x 2)) x) x)
12.0ms	(/ (tan (/ x 2)) x)
38.0ms	(* (sin x) (/ (/ (tan (/ x 2)) x) x))

series309.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (/ (tan (/ x 2)) x) x)
89.0ms	(/ (tan (/ x 2)) x)
151.0ms	(* (sin x) (/ (/ (tan (/ x 2)) x) x))

simplify1.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	2000
3	2000
2	1962
1	631
0	253

prune904.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes43.0ms

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
done	9
1	9
0	8

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.7s	1634×	body	2560	valid
976.0ms	1422×	body	640	valid
705.0ms	1207×	body	1280	valid
585.0ms	2284×	body	80	valid
307.0ms	964×	body	320	valid
125.0ms	489×	body	160	valid