Details

sample171.0ms

Algorithm

intervals

Results

55.0ms	56×	body	1280	valid
47.0ms	22×	body	2560	valid
24.0ms	35×	body	640	valid
17.0ms	115×	body	80	valid
8.0ms	18×	body	320	valid
4.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize59.0ms

Local error

Found 3 expressions with local error:

4.5b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
32.1b	(tan (/ x (* y 2.0)))
32.1b	(sin (/ x (* y 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

3 → 49

Calls

3 calls:

10.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
3.0ms	(tan (/ x (* y 2.0)))
4.0ms	(sin (/ x (* y 2.0)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
51.0ms	(tan (/ x (* y 2.0)))
14.0ms	(sin (/ x (* y 2.0)))

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	3055
2	502
1	152
0	83

prune466.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune99.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 29.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
4.5b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
32.1b	(tan (/ x (* y 2.0)))
32.1b	(sin (/ x (* y 2.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`tan-quot`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `div-inv` `expm1-udef` `associate-/l/`

Counts

4 → 60

Calls

4 calls:

0.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
10.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
3.0ms	(tan (/ x (* y 2.0)))
9.0ms	(sin (/ x (* y 2.0)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
62.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
57.0ms	(tan (/ x (* y 2.0)))
12.0ms	(sin (/ x (* y 2.0)))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3579
2	602
1	188
0	100

prune695.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 29.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ x y) (/ x y)) E)
0.2b	(* (/ x y) (/ x y))
0.4b	(+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1))
19.7b	(log1p (+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `add-exp-log`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cbrt-cube` `add-cube-cbrt`
22×	`prod-exp`
16×	`pow1` `associate-r`
14×	`associate-l`
13×	`swap-sqr` `cbrt-unprod`
12×	`div-exp`
8×	`cbrt-undiv`
6×	`add-log-exp`
5×	`expm1-log1p-u` `e-exp-1` `associate-*l/` `unswap-sqr`
4×	`pow-prod-down` `log1p-expm1-u` `div-inv`
3×	`fma-def`
2×	`frac-times` `associate-r/` `-commutative`
1×	`pow2` `+-commutative` `associate-+r+` `log1p-udef` `sum-log` `flip3-+` `pow-plus` `log1p-expm1` `pow-sqr` `pow-prod-up` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 133

Calls

4 calls:

64.0ms	(* (* (/ x y) (/ x y)) E)
28.0ms	(* (/ x y) (/ x y))
8.0ms	(+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1))
0.0ms	(log1p (+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* (/ x y) (/ x y)) E)
47.0ms	(* (/ x y) (/ x y))
108.0ms	(+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1))
177.0ms	(log1p (+ E (fma 0.125 (* (* (/ x y) (/ x y)) E) -1)))

simplify4.6s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	4877
1	676
0	211

prune758.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 29.5b

regimes716.0ms

Accuracy

0% (2.4b remaining)

Error of 28.7b against oracle of 26.4b and baseline of 28.7b

bsearch0.0ms

simplify0.0ms

Iterations

Iter	Nodes
done	1
0	1

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	1425×	body	1280	valid
2.0s	656×	body	2560	valid
827.0ms	984×	body	640	valid
633.0ms	4068×	body	80	valid
294.0ms	571×	body	320	valid
159.0ms	296×	body	160	valid