Details

sample159.0ms

Algorithm

intervals

Results

65.0ms	41×	body	1280	valid
28.0ms	15×	body	2560	valid
21.0ms	36×	body	640	valid
18.0ms	137×	body	80	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize15.0ms

Local error

Found 3 expressions with local error:

8.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.7b	(sin (/ x (* y 2.0)))
27.1b	(tan (/ x (* y 2.0)))

rewrite16.0ms

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:

9.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
4.0ms	(sin (/ x (* y 2.0)))
3.0ms	(tan (/ x (* y 2.0)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
11.0ms	(sin (/ x (* y 2.0)))
49.0ms	(tan (/ x (* y 2.0)))

simplify1.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	3100
2	502
1	152
0	83

prune402.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.6b

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

prune61.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
8.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.7b	(sin (/ x (* y 2.0)))
27.1b	(tan (/ x (* y 2.0)))

rewrite28.0ms

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:

1.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
17.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
3.0ms	(tan (/ x (* y 2.0)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
73.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
17.0ms	(sin (/ x (* y 2.0)))
65.0ms	(tan (/ x (* y 2.0)))

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3597
2	602
1	188
0	100

prune500.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ x y) (/ x y)) E)
0.2b	(* (/ x y) (/ x y))
1.0b	(- E 1)
16.3b	(log1p (fma 0.125 (* (* (/ x y) (/ x y)) E) (- E 1)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

35.0ms	(* (* (/ x y) (/ x y)) E)
23.0ms	(* (/ x y) (/ x y))
5.0ms	(- E 1)
0.0ms	(log1p (fma 0.125 (* (* (/ x y) (/ x y)) E) (- E 1)))

series235.0ms

Counts

4 → 10

Calls

4 calls:

74.0ms	(* (* (/ x y) (/ x y)) E)
33.0ms	(* (/ x y) (/ x y))
0.0ms	(- E 1)
128.0ms	(log1p (fma 0.125 (* (* (/ x y) (/ x y)) E) (- E 1)))

simplify792.0ms

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
1	718
0	233

prune919.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 24.6b

regimes926.0ms

Accuracy

41.7% (1.4b remaining)

Error of 27.5b against oracle of 26.0b and baseline of 28.5b

bsearch2.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	15

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.1s	1398×	body	1280	valid
1.6s	664×	body	2560	valid
1.3s	4110×	body	80	valid
865.0ms	951×	body	640	valid
314.0ms	548×	body	320	valid
171.0ms	329×	body	160	valid