Details

sample230.0ms

Algorithm

intervals

Results

103.0ms	129×	body	1280	valid
67.0ms	25×	body	2560	valid
39.0ms	69×	body	640	valid
7.0ms	18×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize16.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
1.9b	(cos (+ x eps))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

12.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series114.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (cos (+ x eps)) (cos x))
47.0ms	(cos (+ x eps))

simplify3.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3416
3	1158
2	424
1	202
0	93

prune261.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
2.0b	(sin (/ (fma 2 x eps) 2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

60.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
23.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series246.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
99.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
40.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2020
2	602
1	226
0	102

prune381.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.5b	(log1p (sin (/ (fma 2 x eps) 2)))
2.0b	(sin (/ (fma 2 x eps) 2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
37.0ms	(* (sin (* eps 1/2)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
1.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
132.0ms	(* (sin (* eps 1/2)) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
61.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
39.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
4	2418
3	1065
2	416
1	177
0	92

prune456.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma 2 x eps) 2)))
2.0b	(sin (/ (fma 2 x eps) 2))
2.0b	(sin (/ (fma 2 x eps) 2))
2.0b	(sin (/ (fma 2 x eps) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

3.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
5.0ms	(sin (/ (fma 2 x eps) 2))
5.0ms	(sin (/ (fma 2 x eps) 2))
5.0ms	(sin (/ (fma 2 x eps) 2))

series305.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
50.0ms	(sin (/ (fma 2 x eps) 2))
39.0ms	(sin (/ (fma 2 x eps) 2))
57.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.4s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	2611
3	800
2	262
1	117
0	60

prune349.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes352.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.4b

bsearch242.0ms

Steps

Iters	Range		Point
7	4.263740854872979e-07	7.143616659564812e-05	1.4877491964720032e-05
9	-101227.54480913779	-0.0005350557287305616	-0.0008099166487036783

simplify12.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample8.6s

Algorithm

intervals

Results

5.1s	4444×	body	1280	valid
1.7s	1831×	body	640	valid
1.1s	610×	body	2560	valid
330.0ms	737×	body	320	valid
77.0ms	281×	body	160	valid
12.0ms	97×	body	80	valid