Details

sample215.0ms

Algorithm

intervals

Results

96.0ms	106×	body	1280	valid
57.0ms	56×	body	640	valid
35.0ms	21×	body	2560	valid
8.0ms	21×	body	320	valid
4.0ms	37×	body	80	valid
4.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize26.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
2.5b	(sin (+ x eps))

rewrite61.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series74.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify2.4s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3934
3	1269
2	446
1	203
0	92

prune190.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

11.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series107.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
30.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
4	2632
3	983
2	353
1	150
0	70

prune274.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `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:

10.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series275.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
71.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
71.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
31.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
4	3626
3	1297
2	462
1	206
0	97

prune333.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (fma 2 x eps) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
0.4b	(log (exp (cos (/ (fma 2 x eps) 2))))
2.5b	(cos (/ (fma 2 x eps) 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 73

Calls

4 calls:

5.0ms	(exp (cos (/ (fma 2 x eps) 2)))
25.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
6.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
3.0ms	(cos (/ (fma 2 x eps) 2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(exp (cos (/ (fma 2 x eps) 2)))
53.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (fma 2 x eps) 2)))))
25.0ms	(log (exp (cos (/ (fma 2 x eps) 2))))
25.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
4	3996
3	1418
2	547
1	234
0	116

prune354.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

regimes176.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.6b

bsearch116.0ms

Steps

Iters	Range		Point
4	7.81566744931325e-09	1.2368458821499648e-08	1.1087986248072222e-08
11	-3168283.462966651	-1.7028068208877994e-13	-1.1998709236678226e-08

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	3281×	body	1280	valid
1.0s	1826×	body	640	valid
700.0ms	629×	body	2560	valid
212.0ms	762×	body	320	valid
93.0ms	358×	body	160	valid
90.0ms	1144×	body	80	valid