Details

sample186.0ms

Algorithm

intervals

Results

80.0ms	98×	body	1280	valid
42.0ms	24×	body	2560	valid
27.0ms	56×	body	640	valid
7.0ms	22×	body	320	valid
5.0ms	44×	body	80	valid
2.0ms	12×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.7b	(sin (+ x eps))

rewrite115.0ms

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:

91.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (sin (+ x eps)) (sin x))
41.0ms	(sin (+ x eps))

simplify6.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5007
4	3899
3	1262
2	462
1	204
0	92

prune513.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
2.8b	(cos (/ (fma 2 x eps) 2))

rewrite127.0ms

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-cos-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

83.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
31.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
8.0ms	(cos (/ (fma 2 x eps) 2))

series292.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2))))
109.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
45.0ms	(cos (/ (fma 2 x eps) 2))

simplify5.4s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2413
2	632
1	235
0	98

prune904.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* (sin (* 1/2 eps)) 2) (cos (fma 1/2 eps x)))
2.8b	(cos (fma 1/2 eps x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

57.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (fma 1/2 eps x)))
4.0ms	(cos (fma 1/2 eps x))

series188.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (fma 1/2 eps x)))
33.0ms	(cos (fma 1/2 eps x))

simplify5.5s

Counts

38 → 38

Iterations

Iter	Nodes
done	5004
3	1802
2	528
1	174
0	72

prune582.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 1/2 eps)) (cos x))
0.1b	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.2b	(* (sin (* 1/2 eps)) (sin x))
0.2b	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `*-commutative`
2×	`flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`fma-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

47.0ms	(* (cos (* 1/2 eps)) (cos x))
58.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
52.0ms	(* (sin (* 1/2 eps)) (sin x))
279.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (cos (* 1/2 eps)) (cos x))
191.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
108.0ms	(* (sin (* 1/2 eps)) (sin x))
346.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify3.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1505
1	447
0	169

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes493.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	42
3	42
2	35
1	29
0	16

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.8s	3263×	body	1280	valid
1.2s	1897×	body	640	valid
1.1s	649×	body	2560	valid
287.0ms	762×	body	320	valid
93.0ms	1093×	body	80	valid
58.0ms	336×	body	160	valid