Details

sample236.0ms

Algorithm

intervals

Results

124.0ms	112×	body	1280	valid
36.0ms	49×	body	640	valid
34.0ms	17×	body	2560	valid
11.0ms	35×	body	80	valid
10.0ms	20×	body	320	valid
7.0ms	23×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize73.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.2b	(sin (+ x eps))

rewrite84.0ms

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:

69.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series74.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
4	3120
3	1109
2	432
1	203
0	92

prune459.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ eps x))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
2.3b	(cos (/ (+ x (+ eps x)) 2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

27.0ms	(+ x (+ eps x))
26.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
20.0ms	(cos (/ (+ x (+ eps x)) 2))

series157.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ x (+ eps x))
80.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
43.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify775.0ms

Counts

62 → 62

Iterations

Iter	Nodes
3	2082
2	678
1	235
0	100

prune722.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))
2.4b	(cos (fma eps 1/2 x))

rewrite36.0ms

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

29.0ms	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))
7.0ms	(cos (fma eps 1/2 x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))
23.0ms	(cos (fma eps 1/2 x))

simplify2.7s

Counts

38 → 38

Iterations

Iter	Nodes
5	3479
4	1512
3	696
2	308
1	135
0	67

prune479.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

18.0ms	(* (cos (* eps 1/2)) (cos x))
36.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
19.0ms	(* (sin (* eps 1/2)) (sin x))
183.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos (* eps 1/2)) (cos x))
117.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
86.0ms	(* (sin (* eps 1/2)) (sin x))
165.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
3	3456
2	1059
1	371
0	163

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	24
1	24
0	19

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.6s	3306×	body	1280	valid
1.6s	1898×	body	640	valid
1.5s	630×	body	2560	valid
349.0ms	756×	body	320	valid
150.0ms	1058×	body	80	valid
104.0ms	352×	body	160	valid