Details

sample185.0ms

Algorithm

intervals

Results

84.0ms	125×	body	1280	valid
32.0ms	23×	body	2560	valid
26.0ms	37×	body	320	valid
25.0ms	59×	body	640	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize21.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite22.0ms

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` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

13.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series124.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (cos (+ x eps)) (cos x))
36.0ms	(cos (+ x eps))

simplify3.4s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3416
3	1175
2	423
1	200
0	91

prune268.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
3.9b	(sin (/ (fma 2 x eps) 2))

rewrite48.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

41.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series118.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
34.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.4s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
4	2049
3	875
2	335
1	144
0	67

prune273.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (fma 1/2 eps x)) (sin (* eps 1/2)))
3.9b	(sin (fma 1/2 eps x))

rewrite19.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

16.0ms	(* (sin (fma 1/2 eps x)) (sin (* eps 1/2)))
2.0ms	(sin (fma 1/2 eps x))

series119.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (sin (fma 1/2 eps x)) (sin (* eps 1/2)))
32.0ms	(sin (fma 1/2 eps x))

simplify3.1s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
5	3851
4	1615
3	805
2	352
1	142
0	71

prune323.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
0.1b	(* (sin (* 1/2 eps)) (cos x))
0.2b	(* (cos (* 1/2 eps)) (sin x))
0.3b	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

rewrite136.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `fma-def` `sin-cos-mult`

Counts

4 → 77

Calls

4 calls:

21.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
16.0ms	(* (sin (* 1/2 eps)) (cos x))
17.0ms	(* (cos (* 1/2 eps)) (sin x))
79.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
88.0ms	(* (sin (* 1/2 eps)) (cos x))
69.0ms	(* (cos (* 1/2 eps)) (sin x))
192.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

simplify2.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	3983
2	1162
1	371
0	154

prune558.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes289.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.4s	4442×	body	1280	valid
1.4s	1831×	body	640	valid
1.0s	645×	body	2560	valid
225.0ms	731×	body	320	valid
52.0ms	259×	body	160	valid
8.0ms	92×	body	80	valid