Details

sample133.0ms

Algorithm

intervals

Results

71.0ms	144×	body	1280	valid
25.0ms	25×	body	2560	valid
18.0ms	61×	body	640	valid
5.0ms	23×	body	320	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite28.0ms

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:

19.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series122.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (cos (+ x eps)) (cos x))
31.0ms	(cos (+ x eps))

simplify933.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune261.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(fma (sin eps) (sin x) (cos x))
2.1b	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

20.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin eps) (sin x) (cos x))
12.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))

series380.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (cos x) (cos eps))
113.0ms	(fma (sin eps) (sin x) (cos x))
214.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))

simplify1.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
2	976
1	241
0	108

prune494.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.2b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (sin eps) (sin x) (cos x))
2.1b	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma (sin eps) (sin x) (cos x))
0.0ms	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

series308.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma (sin eps) (sin x) (cos x))
213.0ms	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

simplify1.4s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1429
2	328
1	98
0	49

prune351.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 17.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sin eps) (sin x))
0.2b	(+ (* (sin eps) (sin x)) (cos x))
2.1b	(fma (cos x) (cos eps) (- (+ (* (sin eps) (sin x)) (cos x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `sin-mult` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

13.0ms	(* (sin eps) (sin x))
14.0ms	(+ (* (sin eps) (sin x)) (cos x))
0.0ms	(fma (cos x) (cos eps) (- (+ (* (sin eps) (sin x)) (cos x))))

series364.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(* (sin eps) (sin x))
103.0ms	(+ (* (sin eps) (sin x)) (cos x))
180.0ms	(fma (cos x) (cos eps) (- (+ (* (sin eps) (sin x)) (cos x))))

simplify1.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	825
1	221
0	93

prune383.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 17.2b

regimes386.0ms

Accuracy

79.4% (2.1b remaining)

Error of 16.3b against oracle of 14.3b and baseline of 24.2b

bsearch189.0ms

Steps

Iters	Range		Point
8	5.348857464772318e-40	1.6639527246399473e-35	1.6288612552274203e-35
10	-3.2052418334402957e-07	-8.353467643873847e-20	-3.2621509394801617e-09

simplify14.0ms

Iterations

Iter	Nodes
done	45
2	45
1	38
0	29

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	4442×	body	1280	valid
1.4s	1861×	body	640	valid
1.1s	651×	body	2560	valid
235.0ms	683×	body	320	valid
59.0ms	299×	body	160	valid
6.0ms	64×	body	80	valid