Details

sample155.0ms

Algorithm

intervals

Results

87.0ms	147×	body	1280	valid
27.0ms	20×	body	2560	valid
17.0ms	55×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite32.0ms

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:

21.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series121.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (cos (+ x eps)) (cos x))
32.0ms	(cos (+ x eps))

simplify915.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune305.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

16.0ms	(* (cos x) (cos eps))
28.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
19.0ms	(* (sin x) (sin eps))
85.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos x) (cos eps))
122.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
79.0ms	(* (sin x) (sin eps))
169.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify2.0s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1785
1	407
0	168

prune754.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin eps) (sin x))
0.2b	(* (sin eps) (sin x))
2.0b	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
51.2b	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`associate-+r+`
9×	`prod-diff` `add-log-exp`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-udef`
2×	`sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `associate--l+` `flip-+` `distribute-lft-out--`

Counts

4 → 85

Calls

4 calls:

16.0ms	(* (sin eps) (sin x))
17.0ms	(* (sin eps) (sin x))
18.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
0.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin eps) (sin x))
77.0ms	(* (sin eps) (sin x))
311.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (fma (- (sin eps)) (sin x) (* (sin eps) (sin x))) (cos x)))
58.0ms	(fma (- (sin eps)) (sin x) (* (sin eps) (sin x)))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1169
1	296
0	129

prune764.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
2.0b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
2.0b	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `exp-sum` `add-cube-cbrt`
9×	`prod-diff` `add-log-exp`
8×	`log-prod`
6×	`exp-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `log1p-expm1-u`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `fma-udef` `rem-exp-log`
1×	`log-div` `flip3--` `fma-neg` `rem-log-exp` `flip--` `associate--r+`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
21.0ms	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
9.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
18.0ms	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (sin x) (sin eps) (cos x))
242.0ms	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
230.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
208.0ms	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	940
1	253
0	121

prune647.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

regimes317.0ms

Accuracy

83.9% (1.6b remaining)

Error of 16.3b against oracle of 14.7b and baseline of 24.6b

bsearch227.0ms

Steps

Iters	Range		Point
10	7.42116589675916e-09	160.65039477392645	9.272024129006377e-08
9	-0.003292329160956242	-6.8406817238881764e-12	-2.1666122890233487e-07

simplify9.0ms

Iterations

Iter	Nodes
done	49
1	49
0	37

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.9s	4435×	body	1280	valid
996.0ms	637×	body	2560	valid
993.0ms	1874×	body	640	valid
274.0ms	665×	body	320	valid
59.0ms	307×	body	160	valid
7.0ms	82×	body	80	valid