Details

sample185.0ms

Algorithm

intervals

Results

101.0ms	137×	body	1280	valid
30.0ms	68×	body	640	valid
24.0ms	15×	body	2560	valid
8.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize54.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite20.0ms

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:

12.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify1.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune300.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.8b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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))
11.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* (cos x) (cos eps))
73.0ms	(fma (sin eps) (sin x) (cos x))
199.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))

simplify1.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
2	976
1	241
0	108

prune485.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.6b

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

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))
1.0ms	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

series286.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(fma (sin eps) (sin x) (cos x))
211.0ms	(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

prune368.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(exp (- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x))))
2.1b	(- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))
2.2b	(log (exp (- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))))

rewrite48.0ms

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 eps) (cos x)) (fma (sin x) (sin eps) (cos x))))
10.0ms	(- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))
15.0ms	(log (exp (- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (sin x) (sin eps) (cos x))
168.0ms	(exp (- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x))))
206.0ms	(- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))
167.0ms	(log (exp (- (* (cos eps) (cos x)) (fma (sin x) (sin eps) (cos x)))))

simplify1.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	961
1	248
0	121

prune681.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.6b

regimes318.0ms

Accuracy

87.4% (1.2b remaining)

Error of 15.7b against oracle of 14.5b and baseline of 24.3b

bsearch232.0ms

Steps

Iters	Range		Point
9	1.693076858683966e-08	0.030359728269424062	2.307757405863471e-07
11	-33326255562.233612	-1.7653271249463014e-22	-3.7351865282164835e-06

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample6.9s

Algorithm

intervals

Results

4.4s	4429×	body	1280	valid
925.0ms	656×	body	2560	valid
890.0ms	1835×	body	640	valid
216.0ms	704×	body	320	valid
110.0ms	285×	body	160	valid
8.0ms	91×	body	80	valid