Details

sample195.0ms

Algorithm

intervals

Results

111.0ms	143×	body	1280	valid
33.0ms	22×	body	2560	valid
21.0ms	45×	body	640	valid
9.0ms	30×	body	320	valid
2.0ms	14×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize24.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite43.0ms

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

series87.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
31.0ms	(cos (+ x eps))

simplify1.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune342.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.7b

localize24.0ms

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))
2.7b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite109.0ms

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:

11.0ms	(* (cos x) (cos eps))
13.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
71.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series471.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos x) (cos eps))
129.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
81.0ms	(* (sin x) (sin eps))
195.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify2.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1785
1	407
0	168

prune685.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
0.1b	(fma (sin x) (sin eps) (cos x))
2.7b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
2.8b	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

rewrite68.0ms

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:

23.0ms	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
0.0ms	(fma (sin x) (sin eps) (cos x))
16.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
26.0ms	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

series746.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
81.0ms	(fma (sin x) (sin eps) (cos x))
176.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))
237.0ms	(log (exp (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	939
1	253
0	121

prune686.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.6b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
4.2b	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
69×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
64×	`add-cube-cbrt`
61×	`times-frac`
57×	`prod-diff`
34×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
27×	`cos-mult` `sin-mult`
19×	`fma-neg`
18×	`difference-of-squares`
16×	`prod-exp` `cbrt-unprod` `associate-/l/`
15×	`associate-/r/`
12×	`associate-l/` `associate-r/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `div-inv` `sub-div`
4×	`expm1-log1p-u` `pow-plus` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*`
2×	`pow2` `flip3--` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`associate--l-` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `distribute-lft-out--`

Counts

4 → 225

Calls

4 calls:

46.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
180.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
38.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
372.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series1.1s

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
341.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
91.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
592.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify3.3s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4806
1	878
0	308

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 16.5b

regimes508.0ms

Accuracy

81.4% (1.9b remaining)

Error of 16.5b against oracle of 14.6b and baseline of 24.7b

bsearch242.0ms

Steps

Iters	Range		Point
6	1.2909757615257876e-26	9.893628188745239e-26	9.775851168574081e-26
10	-1212215.9807367995	-5.980124527132304e-10	-3.934754991620558e-08

simplify16.0ms

Iterations

Iter	Nodes
done	59
2	59
1	58
0	47

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.6s	4444×	body	1280	valid
1.2s	655×	body	2560	valid
783.0ms	1858×	body	640	valid
296.0ms	708×	body	320	valid
54.0ms	75×	body	80	valid
51.0ms	260×	body	160	valid