Details

sample91.0ms

Algorithm

intervals

Results

46.0ms	113×	body	1280	valid
15.0ms	18×	body	2560	valid
13.0ms	60×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify70.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220
done	5002	220

prune108.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

15.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
11.0ms	(* (cos x) (sin eps))
57.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (sin x) (cos eps))
48.0ms	(* (cos x) (sin eps))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify47.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5001	741
done	5001	741

prune269.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
2.2b	(- (cos eps) 1)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
12.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series177.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify95.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	325
3	5001	303
done	5001	303

prune252.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1))
0.3b	(* (cos eps) (cos eps))
0.4b	(+ (cos eps) 1)
2.2b	(- (* (cos eps) (cos eps)) 1)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`pow1` `add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out` `add-log-exp`
6×	`difference-of-sqr-1` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l` `prod-diff`
2×	`sqr-cos` `expm1-def` `flip3--` `flip3-+` `prod-exp` `sub-1-cos` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

33.0ms	(/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1))
10.0ms	(* (cos eps) (cos eps))
7.0ms	(+ (cos eps) 1)
12.0ms	(- (* (cos eps) (cos eps)) 1)

series116.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1))
16.0ms	(* (cos eps) (cos eps))
10.0ms	(+ (cos eps) 1)
32.0ms	(- (* (cos eps) (cos eps)) 1)

simplify56.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	424	934
1	2138	817
2	5002	804
done	5002	804

prune451.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes115.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	16
1	31	16
2	33	16
3	33	16
done	33	16

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3326×	body	1280	valid
603.0ms	673×	body	2560	valid
443.0ms	1887×	body	640	valid
109.0ms	706×	body	320	valid
53.0ms	1078×	body	80	valid
34.0ms	330×	body	160	valid