Details

sample91.0ms

Algorithm

intervals

Results

44.0ms	135×	body	1280	valid
21.0ms	24×	body	2560	valid
13.0ms	60×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize12.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
1.9b	(cos (+ x eps))

rewrite13.0ms

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` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (253.0ms)

Iter	Nodes	Cost
0	91	664
1	198	540
2	533	453
3	2210	389
done	5000	389

prune111.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
2.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

16.0ms	(+ (+ x eps) x)
49.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
57.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.6s

Counts

60 → 60

Iterations

Useful iterations: 3 (295.0ms)

Iter	Nodes	Cost
0	99	766
1	225	694
2	680	615
3	2762	551
done	5001	551

prune200.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (fma x 1 (* 1/2 eps)))))
0.3b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (fma x 1 (* 1/2 eps))))))
0.5b	(log1p (sin (fma x 1 (* 1/2 eps))))
2.0b	(sin (fma x 1 (* 1/2 eps)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `sin-sum` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (fma x 1 (* 1/2 eps)))))
12.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (fma x 1 (* 1/2 eps))))))
0.0ms	(log1p (sin (fma x 1 (* 1/2 eps))))
1.0ms	(sin (fma x 1 (* 1/2 eps)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(expm1 (log1p (sin (fma x 1 (* 1/2 eps)))))
85.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (fma x 1 (* 1/2 eps))))))
47.0ms	(log1p (sin (fma x 1 (* 1/2 eps))))
28.0ms	(sin (fma x 1 (* 1/2 eps)))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	93	909
1	173	626
2	523	552
3	1846	548
done	5001	548

prune225.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin (* 1/2 eps)))
0.2b	(expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))))
0.2b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))))
0.5b	(log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 62

Calls

4 calls:

5.0ms	(* (cos x) (sin (* 1/2 eps)))
0.0ms	(expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))))
12.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))))
0.0ms	(log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin (* 1/2 eps)))
128.0ms	(expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))))
169.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))))
109.0ms	(log1p (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps)))))

simplify5.0s

Counts

74 → 74

Iterations

Useful iterations: 3 (345.0ms)

Iter	Nodes	Cost
0	118	1459
1	246	1265
2	815	1098
3	3211	1092
done	5000	1092

prune291.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	32	24
2	38	24
done	38	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4415×	body	1280	valid
563.0ms	649×	body	2560	valid
389.0ms	1833×	body	640	valid
107.0ms	712×	body	320	valid
31.0ms	307×	body	160	valid
4.0ms	84×	body	80	valid