Details

sample230.0ms

Algorithm

intervals

Results

134.0ms	126×	body	1280	valid
38.0ms	27×	body	2560	valid
32.0ms	66×	body	640	valid
10.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	5×	body	80	valid

simplify17.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize26.0ms

Local error

Found 2 expressions with local error:

4.6b	(cos (+ x eps))
0.9b	(- (cos (+ x eps)) (cos x))

rewrite27.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

15.0ms	(cos (+ x eps))
11.0ms	(- (cos (+ x eps)) (cos x))

series90.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

61.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify1.2s

Counts: 48 → 48

prune554.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

4.8b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `fma-def` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

69.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
55.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
39.0ms	(sin (/ (+ x (+ eps x)) 2))
16.0ms	(+ x (+ eps x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

97.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
94.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
33.0ms	(sin (/ (+ x (+ eps x)) 2))
28.0ms	(+ x (+ eps x))

simplify1.6s

Counts: 87 → 87

prune950.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

4.8b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
0.3b	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b	(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

Slowest

44.0ms	(sin (/ (+ x (+ eps x)) 2))
20.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
1.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
92.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
65.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
53.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.1s

Counts: 67 → 67

prune766.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 2 expressions with local error:

4.8b	(sin (fma eps 1/2 x))
0.3b	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

Slowest

26.0ms	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))
2.0ms	(sin (fma eps 1/2 x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

76.0ms	(* (* -2 (sin (fma eps 1/2 x))) (sin (* eps 1/2)))
39.0ms	(sin (fma eps 1/2 x))

simplify3.0s

Counts: 38 → 38

prune381.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes140.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.1s	4438×	body	1280	valid
1.6s	635×	body	2560	valid
1.2s	1939×	body	640	valid
279.0ms	631×	body	320	valid
70.0ms	282×	body	160	valid
10.0ms	75×	body	80	valid