Details

sample217.0ms

Algorithm

intervals

Results

128.0ms	147×	body	1280	valid
33.0ms	54×	body	640	valid
27.0ms	16×	body	2560	valid
16.0ms	30×	body	320	valid
2.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize15.0ms

Local error

Found 2 expressions with local error:

2.7b	(cos (+ x eps))
1.2b	(- (cos (+ x eps)) (cos x))

rewrite19.0ms

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

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

series98.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

80.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify1.3s

Counts: 48 → 48

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 3 expressions with local error:

2.6b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

Slowest

101.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
41.0ms	(sin (/ (+ x (+ eps x)) 2))
17.0ms	(+ x (+ eps x))

series194.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

102.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
47.0ms	(+ x (+ eps x))
45.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify922.0ms

Counts: 62 → 62

prune631.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

2.6b	(sin (/ (+ x (+ eps x)) 2))
0.5b	(log1p (sin (/ (+ x (+ eps x)) 2)))
0.3b	(* (sin (/ eps 2)) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))
0.2b	(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `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

31.0ms	(sin (/ (+ x (+ eps x)) 2))
21.0ms	(* (sin (/ eps 2)) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))
1.0ms	(log1p (sin (/ (+ x (+ eps x)) 2)))
0.0ms	(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(* (sin (/ eps 2)) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))
85.0ms	(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
66.0ms	(log1p (sin (/ (+ x (+ eps x)) 2)))
58.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.7s

Counts: 67 → 67

prune849.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

2.6b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
0.2b	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b	(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite39.0ms

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

27.0ms	(sin (/ (+ x (+ eps x)) 2))
10.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
0.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
88.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
76.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
47.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts: 67 → 67

prune720.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes245.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.4b

bsearch299.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.5s	4472×	body	1280	valid
1.2s	650×	body	2560	valid
1.1s	1860×	body	640	valid
287.0ms	645×	body	320	valid
74.0ms	299×	body	160	valid
9.0ms	74×	body	80	valid