Details

sample249.0ms

Algorithm

intervals

Results

144.0ms	137×	body	1280	valid
41.0ms	22×	body	2560	valid
37.0ms	58×	body	640	valid
12.0ms	28×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize25.0ms

Local error

Found 2 expressions with local error:

4.5b	(cos (+ x eps))
1.6b	(- (cos (+ x eps)) (cos x))

rewrite39.0ms

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

23.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series126.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

99.0ms	(- (cos (+ x eps)) (cos x))
27.0ms	(cos (+ x eps))

simplify1.2s

Counts: 48 → 48

prune514.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

4.4b	(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))))

rewrite210.0ms

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

81.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
73.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
41.0ms	(sin (/ (+ x (+ eps x)) 2))
13.0ms	(+ x (+ eps x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

91.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
65.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
49.0ms	(sin (/ (+ x (+ eps x)) 2))
43.0ms	(+ x (+ eps x))

simplify1.4s

Counts: 87 → 87

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

4.4b	(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))))

rewrite53.0ms

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

36.0ms	(sin (/ (+ x (+ eps x)) 2))
15.0ms	(* (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))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

115.0ms	(* (sin (/ eps 2)) (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))
81.0ms	(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
79.0ms	(log1p (sin (/ (+ x (+ eps x)) 2)))
38.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts: 67 → 67

prune911.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

4.4b	(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)))

rewrite51.0ms

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

30.0ms	(sin (/ (+ x (+ eps x)) 2))
20.0ms	(* (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))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
72.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
71.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
36.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.2s

Counts: 67 → 67

prune837.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes350.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch221.0ms

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.3s	4478×	body	1280	valid
1.5s	1828×	body	640	valid
1.3s	648×	body	2560	valid
376.0ms	655×	body	320	valid
82.0ms	316×	body	160	valid
10.0ms	75×	body	80	valid