Details

sample186.0ms

Algorithm

intervals

Results

111.0ms	116×	body	1280	valid
26.0ms	20×	body	2560	valid
25.0ms	52×	body	640	valid
5.0ms	43×	body	80	valid
5.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize23.0ms

Local error

Found 2 expressions with local error:

3.2b	(sin (+ x eps))
0.6b	(- (sin (+ x eps)) (sin x))

rewrite94.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

80.0ms	(- (sin (+ x eps)) (sin x))
13.0ms	(sin (+ x eps))

series104.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

75.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify1.4s

Counts: 48 → 48

prune410.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 3 expressions with local error:

3.1b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite61.0ms

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-cos-mult` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

Slowest

23.0ms	(+ x (+ eps x))
20.0ms	(cos (/ (+ x (+ eps x)) 2))
17.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

73.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
31.0ms	(+ x (+ eps x))

simplify906.0ms

Counts: 62 → 62

prune521.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.3b	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))

rewrite47.0ms

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

26.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
0.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
66.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
53.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
34.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify865.0ms

Counts: 67 → 67

prune713.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

3.1b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(log1p (cos (/ (+ x (+ eps x)) 2)))
0.2b	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
0.2b	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))

rewrite41.0ms

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

21.0ms	(cos (/ (+ x (+ eps x)) 2))
17.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
1.0ms	(log1p (cos (/ (+ x (+ eps x)) 2)))
0.0ms	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
76.0ms	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
75.0ms	(log1p (cos (/ (+ x (+ eps x)) 2)))
42.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify838.0ms

Counts: 67 → 67

prune595.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes251.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 15.3b

bsearch179.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.0s	3322×	body	1280	valid
1.6s	628×	body	2560	valid
1.4s	1841×	body	640	valid
338.0ms	751×	body	320	valid
146.0ms	1098×	body	80	valid
132.0ms	360×	body	160	valid