Details

sample218.0ms

Algorithm

intervals

Results

109.0ms	88×	body	1280	valid
43.0ms	27×	body	2560	valid
34.0ms	61×	body	640	valid
11.0ms	28×	body	320	valid
5.0ms	41×	body	80	valid
3.0ms	11×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize13.0ms

Local error

Found 2 expressions with local error:

4.7b	(sin (+ x eps))
1.2b	(- (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

86.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

68.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify1.5s

Counts: 48 → 48

prune448.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

4.6b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite70.0ms

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

29.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
21.0ms	(+ x (+ eps x))
20.0ms	(cos (/ (+ x (+ eps x)) 2))

series150.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

82.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
39.0ms	(+ x (+ eps x))
29.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify944.0ms

Counts: 62 → 62

prune606.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.2b	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))

rewrite48.0ms

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

25.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
20.0ms	(cos (/ (+ x (+ eps x)) 2))
1.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
78.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
65.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
41.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify872.0ms

Counts: 67 → 67

prune778.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.3b	(expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.2b	(log1p (log1p (expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

Slowest

21.0ms	(cos (/ (+ x (+ eps x)) 2))
0.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
0.0ms	(expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.0ms	(log1p (log1p (expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))
93.0ms	(log1p (log1p (expm1 (expm1 (cos (/ (+ x (+ eps x)) 2))))))
79.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
34.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.2s

Counts: 58 → 58

prune710.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

regimes228.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch277.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.9s	3308×	body	1280	valid
1.3s	1875×	body	640	valid
1.3s	635×	body	2560	valid
336.0ms	748×	body	320	valid
145.0ms	1072×	body	80	valid
101.0ms	362×	body	160	valid