Details

sample162.0ms

Algorithm

intervals

Results

88.0ms	103×	body	1280	valid
26.0ms	22×	body	2560	valid
23.0ms	52×	body	640	valid
10.0ms	31×	body	320	valid
4.0ms	41×	body	80	valid
2.0ms	7×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 2 expressions with local error:

4.4b	(sin (+ x eps))
0.9b	(- (sin (+ x eps)) (sin x))

rewrite60.0ms

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

52.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

53.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.4s

Counts: 48 → 48

prune523.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 3 expressions with local error:

4.2b	(cos (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite62.0ms

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	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
11.0ms	(+ x (+ eps x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

92.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
46.0ms	(+ x (+ eps x))
41.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify930.0ms

Counts: 62 → 62

prune698.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
0.1b	(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 73

Calls

4 calls:

Slowest

37.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))
37.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
36.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
30.0ms	(cos (/ (+ x (+ eps x)) 2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
54.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
46.0ms	(cos (/ (+ x (+ eps x)) 2))
44.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify1.2s

Counts: 85 → 85

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize84.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ x (+ eps x)) 2))
4.2b	(cos (/ (+ x (+ eps x)) 2))
4.2b	(cos (/ (+ x (+ eps x)) 2))
0.6b	(* (exp (cos (/ (+ x (+ eps x)) 2))) (exp (cos (/ (+ x (+ eps x)) 2))))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

18×	`exp-prod`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `add-exp-log` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

Slowest

201.0ms	(* (exp (cos (/ (+ x (+ eps x)) 2))) (exp (cos (/ (+ x (+ eps x)) 2))))
38.0ms	(cos (/ (+ x (+ eps x)) 2))
37.0ms	(cos (/ (+ x (+ eps x)) 2))
24.0ms	(cos (/ (+ x (+ eps x)) 2))

series216.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(* (exp (cos (/ (+ x (+ eps x)) 2))) (exp (cos (/ (+ x (+ eps x)) 2))))
46.0ms	(cos (/ (+ x (+ eps x)) 2))
44.0ms	(cos (/ (+ x (+ eps x)) 2))
43.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify926.0ms

Counts: 79 → 79

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes253.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch120.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.5s	3363×	body	1280	valid
1.4s	1785×	body	640	valid
1.2s	648×	body	2560	valid
292.0ms	751×	body	320	valid
135.0ms	1108×	body	80	valid
92.0ms	345×	body	160	valid