Details

sample181.0ms

Algorithm

intervals

Results

84.0ms	103×	body	1280	valid
29.0ms	49×	body	640	valid
24.0ms	16×	body	2560	valid
23.0ms	35×	body	320	valid
5.0ms	41×	body	80	valid
3.0ms	12×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize59.0ms

Local error

Found 2 expressions with local error:

2.6b	(sin (+ x eps))
1.9b	(- (sin (+ x eps)) (sin x))

rewrite47.0ms

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

36.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(- (sin (+ x eps)) (sin x))
31.0ms	(sin (+ x eps))

simplify1.3s

Counts: 48 → 48

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 3 expressions with local error:

2.6b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite88.0ms

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

32.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
31.0ms	(cos (/ (+ x (+ eps x)) 2))
23.0ms	(+ x (+ eps x))

series149.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

75.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
37.0ms	(+ x (+ eps x))
37.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify778.0ms

Counts: 62 → 62

prune741.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

2.7b	(cos (fma eps 1/2 x))
0.2b	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

Slowest

25.0ms	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))
3.0ms	(cos (fma eps 1/2 x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

71.0ms	(* (cos (fma eps 1/2 x)) (sin (* 1/2 eps)))
24.0ms	(cos (fma eps 1/2 x))

simplify1.6s

Counts: 38 → 38

prune529.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))
0.2b	(* (sin (* eps 1/2)) (sin x))
0.1b	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
0.1b	(* (cos (* eps 1/2)) (cos x))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 88

Calls

4 calls:

Slowest

205.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))
50.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
20.0ms	(* (sin (* eps 1/2)) (sin x))
18.0ms	(* (cos (* eps 1/2)) (cos x))

series442.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))
143.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
85.0ms	(* (sin (* eps 1/2)) (sin x))
66.0ms	(* (cos (* eps 1/2)) (cos x))

simplify2.4s

Counts: 100 → 100

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch5.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.4s	3343×	body	1280	valid
1.4s	1847×	body	640	valid
1.3s	650×	body	2560	valid
372.0ms	766×	body	320	valid
190.0ms	1036×	body	80	valid
104.0ms	358×	body	160	valid