Details

sample228.0ms

Algorithm

intervals

Results

123.0ms	99×	body	1280	valid
46.0ms	28×	body	2560	valid
34.0ms	59×	body	640	valid
9.0ms	24×	body	320	valid
4.0ms	34×	body	80	valid
3.0ms	12×	body	160	valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

(- (sin (+ x eps)) (sin x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize12.0ms

Local error

Found 2 expressions with local error:

2.5b	(sin (+ x eps))
1.5b	(- (sin (+ x eps)) (sin x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

2 calls:

Slowest

7.0ms	(- (sin (+ x eps)) (sin x))
2.0ms	(sin (+ x eps))

series62.0ms

Calls

2 calls:

Slowest

46.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

simplify605.0ms

Calls

13 calls:

Slowest

348.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
77.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
56.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
46.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
16.0ms	(- (sin (+ x eps)) (sin x))

prune334.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
0.3b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`associate-l`
2×	`*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

17.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
15.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms	(cos (/ (+ x (+ eps x)) 2))
2.0ms	(+ x (+ eps x))

series214.0ms

Calls

4 calls:

Slowest

88.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
78.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
26.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(+ x (+ eps x))

simplify1.4s

Calls

21 calls:

Slowest

398.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
270.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
141.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
124.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
81.0ms	(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune699.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

2.5b	(cos (+ (* 1/2 eps) x))
0.3b	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))
0.0b	(* (sin (* 1/2 eps)) 2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`associate-l`
3×	`associate-r` `insert-posit16` `add-log-exp`
2×	`*-commutative`
1×	`cos-sum` `pow-prod-down` `prod-exp` `cbrt-unprod`

Calls

3 calls:

Slowest

25.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))
8.0ms	(* (sin (* 1/2 eps)) 2)
4.0ms	(cos (+ (* 1/2 eps) x))

series95.0ms

Calls

3 calls:

Slowest

57.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))
24.0ms	(* (sin (* 1/2 eps)) 2)
14.0ms	(cos (+ (* 1/2 eps) x))

simplify1.2s

Calls

19 calls:

Slowest

436.0ms	(* (* (* (* (sin (* 1/2 eps)) 2) (* (sin (* 1/2 eps)) 2)) (* (sin (* 1/2 eps)) 2)) (* (* (cos (+ (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x))) (cos (+ (* 1/2 eps) x))))
234.0ms	(- eps (+ (* 1/6 (pow eps 3)) (* 1/2 (* x (pow eps 2)))))
199.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
82.0ms	(- (+ eps (* 1/1920 (pow eps 5))) (* 1/24 (pow eps 3)))
45.0ms	(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))

prune517.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

54.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
26.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
7.0ms	(* (sin (* 1/2 eps)) (sin x))
6.0ms	(* (cos (* 1/2 eps)) (cos x))

series331.0ms

Calls

4 calls:

Slowest

124.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
103.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
58.0ms	(* (sin (* 1/2 eps)) (sin x))
45.0ms	(* (cos (* 1/2 eps)) (cos x))

simplify3.8s

Calls

48 calls:

Slowest

332.0ms	(- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x))))
330.0ms	(* 2 (* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (sin (* 1/2 eps))))
288.0ms	(* 2 (* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (sin (* 1/2 eps))))
288.0ms	(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
248.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes139.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch7.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.7s	3234×	body	1280	valid
1.3s	1829×	body	640	valid
1.3s	658×	body	2560	valid
394.0ms	804×	body	320	valid
238.0ms	1119×	body	80	valid
153.0ms	356×	body	160	valid