Details

sample218.0ms

Algorithm

intervals

Results

103.0ms	100×	body	1280	valid
44.0ms	23×	body	2560	valid
34.0ms	52×	body	640	valid
15.0ms	31×	body	320	valid
6.0ms	40×	body	80	valid
3.0ms	10×	body	160	valid

simplify59.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

59.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize18.0ms

Local error

Found 2 expressions with local error:

2.8b	(sin (+ x eps))
2.1b	(- (sin (+ x eps)) (sin x))

rewrite34.0ms

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`

Counts

2 → 26

Calls

2 calls:

Slowest

27.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series78.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

53.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify746.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

350.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
169.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
80.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
57.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
19.0ms	(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune295.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

Slowest

36.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
29.0ms	(cos (/ (+ x (+ eps x)) 2))
13.0ms	(+ x (+ eps x))
10.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
100.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(+ x (+ eps x))

simplify3.0s

Counts

35 → 74

Calls

35 calls:

Slowest

644.0ms	(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
539.0ms	(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
337.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
325.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
256.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune748.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 2 expressions with local error:

2.6b	(cos (+ (* 1/2 eps) x))
0.2b	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

Slowest

48.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))
11.0ms	(cos (+ (* 1/2 eps) x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (+ (* 1/2 eps) x)))
22.0ms	(cos (+ (* 1/2 eps) x))

simplify1.4s

Counts

17 → 34

Calls

17 calls:

Slowest

481.0ms	(* (* (* (* (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))))
337.0ms	(* (* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* 2 2) 2)) (* (* (cos (+ (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x))) (cos (+ (* 1/2 eps) x))))
179.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
134.0ms	(- eps (+ (* 1/6 (pow eps 3)) (* 1/2 (* x (pow eps 2)))))
46.0ms	(+ (+ (log (sin (* 1/2 eps))) (log 2)) (log (cos (+ (* 1/2 eps) x))))

prune387.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

Slowest

170.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
30.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
24.0ms	(* (sin (* 1/2 eps)) (sin x))
23.0ms	(* (cos (* 1/2 eps)) (cos x))

series445.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

203.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
116.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
63.0ms	(* (cos (* 1/2 eps)) (cos x))
62.0ms	(* (sin (* 1/2 eps)) (sin x))

simplify5.4s

Counts

55 → 94

Calls

55 calls:

Slowest

366.0ms	(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
352.0ms	(* (* (* (cos (* 1/2 eps)) (cos (* 1/2 eps))) (cos (* 1/2 eps))) (* (* (cos x) (cos x)) (cos x)))
334.0ms	(* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (sin x) (sin x)) (sin x)))
328.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
326.0ms	(* 2 (* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (sin (* 1/2 eps))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch7.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.6s	3297×	body	1280	valid
1.5s	1848×	body	640	valid
1.3s	658×	body	2560	valid
400.0ms	774×	body	320	valid
178.0ms	1093×	body	80	valid
92.0ms	330×	body	160	valid