Details

sample165.0ms

Algorithm

intervals

Results

75.0ms	108×	body	1280	valid
47.0ms	19×	body	2560	valid
20.0ms	48×	body	640	valid
8.0ms	25×	body	320	valid
4.0ms	42×	body	80	valid
3.0ms	14×	body	160	valid

simplify9.0ms

Calls

1 calls:

Slowest

9.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize15.0ms

Local error

Found 2 expressions with local error:

3.0b	(sin (+ x eps))
1.6b	(- (sin (+ x eps)) (sin x))

rewrite10.0ms

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))

series77.0ms

Calls

2 calls:

Slowest

63.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

simplify597.0ms

Calls

13 calls:

Slowest

347.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
66.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
54.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
53.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
14.0ms	(- (sin (+ x eps)) (sin x))

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

2.9b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

15.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
5.0ms	(cos (/ (+ x (+ eps x)) 2))
2.0ms	(+ x (+ eps x))

series112.0ms

Calls

3 calls:

Slowest

65.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
20.0ms	(+ x (+ eps x))

simplify1.0s

Calls

17 calls:

Slowest

277.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
183.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
159.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
70.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
52.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune539.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ x (+ eps x)) 2))
2.9b	(cos (/ (+ x (+ eps x)) 2))
2.9b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Calls

4 calls:

Slowest

14.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
3.0ms	(cos (/ (+ x (+ eps x)) 2))
3.0ms	(cos (/ (+ x (+ eps x)) 2))
3.0ms	(cos (/ (+ x (+ eps x)) 2))

series104.0ms

Calls

4 calls:

Slowest

28.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
26.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cos (/ (+ x (+ eps x)) 2))
24.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Calls

15 calls:

Slowest

315.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
297.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
294.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
282.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
74.0ms	(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune669.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ x (+ eps x)) 2))
2.9b	(cos (/ (+ x (+ eps x)) 2))
2.9b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Calls

4 calls:

Slowest

3.0ms	(cos (/ (+ x (+ eps x)) 2))
3.0ms	(cos (/ (+ x (+ eps x)) 2))
3.0ms	(cos (/ (+ x (+ eps x)) 2))
1.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))

series165.0ms

Calls

4 calls:

Slowest

95.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))
27.0ms	(cos (/ (+ x (+ eps x)) 2))
22.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.7s

Calls

15 calls:

Slowest

315.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
303.0ms	(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
301.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
278.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
61.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune651.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.5b

regimes276.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.8b

bsearch302.0ms

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.5s	3311×	body	1280	valid
1.4s	1826×	body	640	valid
1.4s	636×	body	2560	valid
439.0ms	814×	body	320	valid
138.0ms	1066×	body	80	valid
97.0ms	347×	body	160	valid