Details

sample231.0ms

Algorithm

intervals

Results

123.0ms	109×	body	1280	valid
45.0ms	62×	body	640	valid
32.0ms	16×	body	2560	valid
10.0ms	23×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify10.0ms

Calls

1 calls:

Slowest

10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize13.0ms

Local error

Found 2 expressions with local error:

2.5b	(sin (+ x eps))
1.2b	(- (sin (+ x eps)) (sin x))

rewrite45.0ms

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

42.0ms	(- (sin (+ x eps)) (sin x))
2.0ms	(sin (+ x eps))

series57.0ms

Calls

2 calls:

Slowest

39.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify667.0ms

Calls

13 calls:

Slowest

423.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
73.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
70.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
30.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
20.0ms	(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune345.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b	(/ (+ x (+ eps x)) 2)
0.0b	(+ x (+ eps x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
12.0ms	(/ (+ x (+ eps x)) 2)
4.0ms	(cos (/ (+ x (+ eps x)) 2))
2.0ms	(+ x (+ eps x))

series159.0ms

Calls

4 calls:

Slowest

84.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
27.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(/ (+ x (+ eps x)) 2)
22.0ms	(+ x (+ eps x))

simplify2.0s

Calls

24 calls:

Slowest

523.0ms	(- (* x x) (* (+ eps x) (+ eps x)))
462.0ms	(+ (pow x 3) (pow (+ eps x) 3))
314.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
156.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
148.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune697.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite10.0ms

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)))

series163.0ms

Calls

4 calls:

Slowest

102.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))
23.0ms	(cos (/ (+ x (+ eps x)) 2))
21.0ms	(cos (/ (+ x (+ eps x)) 2))
16.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Calls

15 calls:

Slowest

300.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
299.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
283.0ms	(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
252.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
70.0ms	(pow (cos (* 1/2 (+ (* 2 x) eps))) 1/3)

prune718.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
2.5b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (cos (/ (+ x (+ eps x)) 2)))

rewrite16.0ms

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

6.0ms	(cos (/ (+ x (+ eps x)) 2))
6.0ms	(cos (/ (+ x (+ eps x)) 2))
3.0ms	(cos (/ (+ x (+ eps x)) 2))
1.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))

series125.0ms

Calls

4 calls:

Slowest

74.0ms	(cbrt (cos (/ (+ x (+ eps x)) 2)))
19.0ms	(cos (/ (+ x (+ eps x)) 2))
16.0ms	(cos (/ (+ x (+ eps x)) 2))
16.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.5s

Calls

15 calls:

Slowest

280.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
269.0ms	(- 1 (+ (* 1/6 (* x eps)) (* 1/6 (pow x 2))))
255.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
225.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
59.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune699.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes169.0ms

Accuracy

98.1% (0.3b remaining)

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

bsearch278.0ms

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.5s	3275×	body	1280	valid
1.7s	617×	body	2560	valid
1.4s	1826×	body	640	valid
357.0ms	764×	body	320	valid
199.0ms	1117×	body	80	valid
113.0ms	401×	body	160	valid