Details

sample237.0ms

Algorithm

intervals

Results

124.0ms	106×	body	1280	valid
45.0ms	61×	body	640	valid
33.0ms	17×	body	2560	valid
13.0ms	28×	body	320	valid
5.0ms	35×	body	80	valid
3.0ms	9×	body	160	valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize26.0ms

Local error

Found 2 expressions with local error:

4.4b	(sin (+ x eps))
1.0b	(- (sin (+ x eps)) (sin x))

rewrite92.0ms

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

48.0ms	(- (sin (+ x eps)) (sin x))
43.0ms	(sin (+ x eps))

series83.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

58.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify2.1s

Counts

33 → 48

Calls

33 calls:

Slowest

254.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
199.0ms	(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
198.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
164.0ms	(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
157.0ms	(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune424.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

4.3b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite56.0ms

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-+` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

Slowest

24.0ms	(cos (/ (+ x (+ eps x)) 2))
20.0ms	(+ x (+ eps x))
11.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series522.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

392.0ms	(cos (/ (+ x (+ eps x)) 2))
102.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
29.0ms	(+ x (+ eps x))

simplify1.5s

Counts

25 → 61

Calls

25 calls:

Slowest

435.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
390.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
163.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
54.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
46.0ms	(+ (log (cos (/ (+ x (+ eps x)) 2))) (log (sin (/ eps 2))))

prune657.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 2 expressions with local error:

4.3b	(cos (fma 1/2 eps x))
0.2b	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

rewrite17.0ms

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

12.0ms	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
5.0ms	(cos (fma 1/2 eps x))

series82.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

60.0ms	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
21.0ms	(cos (fma 1/2 eps x))

simplify1.3s

Counts

17 → 38

Calls

17 calls:

Slowest

438.0ms	(* (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
403.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
221.0ms	(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
36.0ms	(* (sqrt (cos (fma 1/2 eps x))) (sqrt (sin (/ eps 2))))
25.0ms	(* (cbrt (cos (fma 1/2 eps x))) (cbrt (cos (fma 1/2 eps x))))

prune507.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite267.0ms

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

156.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
40.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
36.0ms	(* (sin (* 1/2 eps)) (sin x))
33.0ms	(* (cos (* 1/2 eps)) (cos x))

series439.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
122.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
73.0ms	(* (sin (* 1/2 eps)) (sin x))
51.0ms	(* (cos (* 1/2 eps)) (cos x))

simplify5.9s

Counts

55 → 100

Calls

55 calls:

Slowest

733.0ms	(* (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
692.0ms	(* (- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))) (sin (/ eps 2)))
506.0ms	(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
431.0ms	(* (* (* (cos (* 1/2 eps)) (cos (* 1/2 eps))) (cos (* 1/2 eps))) (* (* (cos x) (cos x)) (cos x)))
394.0ms	(* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (sin x) (sin x)) (sin x)))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.7s	3285×	body	1280	valid
1.7s	1870×	body	640	valid
1.3s	618×	body	2560	valid
752.0ms	793×	body	320	valid
144.0ms	1103×	body	80	valid
100.0ms	331×	body	160	valid