Details

sample161.0ms

Algorithm

intervals

Results

89.0ms	142×	body	1280	valid
35.0ms	67×	body	640	valid
20.0ms	17×	body	2560	valid
6.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize51.0ms

Local error

Found 2 expressions with local error:

3.0b	(cos (+ x eps))
1.0b	(- (cos (+ x eps)) (cos x))

rewrite21.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

13.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series107.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

90.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify2.3s

Counts

33 → 48

Calls

33 calls:

Slowest

273.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
244.0ms	(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
232.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
215.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
163.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune514.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 3 expressions with local error:

3.0b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite138.0ms

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-+` `sin-mult` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

Slowest

75.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
39.0ms	(sin (/ (+ x (+ eps x)) 2))
22.0ms	(+ x (+ eps x))

series220.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

139.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
56.0ms	(sin (/ (+ x (+ eps x)) 2))
25.0ms	(+ x (+ eps x))

simplify1.7s

Counts

26 → 62

Calls

26 calls:

Slowest

410.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
349.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
264.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
77.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
66.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

prune765.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin (/ (+ x (+ eps x)) 2))
3.0b	(sin (/ (+ x (+ eps x)) 2))
3.0b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

Slowest

39.0ms	(sin (/ (+ x (+ eps x)) 2))
27.0ms	(sin (/ (+ x (+ eps x)) 2))
25.0ms	(sin (/ (+ x (+ eps x)) 2))
9.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
52.0ms	(sin (/ (+ x (+ eps x)) 2))
51.0ms	(sin (/ (+ x (+ eps x)) 2))
45.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts

15 → 56

Calls

15 calls:

Slowest

407.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
337.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
302.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
301.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
294.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune829.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.5b

localize74.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin (/ (+ x (+ eps x)) 2))
3.0b	(sin (/ (+ x (+ eps x)) 2))
3.0b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

Slowest

44.0ms	(sin (/ (+ x (+ eps x)) 2))
28.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(sin (/ (+ x (+ eps x)) 2))
1.0ms	(cbrt (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(cbrt (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
53.0ms	(sin (/ (+ x (+ eps x)) 2))
43.0ms	(sin (/ (+ x (+ eps x)) 2))
43.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.2s

Counts

15 → 56

Calls

15 calls:

Slowest

401.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
312.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
300.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
249.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
243.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune872.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.5b

regimes296.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.4b

bsearch201.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

5.0s	4426×	body	1280	valid
1.7s	1877×	body	640	valid
1.2s	660×	body	2560	valid
303.0ms	693×	body	320	valid
67.0ms	259×	body	160	valid
10.0ms	85×	body	80	valid