Details

sample229.0ms

Algorithm

intervals

Results

151.0ms	141×	body	1280	valid
35.0ms	68×	body	640	valid
20.0ms	12×	body	2560	valid
8.0ms	18×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	5×	body	80	valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize12.0ms

Local error

Found 2 expressions with local error:

4.5b	(cos (+ x eps))
0.7b	(- (cos (+ x eps)) (cos x))

rewrite19.0ms

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

11.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series113.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(- (cos (+ x eps)) (cos x))
35.0ms	(cos (+ x eps))

simplify2.1s

Counts

33 → 48

Calls

33 calls:

Slowest

222.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
218.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
204.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
196.0ms	(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
180.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune527.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

4.1b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `fma-def` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

93.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
60.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
38.0ms	(sin (/ (+ x (+ eps x)) 2))
22.0ms	(+ x (+ eps x))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
119.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
53.0ms	(sin (/ (+ x (+ eps x)) 2))
26.0ms	(+ x (+ eps x))

simplify3.2s

Counts

38 → 87

Calls

38 calls:

Slowest

607.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
543.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
396.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
308.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
278.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 3 expressions with local error:

4.1b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 52

Calls

3 calls:

Slowest

68.0ms	(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
24.0ms	(sin (/ (+ x (+ eps x)) 2))
16.0ms	(+ x (+ eps x))

series225.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

147.0ms	(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
44.0ms	(+ x (+ eps x))
33.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts

24 → 61

Calls

24 calls:

Slowest

606.0ms	(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
525.0ms	(* (* (* (* -2 -2) -2) (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
321.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
206.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
70.0ms	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune804.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 4 expressions with local error:

4.1b	(sin (/ (+ x (+ eps x)) 2))
4.1b	(sin (/ (+ x (+ eps x)) 2))
4.1b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite115.0ms

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

48.0ms	(sin (/ (+ x (+ eps x)) 2))
38.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(sin (/ (+ x (+ eps x)) 2))
10.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
46.0ms	(sin (/ (+ x (+ eps x)) 2))
45.0ms	(sin (/ (+ x (+ eps x)) 2))
37.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify2.5s

Counts

15 → 56

Calls

15 calls:

Slowest

599.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
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)))))))
301.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
286.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)
254.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune864.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.4b

regimes387.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch151.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.9s	4478×	body	1280	valid
1.3s	1915×	body	640	valid
1.1s	613×	body	2560	valid
227.0ms	623×	body	320	valid
101.0ms	292×	body	160	valid
10.0ms	79×	body	80	valid