Details

sample239.0ms

Algorithm

intervals

Results

153.0ms	148×	body	1280	valid
34.0ms	20×	body	2560	valid
29.0ms	59×	body	640	valid
4.0ms	13×	body	320	valid
4.0ms	15×	body	160	valid
0.0ms	1×	body	80	valid

simplify14.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize27.0ms

Local error

Found 2 expressions with local error:

3.2b	(cos (+ x eps))
2.0b	(- (cos (+ x eps)) (cos x))

rewrite37.0ms

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

23.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series126.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

98.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify1.4s

Counts: 48 → 48

prune547.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

3.1b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))

rewrite187.0ms

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

77.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
69.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
20.0ms	(+ x (+ eps x))
19.0ms	(sin (/ (+ x (+ eps x)) 2))

series238.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
83.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
43.0ms	(sin (/ (+ x (+ eps x)) 2))
25.0ms	(+ x (+ eps x))

simplify1.3s

Counts: 87 → 87

prune999.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

3.1b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ eps x)) 2)))
0.0b	(+ x (+ eps x))

rewrite91.0ms

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

55.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ eps x)) 2)))
24.0ms	(sin (/ (+ x (+ eps x)) 2))
11.0ms	(+ x (+ eps x))

series157.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

87.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ eps x)) 2)))
43.0ms	(sin (/ (+ x (+ eps x)) 2))
27.0ms	(+ x (+ eps x))

simplify1.7s

Counts: 61 → 61

prune703.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

3.1b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
0.3b	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.2b	(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `associate-l` `log1p-expm1` `*-commutative` `expm1-udef`

Counts

4 → 55

Calls

4 calls:

Slowest

23.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
0.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))
86.0ms	(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
66.0ms	(expm1 (sin (/ (+ x (+ eps x)) 2)))
44.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify3.2s

Counts: 67 → 67

prune692.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes294.0ms

Accuracy

98% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 16.2b

bsearch268.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.7s	4466×	body	1280	valid
1.6s	1855×	body	640	valid
1.1s	628×	body	2560	valid
316.0ms	688×	body	320	valid
97.0ms	290×	body	160	valid
9.0ms	73×	body	80	valid