Details

sample90.0ms

Algorithm

intervals

Results

48.0ms	64×	body	10240	exit
22.0ms	271×	body	80	valid
3.0ms	3×	body	1280	valid
2.0ms	8×	body	320	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	160	valid

simplify34.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

34.0ms

(- (log (+ 1 (exp x))) (* x y))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.7b	(log (+ 1 (exp x)))
0.0b	(+ 1 (exp x))
0.0b	(- (log (+ 1 (exp x))) (* x y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

Slowest

13.0ms	(- (log (+ 1 (exp x))) (* x y))
8.0ms	(+ 1 (exp x))
8.0ms	(log (+ 1 (exp x)))

series138.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

71.0ms	(log (+ 1 (exp x)))
51.0ms	(- (log (+ 1 (exp x))) (* x y))
16.0ms	(+ 1 (exp x))

simplify769.0ms

Counts

25 → 57

Calls

25 calls:

Slowest

118.0ms	(log (+ (pow 1 3) (pow (exp x) 3)))
88.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
83.0ms	(/ (+ 1 (exp x)) (exp (* x y)))
83.0ms	(log (+ (pow 1 3) (pow (exp x) 3)))
66.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))

prune599.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(log (sqrt (+ 1 (exp x))))
1.4b	(log (sqrt (+ 1 (exp x))))
0.0b	(sqrt (+ 1 (exp x)))
0.0b	(sqrt (+ 1 (exp x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 76

Calls

4 calls:

Slowest

12.0ms	(sqrt (+ 1 (exp x)))
6.0ms	(sqrt (+ 1 (exp x)))
4.0ms	(log (sqrt (+ 1 (exp x))))
4.0ms	(log (sqrt (+ 1 (exp x))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(log (sqrt (+ 1 (exp x))))
144.0ms	(log (sqrt (+ 1 (exp x))))
34.0ms	(sqrt (+ 1 (exp x)))
32.0ms	(sqrt (+ 1 (exp x)))

simplify2.3s

Counts

50 → 88

Calls

50 calls:

Slowest

376.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
345.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
246.0ms	(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
190.0ms	(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
174.0ms	(log (sqrt (+ (pow 1 3) (pow (exp x) 3))))

prune962.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

6.8b	(log (+ (* x (* x 1/2)) (+ x 2)))
0.0b	(+ (* x (* x 1/2)) (+ x 2))
0.0b	(- (log (+ (* x (* x 1/2)) (+ x 2))) (* x y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
6×	`log-prod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `log-div` `add-exp-log`
3×	`sum-log` `flip3-+` `add-cbrt-cube` `associate--l+` `flip-+` `insert-posit16`
2×	`associate--l-`
1×	`+-commutative` `associate-+r+` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 47

Calls

3 calls:

Slowest

21.0ms	(log (+ (* x (* x 1/2)) (+ x 2)))
19.0ms	(- (log (+ (* x (* x 1/2)) (+ x 2))) (* x y))
19.0ms	(+ (* x (* x 1/2)) (+ x 2))

series148.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

82.0ms	(- (log (+ (* x (* x 1/2)) (+ x 2))) (* x y))
45.0ms	(log (+ (* x (* x 1/2)) (+ x 2)))
21.0ms	(+ (* x (* x 1/2)) (+ x 2))

simplify3.7s

Counts

23 → 56

Calls

23 calls:

Slowest

514.0ms	(* (exp (* x (* x 1/2))) (exp (+ x 2)))
367.0ms	(log (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3)))
341.0ms	(log (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3)))
303.0ms	(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))
290.0ms	(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))

prune550.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

12.0b	(posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))
6.8b	(log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2)))))
0.0b	(+ (* x (* x 1/2)) (+ x 2))
0.0b	(- (log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))) (* x y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16`
3×	`sum-log` `associate--l+`
1×	`+-commutative` `associate-+r+` `sub-neg` `flip3-+` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip-+` `remove-posit16` `flip--`

Counts

4 → 52

Calls

4 calls:

Slowest

19.0ms	(+ (* x (* x 1/2)) (+ x 2))
11.0ms	(- (log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))) (* x y))
1.0ms	(log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2)))))
0.0ms	(posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

78.0ms	(- (log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))) (* x y))
43.0ms	(log (posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2)))))
33.0ms	(+ (* x (* x 1/2)) (+ x 2))
31.0ms	(posit16->real (real->posit16 (+ (* x (* x 1/2)) (+ x 2))))

simplify2.9s

Counts

23 → 64

Calls

23 calls:

Slowest

472.0ms	(* (exp (* x (* x 1/2))) (exp (+ x 2)))
349.0ms	(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))
324.0ms	(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))
291.0ms	(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ -1 x))))
253.0ms	(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ -1 x))) (* x y)))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes83.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch2.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	2437×	body	10240	exit
839.0ms	8476×	body	80	valid
180.0ms	266×	body	640	valid
104.0ms	111×	body	1280	valid
54.0ms	164×	body	320	valid
23.0ms	103×	body	160	valid