Details

sample116.0ms

Algorithm

intervals

Results

33.0ms	63×	body	1280	valid
30.0ms	66×	body	10240	exit
24.0ms	62×	body	640	valid
7.0ms	94×	body	80	valid
7.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid

simplify35.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

35.0ms

(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize8.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
10×	`difference-of-squares`
9×	`prod-diff`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `expm1-def` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 80

Calls

2 calls:

Slowest

14.0ms	(/ (exp x) (- (exp x) 1))
10.0ms	(- (exp x) 1)

series49.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

33.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify2.2s

Counts

88 → 86

Calls

88 calls:

Slowest

235.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
213.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
71.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))
66.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
63.0ms	(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))

prune563.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ (exp x) (expm1 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

Slowest

13.0ms

(/ (exp x) (expm1 x))

series47.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

47.0ms

(/ (exp x) (expm1 x))

simplify746.0ms

Counts

28 → 33

Calls

28 calls:

Slowest

461.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
47.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
41.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
24.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
15.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (expm1 x)))

prune172.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x 1/12 (+ 1/2 (/ 1 x)))
0.0b	(+ 1/2 (/ 1 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef` `div-inv`

Counts

2 → 30

Calls

2 calls:

Slowest

12.0ms	(+ 1/2 (/ 1 x))
1.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))

series51.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

28.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))
23.0ms	(+ 1/2 (/ 1 x))

simplify234.0ms

Counts

11 → 36

Calls

11 calls:

Slowest

49.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
45.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
28.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
25.0ms	(* (exp 1/2) (exp (/ 1 x)))
19.0ms	(+ (/ 1 x) 1/2)

prune282.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize55.0ms

Local error

Found 3 expressions with local error:

59.6b	(posit16->real (real->posit16 (fma x 1/12 (+ 1/2 (/ 1 x)))))
0.1b	(fma x 1/12 (+ 1/2 (/ 1 x)))
0.0b	(+ 1/2 (/ 1 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef` `div-inv` `remove-posit16`

Counts

3 → 41

Calls

3 calls:

Slowest

12.0ms	(+ 1/2 (/ 1 x))
1.0ms	(posit16->real (real->posit16 (fma x 1/12 (+ 1/2 (/ 1 x)))))
0.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))

series61.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

27.0ms	(posit16->real (real->posit16 (fma x 1/12 (+ 1/2 (/ 1 x)))))
19.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))
16.0ms	(+ 1/2 (/ 1 x))

simplify337.0ms

Counts

14 → 50

Calls

14 calls:

Slowest

48.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
48.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
46.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
38.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
32.0ms	(* (exp 1/2) (exp (/ 1 x)))

prune515.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes46.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	2560×	body	10240	exit
1.0s	2285×	body	1280	valid
642.0ms	2841×	body	80	valid
620.0ms	1668×	body	640	valid
195.0ms	827×	body	320	valid
48.0ms	380×	body	160	valid