Details

sample250.0ms

Algorithm

intervals

Results

76.0ms	52×	body	1280	valid
66.0ms	58×	body	10240	exit
46.0ms	308×	body	80	valid
27.0ms	45×	body	640	valid
12.0ms	24×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.7s

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize40.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
0.0b	(* x (- -1 eps))
0.0b	(* x (- -1 eps))
0.0b	(exp (- (* x eps) x))

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

4786×	`prod-diff`
3393×	`exp-sum`
2705×	`*-un-lft-identity`
2700×	`add-sqr-sqrt`
2687×	`add-cube-cbrt`
1977×	`associate-+l+`
1876×	`times-frac`
1716×	`distribute-rgt-in` `distribute-lft-in`
314×	`sub-neg`
25×	`div-inv`
19×	`add-log-exp`
10×	`associate-r`
8×	`pow1` `add-cbrt-cube` `frac-add` `add-exp-log`
6×	`sum-log` `fma-def` `associate-l` `distribute-lft-out`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `flip3-+` `exp-diff` `diff-log` `flip-+`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`+-commutative` `associate-+r+` `associate-+l-`

Counts

4 → 2127

Calls

4 calls:

Slowest

508.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
34.0ms	(exp (- (* x eps) x))
29.0ms	(* x (- -1 eps))
29.0ms	(* x (- -1 eps))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
69.0ms	(* x (- -1 eps))
69.0ms	(* x (- -1 eps))
27.0ms	(exp (- (* x eps) x))

simplify2.7s

Counts: 2139 → 2139

prune45.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 3 expressions with local error:

6.6b	(- (fma 2/3 (* (* x x) x) 2) (* x x))
0.1b	(* (* x x) x)
0.0b	(fma 2/3 (* (* x x) x) 2)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity` `pow-plus` `pow-prod-up` `add-cube-cbrt`
5×	`add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 65

Calls

3 calls:

Slowest

18.0ms	(* (* x x) x)
10.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))
0.0ms	(fma 2/3 (* (* x x) x) 2)

series229.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

111.0ms	(fma 2/3 (* (* x x) x) 2)
66.0ms	(* (* x x) x)
52.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))

simplify935.0ms

Counts: 74 → 74

prune767.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

7.2b	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
6.6b	(- (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))) (* x x))
0.1b	(* (* x x) x)
0.0b	(fma 2/3 (* (* x x) x) 2)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `pow-sqr`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `*-commutative` `fma-udef` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

30.0ms	(* (* x x) x)
10.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))) (* x x))
1.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
0.0ms	(fma 2/3 (* (* x x) x) 2)

series381.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
115.0ms	(fma 2/3 (* (* x x) x) 2)
70.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))) (* x x))
64.0ms	(* (* x x) x)

simplify2.3s

Counts: 87 → 87

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize78.0ms

Local error

Found 4 expressions with local error:

7.2b	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
7.2b	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
6.6b	(- (* (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))) (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))) (* x x))
4.5b	(sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`remove-posit16`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

Slowest

21.0ms	(- (* (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))) (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))) (* x x))
2.0ms	(sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))
1.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
1.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
133.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))
65.0ms	(sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))
54.0ms	(- (* (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2)))) (sqrt (posit16->real (real->posit16 (fma 2/3 (* (* x x) x) 2))))) (* x x))

simplify943.0ms

Counts: 68 → 68

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes191.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.3b

bsearch325.0ms

end0.0ms

sample12.3s

Algorithm

intervals

Results

4.2s	1942×	body	10240	exit
2.8s	10080×	body	80	valid
2.5s	1773×	body	1280	valid
1.3s	1261×	body	640	valid
587.0ms	283×	body	160	valid
491.0ms	621×	body	320	valid