Details

sample352.0ms

Algorithm

intervals

Results

117.0ms	87×	body	10240	exit
111.0ms	60×	body	1280	valid
57.0ms	330×	body	80	valid
30.0ms	40×	body	640	valid
10.0ms	20×	body	320	valid
5.0ms	12×	body	160	valid

simplify2.1s

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize66.0ms

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

rewrite974.0ms

Algorithm

rewrite-expression-head

Rules

4849×	`prod-diff`
3496×	`exp-sum`
2782×	`*-un-lft-identity`
2775×	`add-sqr-sqrt`
2766×	`add-cube-cbrt`
1977×	`associate-+l+`
1975×	`times-frac`
1749×	`distribute-rgt-in` `distribute-lft-in`
323×	`sub-neg`
33×	`associate-/l*`
27×	`div-inv`
16×	`add-log-exp`
10×	`add-cbrt-cube`
8×	`frac-add` `add-exp-log`
6×	`pow1` `associate-/r*` `sum-log` `fma-def` `distribute-lft-out`
5×	`associate-r`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`flip3-+` `exp-diff` `associate-l` `flip-+` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `diff-log` `div-exp` `associate-*r/`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `unswap-sqr` `associate-/l/`

Counts

4 → 2228

Calls

4 calls:

Slowest

532.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
69.0ms	(/ (exp (- (* x eps) x)) eps)
28.0ms	(/ (exp (* x (- -1 eps))) eps)
28.0ms	(* x (- -1 eps))

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
54.0ms	(* x (- -1 eps))
44.0ms	(/ (exp (- (* x eps) x)) eps)
32.0ms	(/ (exp (* x (- -1 eps))) eps)

simplify2.5s

Counts: 2240 → 2240

prune45.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 3 expressions with local error:

5.2b	(- (fma 2/3 (* (* x x) x) 2) (* x x))
0.1b	(* (* x x) x)
0.0b	(fma 2/3 (* (* x x) x) 2)

rewrite37.0ms

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

29.0ms	(* (* x x) x)
7.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))
0.0ms	(fma 2/3 (* (* x x) x) 2)

series223.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

129.0ms	(fma 2/3 (* (* x x) x) 2)
51.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))
43.0ms	(* (* x x) x)

simplify914.0ms

Counts: 74 → 74

prune662.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 3 expressions with local error:

5.2b	(- (fma (* (* x x) x) 2/3 2) (* x x))
0.1b	(* (* x x) x)
0.0b	(fma (* (* x x) x) 2/3 2)

rewrite40.0ms

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

28.0ms	(* (* x x) x)
10.0ms	(- (fma (* (* x x) x) 2/3 2) (* x x))
0.0ms	(fma (* (* x x) x) 2/3 2)

series597.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

404.0ms	(* (* x x) x)
134.0ms	(fma (* (* x x) x) 2/3 2)
58.0ms	(- (fma (* (* x x) x) 2/3 2) (* x x))

simplify671.0ms

Counts: 74 → 74

prune634.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

6.1b	(posit16->real (real->posit16 (- (fma (* (* x x) x) 2/3 2) (* x x))))
5.2b	(- (fma (* (* x x) x) 2/3 2) (* x x))
0.1b	(* (* x x) x)
0.0b	(fma (* (* x x) x) 2/3 2)

rewrite28.0ms

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` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

Slowest

17.0ms	(* (* x x) x)
9.0ms	(- (fma (* (* x x) x) 2/3 2) (* x x))
0.0ms	(posit16->real (real->posit16 (- (fma (* (* x x) x) 2/3 2) (* x x))))
0.0ms	(fma (* (* x x) x) 2/3 2)

series231.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(fma (* (* x x) x) 2/3 2)
52.0ms	(posit16->real (real->posit16 (- (fma (* (* x x) x) 2/3 2) (* x x))))
50.0ms	(* (* x x) x)
38.0ms	(- (fma (* (* x x) x) 2/3 2) (* x x))

simplify716.0ms

Counts: 88 → 88

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes199.0ms

Accuracy

97% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 16.9b

bsearch294.0ms

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.1s	1910×	body	10240	exit
2.9s	10029×	body	80	valid
2.5s	1742×	body	1280	valid
1.4s	1219×	body	640	valid
365.0ms	636×	body	320	valid
175.0ms	320×	body	160	valid