Details

sample372.0ms

Algorithm

intervals

Results

166.0ms	87×	body	10240	exit
73.0ms	60×	body	1280	valid
58.0ms	330×	body	80	valid
32.0ms	40×	body	640	valid
12.0ms	20×	body	320	valid
5.0ms	12×	body	160	valid

simplify1.5s

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize63.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
0.0b	(/ (/ 1/2 (exp (+ x (* x eps)))) eps)
0.0b	(/ 1/2 (exp (- x (* x eps))))
0.0b	(/ 1/2 (exp (- x (* x eps))))

rewrite700.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
93×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
28×	`exp-sum`
22×	`associate-/l*`
16×	`add-log-exp`
13×	`associate-/r*` `add-cbrt-cube`
12×	`frac-sub`
10×	`sub-neg` `add-exp-log`
8×	`distribute-lft-out--`
7×	`div-inv`
6×	`diff-log`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `flip3--` `insert-posit16` `flip--`
3×	`clear-num` `frac-2neg` `flip3-+` `frac-add` `flip-+` `distribute-lft-out`
2×	`sum-log` `exp-diff` `associate-/r/` `associate--r+`
1×	`associate--l+` `associate--r-` `difference-of-squares` `associate-/l/`

Counts

4 → 192

Calls

4 calls:

Slowest

634.0ms	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
26.0ms	(/ 1/2 (exp (- x (* x eps))))
22.0ms	(/ (/ 1/2 (exp (+ x (* x eps)))) eps)
15.0ms	(/ 1/2 (exp (- x (* x eps))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

232.0ms	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
49.0ms	(/ (/ 1/2 (exp (+ x (* x eps)))) eps)
37.0ms	(/ 1/2 (exp (- x (* x eps))))
36.0ms	(/ 1/2 (exp (- x (* x eps))))

simplify1.9s

Counts: 204 → 204

prune3.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (* x (* (* x x) 1/3)) (* (* x x) 1/2))
0.1b	(* (* x x) 1/3)
0.1b	(* x (* (* x x) 1/3))
0.0b	(* (* x x) 1/2)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
4×	`insert-posit16`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 75

Calls

4 calls:

Slowest

58.0ms	(- (* x (* (* x x) 1/3)) (* (* x x) 1/2))
48.0ms	(* x (* (* x x) 1/3))
14.0ms	(* (* x x) 1/2)
14.0ms	(* (* x x) 1/3)

series310.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(- (* x (* (* x x) 1/3)) (* (* x x) 1/2))
58.0ms	(* x (* (* x x) 1/3))
45.0ms	(* (* x x) 1/2)
33.0ms	(* (* x x) 1/3)

simplify1.5s

Counts: 87 → 87

prune843.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize50.0ms

Local error

Found 4 expressions with local error:

27.1b	(posit16->real (real->posit16 (* (* x x) 1/3)))
5.2b	(- (* x (posit16->real (real->posit16 (* (* x x) 1/3)))) (* (* x x) 1/2))
0.1b	(* (* x x) 1/3)
0.1b	(* x (posit16->real (real->posit16 (* (* x x) 1/3))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `remove-posit16` `flip--`

Counts

4 → 61

Calls

4 calls:

Slowest

14.0ms	(* (* x x) 1/3)
7.0ms	(- (* x (posit16->real (real->posit16 (* (* x x) 1/3)))) (* (* x x) 1/2))
7.0ms	(* x (posit16->real (real->posit16 (* (* x x) 1/3))))
0.0ms	(posit16->real (real->posit16 (* (* x x) 1/3)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(- (* x (posit16->real (real->posit16 (* (* x x) 1/3)))) (* (* x x) 1/2))
76.0ms	(* x (posit16->real (real->posit16 (* (* x x) 1/3))))
49.0ms	(posit16->real (real->posit16 (* (* x x) 1/3)))
47.0ms	(* (* x x) 1/3)

simplify1.1s

Counts: 73 → 73

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize55.0ms

Local error

Found 4 expressions with local error:

42.4b	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
42.4b	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
42.4b	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
27.1b	(posit16->real (real->posit16 (* (* x x) 1/3)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`remove-posit16`

Counts

4 → 39

Calls

4 calls:

Slowest

6.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
5.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
3.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
0.0ms	(posit16->real (real->posit16 (* (* x x) 1/3)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

59.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
51.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
42.0ms	(cbrt (* x (posit16->real (real->posit16 (* (* x x) 1/3)))))
28.0ms	(posit16->real (real->posit16 (* (* x x) 1/3)))

simplify1.1s

Counts: 51 → 51

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.6b

regimes175.0ms

Accuracy

97% (0.5b remaining)

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

bsearch290.0ms

end0.0ms

sample11.6s

Algorithm

intervals

Results

3.7s	1910×	body	10240	exit
3.0s	10029×	body	80	valid
2.6s	1742×	body	1280	valid
1.1s	1219×	body	640	valid
452.0ms	636×	body	320	valid
175.0ms	320×	body	160	valid