Details

sample382.0ms

Algorithm

intervals

Results

128.0ms	308×	body	80	valid
95.0ms	61×	body	10240	exit
80.0ms	61×	body	1280	valid
38.0ms	38×	body	640	valid
11.0ms	17×	body	320	valid
6.0ms	14×	body	160	valid

simplify280.0ms

Calls

1 calls:

Slowest

279.0ms

(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize54.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.1b	(exp (* x (- -1 eps)))
0.1b	(exp (* x (- -1 eps)))
0.1b	(exp (* x (+ -1 eps)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
48×	`prod-diff`
35×	`add-sqr-sqrt`
30×	`associate--r+`
26×	`exp-sum`
25×	`add-cube-cbrt`
19×	`add-log-exp`
14×	`sub-neg`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`distribute-lft-out--`
8×	`distribute-lft-out`
7×	`div-inv`
6×	`diff-log`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `flip--` `rem-exp-log`
2×	`sum-log` `flip3-+` `flip-+`
1×	`associate--l+` `associate--r-`

Calls

4 calls:

Slowest

122.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
3.0ms	(exp (* x (- -1 eps)))
2.0ms	(exp (* x (- -1 eps)))
2.0ms	(exp (* x (+ -1 eps)))

series213.0ms

Calls

4 calls:

Slowest

143.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
24.0ms	(exp (* x (- -1 eps)))
24.0ms	(exp (* x (- -1 eps)))
22.0ms	(exp (* x (+ -1 eps)))

simplify23.9s

Calls

120 calls:

Slowest

654.0ms	(- (* (+ (pow (/ (exp (* x (+ -1 eps))) eps) 3) (pow (exp (* x (+ -1 eps))) 3)) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (+ (* (/ (exp (* x (+ -1 eps))) eps) (/ (exp (* x (+ -1 eps))) eps)) (- (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (* (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
626.0ms	(fma (- (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))))
558.0ms	(- (* (- (* (/ (exp (* x (+ -1 eps))) eps) (/ (exp (* x (+ -1 eps))) eps)) (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps))))) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
494.0ms	(exp (* -1 (* (- 1 eps) x)))
456.0ms	(- (* (+ (pow (/ (exp (* x (+ -1 eps))) eps) 3) (pow (exp (* x (+ -1 eps))) 3)) (+ (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (* (+ (* (/ (exp (* x (+ -1 eps))) eps) (/ (exp (* x (+ -1 eps))) eps)) (- (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (* (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))) (- (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))))))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 2 expressions with local error:

5.2b	(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.4b	(* 2/3 x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`*-commutative` `fma-udef`

Calls

2 calls:

Slowest

1.0ms	(* 2/3 x)
1.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

series59.0ms

Calls

2 calls:

Slowest

41.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))
18.0ms	(* 2/3 x)

simplify383.0ms

Calls

6 calls:

Slowest

135.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
122.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
115.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
3.0ms	(* 2/3 x)
3.0ms	(* 2/3 x)

prune238.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 3 expressions with local error:

60.3b	(posit16->real (real->posit16 (* 2/3 x)))
5.2b	(fma (* x x) (posit16->real (real->posit16 (* 2/3 x))) (- 2 (* x x)))
0.4b	(* 2/3 x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`*-commutative` `fma-udef` `remove-posit16`

Calls

3 calls:

Slowest

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

series82.0ms

Calls

3 calls:

Slowest

36.0ms	(fma (* x x) (posit16->real (real->posit16 (* 2/3 x))) (- 2 (* x x)))
24.0ms	(posit16->real (real->posit16 (* 2/3 x)))
21.0ms	(* 2/3 x)

simplify368.0ms

Calls

9 calls:

Slowest

134.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
117.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
97.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
3.0ms	(* 2/3 x)
3.0ms	(* 2/3 x)

prune804.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 2 expressions with local error:

5.2b	(fma (* x x) (* x 2/3) (- 2 (* x x)))
0.4b	(* x 2/3)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`*-commutative` `fma-udef`

Calls

2 calls:

Slowest

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

series57.0ms

Calls

2 calls:

Slowest

42.0ms	(fma (* x x) (* x 2/3) (- 2 (* x x)))
15.0ms	(* x 2/3)

simplify440.0ms

Calls

6 calls:

Slowest

157.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
145.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
127.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
3.0ms	(* 2/3 x)
3.0ms	(* 2/3 x)

prune300.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes223.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.4b

bsearch336.0ms

end0.0ms

sample11.9s

Algorithm

intervals

Results

3.4s	1916×	body	10240	exit
3.0s	10088×	body	80	valid
2.8s	1707×	body	1280	valid
1.7s	1291×	body	640	valid
459.0ms	615×	body	320	valid
139.0ms	276×	body	160	valid