Details

sample321.0ms

Algorithm

intervals

Results

81.0ms	54×	body	10240	exit
77.0ms	48×	body	640	valid
67.0ms	53×	body	1280	valid
61.0ms	323×	body	80	valid
9.0ms	17×	body	320	valid
4.0ms	10×	body	160	valid

simplify357.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

357.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`add-sqr-sqrt` `un-div-inv`
18×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-cube-cbrt`
9×	`associate-r` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
2×	`difference-of-squares`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `distribute-lft-out--`

Counts

4 → 180

Calls

4 calls:

Slowest

54.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
30.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
23.0ms	(* (+ 1 eps) x)
18.0ms	(* (- 1 eps) x)

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
45.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
30.0ms	(* (- 1 eps) x)
26.0ms	(* (+ 1 eps) x)

simplify59.3s

Counts

225 → 192

Calls

225 calls:

Slowest

858.0ms	(* (exp (* (- 1 eps) x)) (exp (* (+ 1 eps) x)))
794.0ms	(* (* (+ (* 1 1) (- (* (/ 1 eps) (/ 1 eps)) (* 1 (/ 1 eps)))) (exp (* (- 1 eps) x))) (+ (/ 1 eps) 1))
749.0ms	(* (* (+ (* 1 1) (- (* (/ 1 eps) (/ 1 eps)) (* 1 (/ 1 eps)))) (exp (* (- 1 eps) x))) (+ (/ 1 eps) 1))
688.0ms	(* (exp (* (- 1 eps) x)) (* (+ (* (/ 1 eps) (/ 1 eps)) (+ (* 1 1) (* (/ 1 eps) 1))) (exp (* (+ 1 eps) x))))
668.0ms	(* (exp (* (- 1 eps) x)) (* (+ (* (/ 1 eps) (/ 1 eps)) (+ (* 1 1) (* (/ 1 eps) 1))) (exp (* (+ 1 eps) x))))

prune3.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 2 expressions with local error:

5.0b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

Slowest

27.0ms	(* x (* x x))
1.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series112.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

60.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
52.0ms	(* x (* x x))

simplify1.7s

Counts

20 → 44

Calls

20 calls:

Slowest

502.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
473.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
220.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
210.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
200.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune785.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize52.0ms

Local error

Found 3 expressions with local error:

16.9b	(posit16->real (real->posit16 (* x (* x x))))
5.0b	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `pow-prod-up`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `remove-posit16` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

Slowest

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

series145.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

51.0ms	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
50.0ms	(* x (* x x))
44.0ms	(posit16->real (real->posit16 (* x (* x x))))

simplify1.8s

Counts

23 → 58

Calls

23 calls:

Slowest

505.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
476.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
226.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
225.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
203.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize57.0ms

Local error

Found 4 expressions with local error:

16.9b	(posit16->real (real->posit16 (* x (* x x))))
16.9b	(posit16->real (real->posit16 (* x (* x x))))
5.0b	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
5.0b	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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`
2×	`fma-udef` `remove-posit16`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series249.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(posit16->real (real->posit16 (* x (* x x))))
65.0ms	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
58.0ms	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
55.0ms	(posit16->real (real->posit16 (* x (* x x))))

simplify1.3s

Counts

12 → 56

Calls

12 calls:

Slowest

265.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
236.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
221.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
208.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
198.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes160.0ms

Accuracy

97.2% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 16.0b

bsearch267.0ms

end0.0ms

sample11.3s

Algorithm

intervals

Results

3.5s	1942×	body	10240	exit
2.5s	10040×	body	80	valid
2.4s	1779×	body	1280	valid
1.5s	1306×	body	640	valid
553.0ms	316×	body	160	valid
524.0ms	624×	body	320	valid