Details

sample302.0ms

Algorithm

intervals

Results

88.0ms	304×	body	80	valid
72.0ms	62×	body	1280	valid
68.0ms	55×	body	10240	exit
29.0ms	37×	body	640	valid
19.0ms	28×	body	320	valid
7.0ms	20×	body	160	valid

simplify681.0ms

Calls

1 calls:

Slowest

680.0ms

(/ (- (* (+ 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: 32.8b

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(* x (+ -1 eps))
0.0b	(* x (+ -1 eps))
0.0b	(/ (exp (* x (+ -1 eps))) eps)

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

4771×	`prod-diff`
3404×	`exp-sum`
2721×	`*-un-lft-identity`
2709×	`add-sqr-sqrt`
2683×	`add-cube-cbrt`
1977×	`associate--r+`
1900×	`times-frac`
1706×	`distribute-rgt-in` `distribute-lft-in`
310×	`sub-neg`
26×	`div-inv`
16×	`add-log-exp`
13×	`+-commutative`
11×	`add-exp-log` `distribute-lft-out`
10×	`add-cbrt-cube` `distribute-lft-out--`
9×	`difference-of-squares`
8×	`pow1` `associate-r`
7×	`associate-/l*`
6×	`diff-log` `associate-l`
4×	`expm1-log1p-u` `flip3-+` `fma-neg` `associate-*r/` `frac-sub` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sum-log` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate--r-`

Calls

4 calls:

Slowest

2.1s	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
96.0ms	(/ (exp (* x (+ -1 eps))) eps)
39.0ms	(* x (+ -1 eps))
26.0ms	(* x (+ -1 eps))

series251.0ms

Calls

4 calls:

Slowest

138.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
42.0ms	(/ (exp (* x (+ -1 eps))) eps)
36.0ms	(* x (+ -1 eps))
34.0ms	(* x (+ -1 eps))

simplify7.8m

Calls

2147 calls:

Slowest

861.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
841.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
821.0ms	(- (* (+ (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))))
820.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
813.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))

prune42.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 2 expressions with local error:

6.4b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

36.0ms	(* x (* x x))
1.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series100.0ms

Calls

2 calls:

Slowest

53.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
47.0ms	(* x (* x x))

simplify2.1s

Calls

40 calls:

Slowest

566.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
484.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
268.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
212.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
187.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune595.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize76.0ms

Local error

Found 4 expressions with local error:

6.4b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
4.9b	(posit16->real (real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
2.4b	(real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x))))
0.1b	(* x (* x x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series164.0ms

Calls

4 calls:

Slowest

72.0ms	(* x (* x x))
47.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
45.0ms	(posit16->real (real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
0.0ms	(real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x))))

simplify2.7s

Calls

44 calls:

Slowest

585.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
535.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
221.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
215.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
211.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize90.0ms

Local error

Found 4 expressions with local error:

6.4b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
6.4b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
6.4b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
4.9b	(posit16->real (real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x)))))

rewrite3.0ms

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`
3×	`fma-udef`
1×	`remove-posit16`

Calls

4 calls:

Slowest

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

series240.0ms

Calls

4 calls:

Slowest

75.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
58.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
55.0ms	(posit16->real (real->posit16 (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
52.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify2.6s

Calls

13 calls:

Slowest

233.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
228.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
224.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
220.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
220.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes130.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 16.4b

bsearch314.0ms

end0.0ms

sample11.3s

Algorithm

intervals

Results

4.2s	1981×	body	10240	exit
3.1s	1697×	body	1280	valid
2.0s	10212×	body	80	valid
1.2s	1250×	body	640	valid
364.0ms	622×	body	320	valid
156.0ms	334×	body	160	valid