Details

sample113.0ms

Algorithm

intervals

Results

64.0ms	63×	body	10240	exit
25.0ms	270×	body	80	valid
4.0ms	9×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify46.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

45.0ms

(- (log (+ 1 (exp x))) (* x y))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(log1p (exp x))
0.0b	(- (log1p (exp x)) (* y x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

Slowest

5.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))

series160.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

82.0ms	(- (log1p (exp x)) (* y x))
78.0ms	(log1p (exp x))

simplify605.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

99.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
92.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
70.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
69.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
60.0ms	(/ (+ 1 (exp x)) (exp (* y x)))

prune325.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0b	(fma (fma 1/8 x 1/2) x (log 2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

Slowest

5.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series112.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

58.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
54.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify1.8s

Counts

16 → 39

Calls

16 calls:

Slowest

272.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
249.0ms	(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
223.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
165.0ms	(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))
161.0ms	(fma (* (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (cbrt (fma (fma 1/8 x 1/2) x (log 2)))) (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* x y)))

prune415.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x (- (fma x 1/8 1/2) y) (log 2))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

Slowest

0.0ms

(fma x (- (fma x 1/8 1/2) y) (log 2))

series67.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

67.0ms

(fma x (- (fma x 1/8 1/2) y) (log 2))

simplify621.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

244.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
237.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
138.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune195.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 3 expressions with local error:

38.5b	(posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))
0.0b	(- (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
0.0b	(fma (fma 1/8 x 1/2) x (log 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `remove-posit16` `flip--`

Counts

3 → 43

Calls

3 calls:

Slowest

6.0ms	(- (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
0.0ms	(posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

51.0ms	(- (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
40.0ms	(posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))
34.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify2.3s

Counts

19 → 52

Calls

19 calls:

Slowest

264.0ms	(/ (exp (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))) (exp (* y x)))
233.0ms	(fma (sqrt (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))) (sqrt (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2))))) (- (* x y)))
227.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
204.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
194.0ms	(fma 1 (posit16->real (real->posit16 (fma (fma 1/8 x 1/2) x (log 2)))) (- (* x y)))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes76.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.4s	2387×	body	10240	exit
1.2s	8405×	body	80	valid
148.0ms	270×	body	640	valid
128.0ms	129×	body	1280	valid
101.0ms	181×	body	320	valid
21.0ms	83×	body	160	valid