Details

sample84.0ms

Algorithm

intervals

Results

44.0ms	73×	body	10240	exit
24.0ms	273×	body	80	valid
3.0ms	4×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

22.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b	(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))

series114.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

58.0ms	(log1p (exp x))
56.0ms	(- (log1p (exp x)) (* y x))

simplify685.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

125.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
112.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
91.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
65.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
58.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt (- (log1p (exp x)) (* y x)))
1.1b	(cbrt (- (log1p (exp x)) (* y x)))
1.1b	(cbrt (- (log1p (exp x)) (* y x)))
1.0b	(log1p (exp x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`expm1-log1p-u`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`log1p-udef` `log1p-expm1`

Counts

4 → 60

Calls

4 calls:

Slowest

3.0ms	(cbrt (- (log1p (exp x)) (* y x)))
2.0ms	(cbrt (- (log1p (exp x)) (* y x)))
2.0ms	(cbrt (- (log1p (exp x)) (* y x)))
0.0ms	(log1p (exp x))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

367.0ms	(cbrt (- (log1p (exp x)) (* y x)))
353.0ms	(cbrt (- (log1p (exp x)) (* y x)))
349.0ms	(cbrt (- (log1p (exp x)) (* y x)))
60.0ms	(log1p (exp x))

simplify6.7s

Counts

28 → 72

Calls

28 calls:

Slowest

803.0ms	(- (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y)))))) (+ (* 1/9 (/ (* (pow (log (+ (exp x) 1)) 2) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* (pow x 2) (pow y 2)))) (* 1/3 (/ (* (log (+ (exp x) 1)) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* x y)))))
634.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
556.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
475.0ms	(- (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y)))))) (+ (* 1/9 (/ (* (pow (log (+ (exp x) 1)) 2) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* (pow x 2) (pow y 2)))) (* 1/3 (/ (* (log (+ (exp x) 1)) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* x y)))))
466.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))

prune742.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize34.0ms

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))

rewrite12.0ms

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

11.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series101.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
32.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify1.6s

Counts

16 → 39

Calls

16 calls:

Slowest

263.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
253.0ms	(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
217.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
168.0ms	(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)))
157.0ms	(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))

prune424.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize25.0ms

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))

series52.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

52.0ms

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

simplify526.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

222.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
195.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
107.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune125.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes85.0ms

Accuracy

0% (0.2b 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	2458×	body	10240	exit
1.2s	8373×	body	80	valid
152.0ms	272×	body	640	valid
141.0ms	113×	body	1280	valid
135.0ms	201×	body	320	valid
27.0ms	109×	body	160	valid