Details

sample149.0ms

Algorithm

intervals

Results

85.0ms	86×	body	10240	exit
35.0ms	262×	body	80	valid
7.0ms	7×	body	1280	valid
6.0ms	9×	body	640	valid
3.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify22.0ms

Calls

1 calls:

Slowest

21.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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--`

Calls

2 calls:

Slowest

9.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series123.0ms

Calls

2 calls:

Slowest

63.0ms	(- (log1p (exp x)) (* y x))
60.0ms	(log1p (exp x))

simplify393.0ms

Calls

17 calls:

Slowest

81.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
59.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
36.0ms	(- (log (+ (exp x) 1)) (* x y))
34.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
32.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune337.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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--`

Calls

2 calls:

Slowest

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

series115.0ms

Calls

2 calls:

Slowest

81.0ms	(- (fma x (fma 1/8 x 1/2) (log 2)) (* y x))
34.0ms	(fma x (fma 1/8 x 1/2) (log 2))

simplify1.4s

Calls

16 calls:

Slowest

224.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
202.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
173.0ms	(fma (* (cbrt (fma x (fma 1/8 x 1/2) (log 2))) (cbrt (fma x (fma 1/8 x 1/2) (log 2)))) (cbrt (fma x (fma 1/8 x 1/2) (log 2))) (- (* x y)))
160.0ms	(/ (exp (fma x (fma 1/8 x 1/2) (log 2))) (exp (* y x)))
124.0ms	(fma 1 (fma x (fma 1/8 x 1/2) (log 2)) (- (* x y)))

prune444.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x (- (fma 1/8 x 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`

Calls

1 calls:

Slowest

0.0ms

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

series51.0ms

Calls

1 calls:

Slowest

51.0ms

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

simplify486.0ms

Calls

3 calls:

Slowest

208.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
207.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
70.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune158.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

1.9b	(log (/ (+ 1 (exp x)) (exp (* y x))))
0.3b	(/ (+ 1 (exp x)) (exp (* y x)))
0.0b	(exp (* y x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`log-prod`
6×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `exp-prod` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+` `rem-exp-log`

Calls

3 calls:

Slowest

16.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
5.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))
2.0ms	(exp (* y x))

series125.0ms

Calls

3 calls:

Slowest

72.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))
32.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
20.0ms	(exp (* y x))

simplify2.2s

Calls

54 calls:

Slowest

391.0ms	(/ (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))) (* (* (exp (* y x)) (exp (* y x))) (exp (* y x))))
259.0ms	(+ (* 1/2 (* (pow x 2) (pow y 2))) (+ 1 (* x y)))
157.0ms	(log (/ (* (cbrt (+ 1 (exp x))) (cbrt (+ 1 (exp x)))) (* (cbrt (exp (* y x))) (cbrt (exp (* y x))))))
91.0ms	(log (/ (* (cbrt (+ 1 (exp x))) (cbrt (+ 1 (exp x)))) (sqrt (exp (* y x)))))
87.0ms	(log (/ 1 (* (cbrt (exp (* y x))) (cbrt (exp (* y x))))))

prune748.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes91.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	2419×	body	10240	exit
989.0ms	8434×	body	80	valid
473.0ms	191×	body	320	valid
141.0ms	254×	body	640	valid
124.0ms	145×	body	1280	valid
19.0ms	97×	body	160	valid