Details

sample136.0ms

Algorithm

intervals

Results

79.0ms	72×	body	10240	exit
25.0ms	264×	body	80	valid
5.0ms	8×	body	640	valid
5.0ms	4×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	6×	body	160	valid

simplify24.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

24.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(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))

series129.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

70.0ms	(log1p (exp x))
58.0ms	(- (log1p (exp x)) (* y x))

simplify568.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

89.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
81.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
77.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
76.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
73.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))

prune416.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (log1p (exp x)))
0.7b	(sqrt (log1p (exp x)))
0.5b	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
0.3b	(log1p (exp x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
5×	`expm1-log1p-u`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

4 → 55

Calls

4 calls:

Slowest

2.0ms	(sqrt (log1p (exp x)))
2.0ms	(sqrt (log1p (exp x)))
1.0ms	(log1p (exp x))
0.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

168.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
111.0ms	(sqrt (log1p (exp x)))
99.0ms	(sqrt (log1p (exp x)))
74.0ms	(log1p (exp x))

simplify1.3s

Counts

23 → 67

Calls

23 calls:

Slowest

465.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
462.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
97.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
93.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
41.0ms	(- (log (+ (exp x) 1)) (* x y))

prune783.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (log1p (exp x)))
0.7b	(sqrt (log1p (exp x)))
0.5b	(fma (sqrt (log1p (exp x))) (log (exp (sqrt (log1p (exp x))))) (- (* y x)))
0.3b	(log1p (exp x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
5×	`expm1-log1p-u`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

4 → 55

Calls

4 calls:

Slowest

2.0ms	(sqrt (log1p (exp x)))
2.0ms	(sqrt (log1p (exp x)))
1.0ms	(log1p (exp x))
0.0ms	(fma (sqrt (log1p (exp x))) (log (exp (sqrt (log1p (exp x))))) (- (* y x)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(fma (sqrt (log1p (exp x))) (log (exp (sqrt (log1p (exp x))))) (- (* y x)))
121.0ms	(sqrt (log1p (exp x)))
93.0ms	(sqrt (log1p (exp x)))
63.0ms	(log1p (exp x))

simplify1.1s

Counts

23 → 67

Calls

23 calls:

Slowest

408.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
349.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
98.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
90.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
38.0ms	(- (log (+ (exp x) 1)) (* x y))

prune877.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

14.2b	(cbrt (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))))
0.7b	(* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x)))
0.3b	(log1p (exp x))
0.3b	(log1p (exp x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

33×	`flip3--` `flip--`
32×	`frac-times`
26×	`cbrt-div`
16×	`associate-*l/`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`-un-lft-identity` `associate-r/` `add-cube-cbrt`
6×	`expm1-log1p-u` `add-cbrt-cube` `prod-diff` `add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`log1p-udef` `sub-neg` `log1p-expm1`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

Slowest

41.0ms	(* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x)))
35.0ms	(cbrt (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))))
1.0ms	(log1p (exp x))
1.0ms	(log1p (exp x))

series308.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

111.0ms	(* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x)))
78.0ms	(log1p (exp x))
62.0ms	(log1p (exp x))
57.0ms	(cbrt (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))))

simplify15.6s

Counts

85 → 121

Calls

85 calls:

Slowest

1.4s	(cbrt (* (* (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))) (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))) (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))))
685.0ms	(* (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))) (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))))
674.0ms	(* (+ (log1p (exp x)) (* y x)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
663.0ms	(* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
428.0ms	(* (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))) (- (log1p (exp x)) (* y x)))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes126.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch4.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.3s	2524×	body	10240	exit
861.0ms	8459×	body	80	valid
185.0ms	270×	body	640	valid
120.0ms	126×	body	1280	valid
90.0ms	155×	body	320	valid
28.0ms	126×	body	160	valid