Details

sample84.0ms

Algorithm

intervals

Results

39.0ms	56×	body	10240	exit
21.0ms	267×	body	80	valid
5.0ms	11×	body	640	valid
3.0ms	5×	body	1280	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify39.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

39.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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

10.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series140.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

84.0ms	(log1p (exp x))
56.0ms	(- (log1p (exp x)) (* y x))

simplify615.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

115.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
83.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
82.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
80.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
73.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune387.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (log1p (exp x))))
0.0b	(log1p (exp x))
0.0b	(log1p (log1p (exp x)))
0.0b	(- (expm1 (log1p (log1p (exp x)))) (* y x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

5.0ms	(- (expm1 (log1p (log1p (exp x)))) (* y x))
0.0ms	(log1p (exp x))
0.0ms	(log1p (log1p (exp x)))
0.0ms	(expm1 (log1p (log1p (exp x))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

239.0ms	(expm1 (log1p (log1p (exp x))))
174.0ms	(- (expm1 (log1p (log1p (exp x)))) (* y x))
164.0ms	(log1p (log1p (exp x)))
65.0ms	(log1p (exp x))

simplify1.1s

Counts

25 → 70

Calls

25 calls:

Slowest

296.0ms	(- (+ (* 1/8 (/ (pow x 2) (+ (log 2) 1))) (+ (log (+ (log 2) 1)) (* 1/2 (/ x (+ (log 2) 1))))) (* 1/8 (/ (pow x 2) (pow (+ (log 2) 1) 2))))
156.0ms	(/ (exp (expm1 (log1p (log1p (exp x))))) (exp (* y x)))
126.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (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))))

prune856.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(log (+ 1 (log1p (exp x))))
0.0b	(expm1 (log (+ 1 (log1p (exp x)))))
0.0b	(log1p (exp x))
0.0b	(+ 1 (log1p (exp x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`expm1-log1p-u` `pow1` `add-exp-log` `log1p-expm1-u`
4×	`log-prod` `add-cbrt-cube` `insert-posit16`
3×	`fma-def`
2×	`log-div` `log1p-udef` `expm1-log1p` `sum-log` `log1p-def` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `log1p-expm1` `log-pow` `expm1-udef`

Counts

4 → 63

Calls

4 calls:

Slowest

4.0ms	(+ 1 (log1p (exp x)))
3.0ms	(log (+ 1 (log1p (exp x))))
0.0ms	(expm1 (log (+ 1 (log1p (exp x)))))
0.0ms	(log1p (exp x))

series478.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(expm1 (log (+ 1 (log1p (exp x)))))
152.0ms	(log (+ 1 (log1p (exp x))))
61.0ms	(+ 1 (log1p (exp x)))
59.0ms	(log1p (exp x))

simplify1.1s

Counts

28 → 75

Calls

28 calls:

Slowest

304.0ms	(- (+ (* 1/8 (/ (pow x 2) (+ (log 2) 1))) (+ (log (+ (log 2) 1)) (* 1/2 (/ x (+ (log 2) 1))))) (* 1/8 (/ (pow x 2) (pow (+ (log 2) 1) 2))))
211.0ms	(+ (log 2) (+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1)))
183.0ms	(log (+ (pow 1 3) (pow (log1p (exp x)) 3)))
91.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
79.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune970.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

10.0b	(/ (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))) (+ (log1p (exp x)) (* y x)))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
0.3b	(* (* y x) (* y x))
0.0b	(+ (log1p (exp x)) (* y x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
20×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
18×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
12×	`times-frac`
9×	`prod-exp` `cbrt-unprod`
7×	`add-log-exp`
5×	`pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l*` `difference-of-squares`
3×	`associate-/r*` `fma-def` `pow-plus`
2×	`pow2` `sum-log` `flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `log1p-udef` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

Slowest

40.0ms	(/ (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))) (+ (log1p (exp x)) (* y x)))
22.0ms	(* (* y x) (* y x))
10.0ms	(* (log1p (exp x)) (log1p (exp x)))
5.0ms	(+ (log1p (exp x)) (* y x))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(/ (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))) (+ (log1p (exp x)) (* y x)))
92.0ms	(* (log1p (exp x)) (log1p (exp x)))
69.0ms	(+ (log1p (exp x)) (* y x))
50.0ms	(* (* y x) (* y x))

simplify10.8s

Counts

106 → 134

Calls

106 calls:

Slowest

907.0ms	(sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
813.0ms	(* (* (* (* y y) y) (* (* x x) x)) (* (* (* y y) y) (* (* x x) x)))
638.0ms	(* (* (* (* y x) (* y x)) (* y x)) (* (* (* y x) (* y x)) (* y x)))
536.0ms	(* (cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))) (cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))))
498.0ms	(/ (sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))) (+ (log1p (exp x)) (* y x)))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.7s	2411×	body	10240	exit
897.0ms	8428×	body	80	valid
150.0ms	272×	body	640	valid
94.0ms	101×	body	1280	valid
64.0ms	191×	body	320	valid
18.0ms	88×	body	160	valid