Details

sample117.0ms

Algorithm

intervals

Results

51.0ms	64×	body	10240	exit
42.0ms	271×	body	80	valid
4.0ms	3×	body	1280	valid
3.0ms	8×	body	320	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	160	valid

simplify42.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

42.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b	(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))

series125.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

67.0ms	(log1p (exp x))
59.0ms	(- (log1p (exp x)) (* y x))

simplify594.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

125.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
91.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
76.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
51.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
45.0ms	(/ (+ 1 (exp x)) (exp (* y x)))

prune342.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.7b	(log1p (exp x))
0.0b	(expm1 (log1p (log1p (exp x))))
0.0b	(- (expm1 (log1p (log1p (exp x)))) (* y x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

Slowest

14.0ms	(- (expm1 (log1p (log1p (exp x)))) (* y x))
1.0ms	(log1p (exp x))
0.0ms	(expm1 (log1p (log1p (exp x))))

series408.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

181.0ms	(expm1 (log1p (log1p (exp x))))
161.0ms	(- (expm1 (log1p (log1p (exp x)))) (* y x))
66.0ms	(log1p (exp x))

simplify764.0ms

Counts

21 → 55

Calls

21 calls:

Slowest

171.0ms	(/ (exp (expm1 (log1p (log1p (exp x))))) (exp (* y x)))
122.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
84.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
65.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
53.0ms	(fma (* (cbrt (expm1 (log1p (log1p (exp x))))) (cbrt (expm1 (log1p (log1p (exp x)))))) (cbrt (expm1 (log1p (log1p (exp x))))) (- (* x y)))

prune571.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(log1p (exp x))
0.7b	(log1p (exp x))
0.7b	(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))
0.7b	(sqrt (log1p (exp x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`expm1-log1p-u` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`log1p-udef` `log1p-expm1`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

Slowest

22.0ms	(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))
2.0ms	(sqrt (log1p (exp x)))
1.0ms	(log1p (exp x))
1.0ms	(log1p (exp x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(sqrt (log1p (exp x)))
73.0ms	(log1p (exp x))
69.0ms	(log1p (exp x))
67.0ms	(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))

simplify1.5s

Counts

79 → 104

Calls

79 calls:

Slowest

364.0ms	(- (+ (* 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))))
171.0ms	(* (* (* (sqrt (log1p (exp x))) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))) (* (* (sqrt (log1p (exp x))) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))))
130.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
103.0ms	(* (* (cbrt (sqrt (log1p (exp x)))) (cbrt (sqrt (log1p (exp x))))) (* (cbrt (sqrt (log1p (exp x)))) (cbrt (sqrt (log1p (exp x))))))
102.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

6.8b	(log1p (fma (fma 1/8 x 1/2) x (log 2)))
1.1b	(expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2))))
0.0b	(- (expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
0.0b	(fma (fma 1/8 x 1/2) x (log 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

Slowest

10.0ms	(- (expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
1.0ms	(log1p (fma (fma 1/8 x 1/2) x (log 2)))
0.0ms	(expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2))))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series545.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

218.0ms	(- (expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2)))) (* y x))
173.0ms	(expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2))))
105.0ms	(log1p (fma (fma 1/8 x 1/2) x (log 2)))
49.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify3.2s

Counts

24 → 69

Calls

24 calls:

Slowest

353.0ms	(- (+ (log 1/8) (+ (* 8 (/ (log 2) (pow x 2))) (* 4 (/ 1 x)))) (* 2 (log (/ -1 x))))
307.0ms	(- (+ (log 1/8) (+ (* 8 (/ (log 2) (pow x 2))) (* 4 (/ 1 x)))) (* 2 (log (/ 1 x))))
305.0ms	(- (+ (* 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))))
256.0ms	(/ (exp (expm1 (log1p (fma (fma 1/8 x 1/2) x (log 2))))) (exp (* y x)))
232.0ms	(- (+ (* 8 (/ (exp (- (log 1/8) (* 2 (log (/ 1 x))))) (pow x 2))) (+ (* 4 (/ (exp (- (log 1/8) (* 2 (log (/ 1 x))))) x)) (+ (* 8 (/ (* (log 2) (exp (- (log 1/8) (* 2 (log (/ 1 x)))))) (pow x 2))) (exp (- (log 1/8) (* 2 (log (/ 1 x)))))))) 1)

prune947.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes85.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	2437×	body	10240	exit
985.0ms	8476×	body	80	valid
156.0ms	266×	body	640	valid
112.0ms	111×	body	1280	valid
58.0ms	164×	body	320	valid
23.0ms	103×	body	160	valid