Details

sample101.0ms

Algorithm

intervals

Results

58.0ms	80×	body	10240	exit
19.0ms	258×	body	80	valid
8.0ms	9×	body	1280	valid
4.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	valid

simplify45.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

45.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize22.0ms

Local error

Found 2 expressions with local error:

1.5b	(log1p (exp x))
0.0b	(- (log1p (exp x)) (* y x))

rewrite12.0ms

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

65.0ms	(- (log1p (exp x)) (* y x))
60.0ms	(log1p (exp x))

simplify569.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

94.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
87.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
81.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
57.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
48.0ms	(/ (+ 1 (exp x)) (exp (* y x)))

prune388.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b	(log1p (exp x))
1.1b	(expm1 (log1p (- (log1p (exp x)) (* y x))))
0.0b	(log1p (- (log1p (exp x)) (* y x)))
0.0b	(- (log1p (exp x)) (* y x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

5.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (- (log1p (exp x)) (* y x)))
0.0ms	(log1p (exp x))
0.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))

series794.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))
265.0ms	(log1p (- (log1p (exp x)) (* y x)))
87.0ms	(log1p (exp x))
84.0ms	(- (log1p (exp x)) (* y x))

simplify2.8s

Counts

25 → 70

Calls

25 calls:

Slowest

584.0ms	(- (log -1) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (log (/ -1 x)) (+ (log (/ -1 y)) (+ (/ 1 (* x y)) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
482.0ms	(- (log -1) (+ (log (/ 1 x)) (+ (/ 1 (* x y)) (+ (log (/ 1 y)) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
348.0ms	(- (+ (* 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))))
316.0ms	(+ (log 2) (+ (* 1/8 (pow x 2)) (+ (* 1/2 (/ (* (log 2) x) (+ (log 2) 1))) (* 1/2 (/ x (+ (log 2) 1))))))
188.0ms	(- (exp (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))) (+ (/ (exp (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))) (* x y)) (+ 1 (/ (* (exp (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))) (log (+ (exp x) 1))) (* x y)))))

prune742.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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

6.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series103.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

54.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
49.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify1.7s

Counts

16 → 39

Calls

16 calls:

Slowest

268.0ms	(- (+ (* 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)))
242.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
197.0ms	(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)))
137.0ms	(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))

prune427.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

1.5b	(log1p (exp x))
1.5b	(log1p (exp x))
1.1b	(expm1 (* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x))))))
0.1b	(* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

Slowest

10.0ms	(* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x)))))
0.0ms	(log1p (exp x))
0.0ms	(expm1 (* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x))))))
0.0ms	(log1p (exp x))

series785.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

397.0ms	(expm1 (* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x))))))
274.0ms	(* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x)))))
64.0ms	(log1p (exp x))
50.0ms	(log1p (exp x))

simplify4.0s

Counts

75 → 100

Calls

75 calls:

Slowest

504.0ms	(- (log -1) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (log (/ -1 x)) (+ (log (/ -1 y)) (+ (/ 1 (* x y)) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
474.0ms	(- (log -1) (+ (log (/ 1 x)) (+ (/ 1 (* x y)) (+ (log (/ 1 y)) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
340.0ms	(+ (log 2) (+ (* 1/8 (pow x 2)) (+ (* 1/2 (/ (* (log 2) x) (+ (log 2) 1))) (* 1/2 (/ x (+ (log 2) 1))))))
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))))
184.0ms	(* (* (* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x))))) (sqrt (log1p (- (log1p (exp x)) (* y x))))) (* (* (sqrt (log1p (- (log1p (exp x)) (* y x)))) (sqrt (log1p (- (log1p (exp x)) (* y x))))) (sqrt (log1p (- (log1p (exp x)) (* y x))))))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes141.0ms

Accuracy

97.7% (0.0b remaining)

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

bsearch47.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.8s	2508×	body	10240	exit
989.0ms	8385×	body	80	valid
141.0ms	259×	body	640	valid
122.0ms	133×	body	1280	valid
60.0ms	179×	body	320	valid
21.0ms	95×	body	160	valid