Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	71×	body	1280	valid
22.0ms	85×	body	10240	exit
11.0ms	54×	body	640	valid
4.0ms	93×	body	80	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid

simplify10.0ms

Calls

1 calls:

Slowest

10.0ms

(/ (exp x) (- (exp x) 1))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize7.0ms

Local error

Found 2 expressions with local error:

3.9b	(- (exp x) 1)
0.3b	(/ (exp x) (- (exp x) 1))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
5×	`difference-of-sqr-1`
4×	`associate-/r*` `add-cbrt-cube`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
1×	`cbrt-undiv` `expm1-def` `clear-num` `sub-neg` `frac-2neg` `div-exp` `div-inv`

Calls

2 calls:

Slowest

11.0ms	(/ (exp x) (- (exp x) 1))
4.0ms	(- (exp x) 1)

series41.0ms

Calls

2 calls:

Slowest

23.0ms	(/ (exp x) (- (exp x) 1))
18.0ms	(- (exp x) 1)

simplify1.2s

Calls

43 calls:

Slowest

384.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
184.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
68.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
43.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
39.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune457.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (exp x) (expm1 x))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Calls

1 calls:

Slowest

4.0ms

(/ (exp x) (expm1 x))

series21.0ms

Calls

1 calls:

Slowest

21.0ms

(/ (exp x) (expm1 x))

simplify478.0ms

Calls

28 calls:

Slowest

209.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
29.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
28.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
21.0ms	(/ (exp x) (- (exp x) 1))

prune308.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

2.0b	(expm1 (log1p (/ (exp x) (expm1 x))))
0.3b	(/ (exp x) (expm1 x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube`
3×	`associate-/r` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `div-inv` `expm1-udef`

Calls

2 calls:

Slowest

8.0ms	(/ (exp x) (expm1 x))
0.0ms	(expm1 (log1p (/ (exp x) (expm1 x))))

series186.0ms

Calls

2 calls:

Slowest

155.0ms	(expm1 (log1p (/ (exp x) (expm1 x))))
31.0ms	(/ (exp x) (expm1 x))

simplify766.0ms

Calls

32 calls:

Slowest

257.0ms	(- (+ (* 3/2 (* x (exp (- (log x))))) (+ (* 1/12 (* (pow x 2) (exp (- (log x))))) (exp (- (log x))))) 1)
178.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
32.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
20.0ms	(/ (exp x) (- (exp x) 1))

prune427.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x 1/12 1/2)
0.0b	(+ (/ 1 x) (fma x 1/12 1/2))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

4.0ms	(+ (/ 1 x) (fma x 1/12 1/2))
0.0ms	(fma x 1/12 1/2)

series29.0ms

Calls

2 calls:

Slowest

18.0ms	(fma x 1/12 1/2)
11.0ms	(+ (/ 1 x) (fma x 1/12 1/2))

simplify297.0ms

Calls

11 calls:

Slowest

72.0ms	(* (exp (/ 1 x)) (exp (fma x 1/12 1/2)))
41.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
40.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
38.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
34.0ms	(+ (/ 1 x) (fma x 1/12 1/2))

prune255.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes41.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 23.2b

bsearch33.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2582×	body	10240	exit
1.1s	2225×	body	1280	valid
506.0ms	1685×	body	640	valid
182.0ms	2855×	body	80	valid
154.0ms	821×	body	320	valid
49.0ms	418×	body	160	valid