Details

sample118.0ms

Algorithm

intervals

Results

35.0ms	79×	body	10240	exit
34.0ms	67×	body	1280	valid
21.0ms	57×	body	640	valid
7.0ms	92×	body	80	valid
7.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid

simplify35.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

35.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize14.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
10×	`difference-of-squares`
9×	`prod-diff`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `expm1-def` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 80

Calls

2 calls:

Slowest

13.0ms	(/ (exp x) (- (exp x) 1))
9.0ms	(- (exp x) 1)

series58.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

38.0ms	(/ (exp x) (- (exp x) 1))
20.0ms	(- (exp x) 1)

simplify2.3s

Counts

88 → 86

Calls

88 calls:

Slowest

274.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
248.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
86.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))
79.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
74.0ms	(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (sqrt 1) (sqrt 1))))

prune587.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ (exp x) (expm1 x))

rewrite10.0ms

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`

Counts

1 → 30

Calls

1 calls:

Slowest

9.0ms

(/ (exp x) (expm1 x))

series31.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

31.0ms

(/ (exp x) (expm1 x))

simplify1.1s

Counts

28 → 33

Calls

28 calls:

Slowest

849.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
30.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
23.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
17.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)

prune305.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

1.0ms

(fma x 1/12 (+ 1/2 (/ 1 x)))

series29.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

29.0ms

(fma x 1/12 (+ 1/2 (/ 1 x)))

simplify99.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

41.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
29.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
28.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune92.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(* x 1/12)
0.0b	(+ (* x 1/12) (+ 1/2 (/ 1 x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

Slowest

31.0ms	(+ (* x 1/12) (+ 1/2 (/ 1 x)))
5.0ms	(* x 1/12)

series42.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

23.0ms	(+ (* x 1/12) (+ 1/2 (/ 1 x)))
19.0ms	(* x 1/12)

simplify1.0s

Counts

18 → 44

Calls

18 calls:

Slowest

434.0ms	(* (exp (* x 1/12)) (* (exp 1/2) (exp (/ 1 x))))
275.0ms	(* (exp (* x 1/12)) (exp (+ 1/2 (/ 1 x))))
155.0ms	(* (* (* x x) x) (* (* 1/12 1/12) 1/12))
48.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
42.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune295.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes23.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2569×	body	10240	exit
1.0s	2243×	body	1280	valid
603.0ms	1701×	body	640	valid
166.0ms	838×	body	320	valid
165.0ms	2844×	body	80	valid
63.0ms	374×	body	160	valid