Details

sample96.0ms

Algorithm

intervals

Results

34.0ms	67×	body	1280	valid
30.0ms	57×	body	640	valid
12.0ms	172×	body	80	valid
7.0ms	28×	body	320	valid
2.0ms	13×	body	160	valid

simplify34.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

34.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (expm1 x) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 31

Calls

1 calls:

Slowest

4.0ms

(/ (expm1 x) x)

series50.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

50.0ms

(/ (expm1 x) x)

simplify851.0ms

Counts

28 → 34

Calls

28 calls:

Slowest

469.0ms	(/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* x x) x))
125.0ms	(* -1 (/ (- 1 (exp x)) x))
66.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
41.0ms	(/ (* (cbrt (expm1 x)) (cbrt (expm1 x))) (* (cbrt x) (cbrt x)))
30.0ms	(/ (- (exp x) 1) x)

prune289.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (log1p (/ (expm1 x) x)))
0.0b	(/ (expm1 x) x)
0.0b	(log1p (/ (expm1 x) x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

Slowest

8.0ms	(/ (expm1 x) x)
1.0ms	(log1p (/ (expm1 x) x))
1.0ms	(expm1 (log1p (/ (expm1 x) x)))

series780.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

661.0ms	(expm1 (log1p (/ (expm1 x) x)))
67.0ms	(log1p (/ (expm1 x) x))
52.0ms	(/ (expm1 x) x)

simplify2.3s

Counts

36 → 64

Calls

36 calls:

Slowest

572.0ms	(- (+ (/ (exp x) x) (+ (/ (exp x) (pow x 2)) (+ (* 1/3 (/ (pow (exp x) 3) (pow x 3))) (/ (exp x) (pow x 3))))) (+ (/ (pow (exp x) 2) (pow x 3)) (+ (* 1/2 (/ 1 (pow x 2))) (+ (* 1/2 (/ (pow (exp x) 2) (pow x 2))) (+ (* 1/3 (/ 1 (pow x 3))) (/ 1 x))))))
492.0ms	(- (+ (/ (exp x) x) (+ (/ (exp x) (pow x 2)) (+ (* 1/3 (/ (pow (exp x) 3) (pow x 3))) (/ (exp x) (pow x 3))))) (+ (/ (pow (exp x) 2) (pow x 3)) (+ (* 1/2 (/ 1 (pow x 2))) (+ (* 1/2 (/ (pow (exp x) 2) (pow x 2))) (+ (* 1/3 (/ 1 (pow x 3))) (/ 1 x))))))
372.0ms	(/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* x x) x))
174.0ms	(* -1 (/ (- 1 (exp x)) x))
126.0ms	(* -1 (/ (- 1 (exp x)) x))

prune695.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (expm1 x) (/ 1 x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-r`
11×	`times-frac`
10×	`*-un-lft-identity` `add-exp-log`
9×	`add-cube-cbrt`
6×	`add-cbrt-cube`
4×	`prod-exp`
3×	`pow1` `associate-l` `unswap-sqr`
2×	`div-exp` `cbrt-unprod`
1×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

Slowest

13.0ms

(* (expm1 x) (/ 1 x))

series42.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

42.0ms

(* (expm1 x) (/ 1 x))

simplify1.3s

Counts

31 → 42

Calls

31 calls:

Slowest

393.0ms	(* (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (/ 1 x) (/ 1 x)) (/ 1 x)))
240.0ms	(* (* (* (expm1 x) (expm1 x)) (expm1 x)) (/ (* (* 1 1) 1) (* (* x x) x)))
103.0ms	(* -1 (/ (- 1 (exp x)) x))
87.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
59.0ms	(+ (log (expm1 x)) (- 0 (log x)))

prune286.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x 1/6 1/2)
0.0b	(fma x (fma x 1/6 1/2) 1)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 22

Calls

2 calls:

Slowest

0.0ms	(fma x 1/6 1/2)
0.0ms	(fma x (fma x 1/6 1/2) 1)

series69.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

35.0ms	(fma x 1/6 1/2)
34.0ms	(fma x (fma x 1/6 1/2) 1)

simplify352.0ms

Counts

6 → 28

Calls

6 calls:

Slowest

125.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
112.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
82.0ms	(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
15.0ms	(+ (* 1/6 x) 1/2)
8.0ms	(+ (* 1/6 x) 1/2)

prune226.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

994.0ms	2252×	body	1280	valid
507.0ms	1715×	body	640	valid
331.0ms	5443×	body	80	valid
153.0ms	844×	body	320	valid
78.0ms	379×	body	160	valid