Details

sample100.0ms

Algorithm

intervals

Results

33.0ms	84×	body	1280	valid
30.0ms	87×	body	10240	exit
15.0ms	54×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	80×	body	80	valid
2.0ms	13×	body	160	valid

simplify28.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

28.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize16.0ms

Local error

Found 2 expressions with local error:

4.2b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite64.0ms

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

39.0ms	(- (exp x) 1)
23.0ms	(/ (exp x) (- (exp x) 1))

series43.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

27.0ms	(/ (exp x) (- (exp x) 1))
15.0ms	(- (exp x) 1)

simplify4.4s

Counts

121 → 86

Calls

121 calls:

Slowest

383.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1 3)))
309.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
270.0ms	(* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1))
235.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
186.0ms	(* (* (/ (exp x) (- (exp x) 1)) (/ (exp x) (- (exp x) 1))) (/ (exp x) (- (exp x) 1)))

prune639.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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

12.0ms

(/ (exp x) (expm1 x))

series27.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

27.0ms

(/ (exp x) (expm1 x))

simplify1.1s

Counts

43 → 33

Calls

43 calls:

Slowest

385.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
251.0ms	(* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x)))
46.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
29.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
27.0ms	(/ (exp x) (- (exp x) 1))

prune247.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (expm1 x) (exp x))
0.0b	(/ 1 (/ (expm1 x) (exp x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 110

Calls

2 calls:

Slowest

16.0ms	(/ 1 (/ (expm1 x) (exp x)))
15.0ms	(/ (expm1 x) (exp x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

29.0ms	(/ (expm1 x) (exp x))
28.0ms	(/ 1 (/ (expm1 x) (exp x)))

simplify7.9s

Counts

166 → 116

Calls

166 calls:

Slowest

469.0ms	(/ (* (* 1 1) 1) (* (* (/ (expm1 x) (exp x)) (/ (expm1 x) (exp x))) (/ (expm1 x) (exp x))))
437.0ms	(* (* (/ 1 (/ (expm1 x) (exp x))) (/ 1 (/ (expm1 x) (exp x)))) (/ 1 (/ (expm1 x) (exp x))))
435.0ms	(/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (exp x) (exp x)) (exp x)))
365.0ms	(- (+ x (* 1/6 (pow x 3))) (* 1/2 (pow x 2)))
261.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (expm1 x)) (cbrt (expm1 x))) (* (cbrt (exp x)) (cbrt (exp x)))))

prune883.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

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

0.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

32.0ms

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

simplify778.0ms

Counts

14 → 14

Calls

14 calls:

Slowest

287.0ms	(* (* (fma x 1/12 (+ 1/2 (/ 1 x))) (fma x 1/12 (+ 1/2 (/ 1 x)))) (fma x 1/12 (+ 1/2 (/ 1 x))))
128.0ms	(exp (fma x 1/12 (+ 1/2 (/ 1 x))))
45.0ms	(cbrt (fma x 1/12 (+ 1/2 (/ 1 x))))
44.0ms	(sqrt (fma x 1/12 (+ 1/2 (/ 1 x))))
36.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune106.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2286×	body	1280	valid
1.2s	2561×	body	10240	exit
518.0ms	1695×	body	640	valid
299.0ms	2833×	body	80	valid
163.0ms	779×	body	320	valid
53.0ms	409×	body	160	valid