Details

sample103.0ms

Algorithm

intervals

Results

31.0ms	82×	body	10240	exit
25.0ms	55×	body	1280	valid
21.0ms	64×	body	640	valid
7.0ms	32×	body	320	valid
6.0ms	88×	body	80	valid
2.0ms	17×	body	160	valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize11.0ms

Local error

Found 2 expressions with local error:

4.1b	(- (exp x) 1)
0.0b	(/ (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)

series73.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

48.0ms	(/ (exp x) (- (exp x) 1))
24.0ms	(- (exp x) 1)

simplify2.2s

Counts

88 → 86

Calls

88 calls:

Slowest

270.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
245.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
73.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))
66.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
60.0ms	(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))

prune593.0ms

Pruning

2 alts after pruning (2 fresh and 0 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

1.0ms

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

series26.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

26.0ms

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

simplify135.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

50.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
45.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
38.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune85.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

25.9b	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
0.2b	(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
0.1b	(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
0.0b	(/ (exp x) (expm1 x))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
59×	`times-frac` `add-cbrt-cube`
47×	`*-un-lft-identity` `add-cube-cbrt`
41×	`add-exp-log`
26×	`associate-l`
25×	`pow1`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
14×	`associate-r`
13×	`swap-sqr`
11×	`frac-times` `associate-*r/`
7×	`cbrt-div` `associate-*l/`
6×	`pow-prod-up` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow2` `pow-plus` `cube-unmult` `pow-sqr` `*-commutative`
1×	`cbrt-prod` `clear-num` `frac-2neg` `pow1/3` `rem-cbrt-cube`

Counts

4 → 181

Calls

4 calls:

Slowest

72.0ms	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
44.0ms	(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
31.0ms	(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
11.0ms	(/ (exp x) (expm1 x))

series272.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))))
80.0ms	(* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))
46.0ms	(/ (exp x) (expm1 x))
30.0ms	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))

simplify15.3s

Counts

180 → 193

Calls

180 calls:

Slowest

806.0ms	(* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
628.0ms	(* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x))) (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x)))))
541.0ms	(* (/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x))) (* (/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x))) (* (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x))) (/ (exp x) (expm1 x)))))
505.0ms	(+ (- x (log (expm1 x))) (+ (- x (log (expm1 x))) (log (/ (exp x) (expm1 x)))))
489.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

99% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 21.2b

bsearch36.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	2188×	body	1280	valid
1.1s	2570×	body	10240	exit
520.0ms	1682×	body	640	valid
212.0ms	2849×	body	80	valid
162.0ms	853×	body	320	valid
50.0ms	428×	body	160	valid