Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	82×	body	1280	valid
18.0ms	85×	body	10240	exit
9.0ms	50×	body	640	valid
4.0ms	92×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify9.0ms

Calls

1 calls:

Slowest

9.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize8.0ms

Local error

Found 2 expressions with local error:

3.5b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

19.0ms	(/ (exp x) (- (exp x) 1))
4.0ms	(- (exp x) 1)

series40.0ms

Calls

2 calls:

Slowest

26.0ms	(/ (exp x) (- (exp x) 1))
15.0ms	(- (exp x) 1)

simplify882.0ms

Calls

41 calls:

Slowest

262.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
145.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
42.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
35.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
22.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune413.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b	(+ (/ 1 x) 1/2)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `sum-log` `*-commutative`

Calls

3 calls:

Slowest

10.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
4.0ms	(+ (/ 1 x) 1/2)
0.0ms	(* 1/12 x)

series48.0ms

Calls

3 calls:

Slowest

18.0ms	(* 1/12 x)
15.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
14.0ms	(+ (/ 1 x) 1/2)

simplify231.0ms

Calls

10 calls:

Slowest

63.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
40.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
34.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
34.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
18.0ms	(+ (/ 1 x) 1/2)

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize1.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b	(+ (/ 1 x) 1/2)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `sum-log` `*-commutative`

Calls

3 calls:

Slowest

14.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
7.0ms	(+ (/ 1 x) 1/2)
0.0ms	(* 1/12 x)

series67.0ms

Calls

3 calls:

Slowest

24.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
23.0ms	(* 1/12 x)
20.0ms	(+ (/ 1 x) 1/2)

simplify237.0ms

Calls

10 calls:

Slowest

82.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
35.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
35.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
34.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
12.0ms	(+ (/ 1 x) 1/2)

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (* (exp x) (exp x)) (* 1 1))
0.5b	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
0.5b	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
0.0b	(* (exp x) (exp x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
21×	`associate-l`
13×	`add-cbrt-cube`
11×	`pow1`
9×	`add-exp-log`
8×	`difference-of-squares`
6×	`associate-r` `add-log-exp`
4×	`associate-/r*` `associate-/r/` `insert-posit16`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `associate-*l/` `pow-prod-up`

Calls

4 calls:

Slowest

31.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
16.0ms	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
11.0ms	(- (* (exp x) (exp x)) (* 1 1))
7.0ms	(* (exp x) (exp x))

series217.0ms

Calls

4 calls:

Slowest

83.0ms	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
75.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
40.0ms	(- (* (exp x) (exp x)) (* 1 1))
20.0ms	(* (exp x) (exp x))

simplify7.6s

Calls

94 calls:

Slowest

765.0ms	(* (- (* (exp x) (exp x)) (* 1 1)) (- (exp x) 1))
479.0ms	(* 1 (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))))
425.0ms	(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))
418.0ms	(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))
390.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))

prune960.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes176.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.2b

bsearch7.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	2270×	body	1280	valid
920.0ms	2533×	body	10240	exit
535.0ms	1700×	body	640	valid
160.0ms	2850×	body	80	valid
146.0ms	783×	body	320	valid
48.0ms	397×	body	160	valid