Details

sample98.0ms

Algorithm

intervals

Results

28.0ms	82×	body	10240	exit
25.0ms	55×	body	1280	valid
19.0ms	64×	body	640	valid
6.0ms	32×	body	320	valid
5.0ms	88×	body	80	valid
2.0ms	17×	body	160	valid

simplify18.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

18.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

31.0ms	(/ (exp x) (- (exp x) 1))
8.0ms	(- (exp x) 1)

series58.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

42.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify1.9s

Counts

68 → 69

Calls

68 calls:

Slowest

425.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
258.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
78.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
58.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune489.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

Slowest

24.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
9.0ms	(* 1/12 x)

series49.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

30.0ms	(* 1/12 x)
18.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify1.0s

Counts

17 → 39

Calls

17 calls:

Slowest

395.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
324.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
185.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
31.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune274.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

16.0ms	(/ (exp x) (- (exp x) 1))
8.0ms	(- (exp x) 1)

series53.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

37.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify1.8s

Counts

68 → 69

Calls

68 calls:

Slowest

440.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
269.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
75.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
45.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
44.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))

prune532.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

37.8b	(cbrt (* (* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
0.4b	(* 1/12 x)
0.4b	(* 1/12 x)
0.4b	(* 1/12 x)

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

28×	`frac-times`
27×	`flip3-+` `flip-+`
26×	`cbrt-div`
16×	`add-sqr-sqrt`
14×	`associate-*l/`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 94

Calls

4 calls:

Slowest

282.0ms	(cbrt (* (* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
6.0ms	(* 1/12 x)
5.0ms	(* 1/12 x)
5.0ms	(* 1/12 x)

series102.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

29.0ms	(cbrt (* (* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
28.0ms	(* 1/12 x)
26.0ms	(* 1/12 x)
18.0ms	(* 1/12 x)

simplify14.0s

Counts

67 → 106

Calls

67 calls:

Slowest

868.0ms	(cbrt (* (* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))))
823.0ms	(cbrt (* (* (- (* (* 1/12 x) (* 1/12 x)) (* (+ (/ 1 x) 1/2) (+ (/ 1 x) 1/2))) (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))))
751.0ms	(cbrt (* (* (- (* (* 1/12 x) (* 1/12 x)) (* (+ (/ 1 x) 1/2) (+ (/ 1 x) 1/2))) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))))
697.0ms	(cbrt (* (* (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3)) (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))))
662.0ms	(cbrt (* (* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (pow (* 1/12 x) 3) (pow (+ (/ 1 x) 1/2) 3))) (- (* (* 1/12 x) (* 1/12 x)) (* (+ (/ 1 x) 1/2) (+ (/ 1 x) 1/2)))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes97.0ms

Accuracy

99% (0.2b remaining)

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

bsearch32.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	2188×	body	1280	valid
1.0s	2570×	body	10240	exit
498.0ms	1682×	body	640	valid
198.0ms	853×	body	320	valid
162.0ms	2849×	body	80	valid
53.0ms	428×	body	160	valid