Details

sample784.0ms

Algorithm

intervals

Results

507.0ms	282×	body	80	nan
33.0ms	157×	body	80	valid
29.0ms	38×	body	640	valid
28.0ms	26×	body	1280	valid
19.0ms	20×	body	1280	nan
18.0ms	24×	body	320	valid
14.0ms	17×	body	640	nan
13.0ms	17×	body	320	nan
4.0ms	11×	body	160	valid
1.0ms	3×	body	160	nan

simplify447.0ms

Calls

1 calls:

Slowest

446.0ms

(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize61.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b	(* (sqrt 2) t)
0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `sqrt-div` `insert-posit16`
3×	`flip3--` `associate-l` `flip--`
2×	`associate--l+` `associate-/r/`
1×	`distribute-rgt-in` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `diff-log` `div-exp` `-commutative` `div-inv` `associate-/l`

Calls

4 calls:

Slowest

20.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
18.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
13.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
4.0ms	(* (sqrt 2) t)

series1.3s

Calls

4 calls:

Slowest

825.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
259.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
158.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
23.0ms	(* (sqrt 2) t)

simplify9.4s

Calls

46 calls:

Slowest

442.0ms	(- (+ (* 2 (/ t (* (sqrt 2) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x))))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
374.0ms	(sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
367.0ms	(sqrt (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
356.0ms	(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
338.0ms	(/ (sqrt 2) (sqrt (* (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))))

prune989.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
0.8b	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.5b	(* (sqrt 2) t)
0.1b	(/ (* l 2) (/ x l))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r/` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`distribute-rgt-in` `pow1` `associate-+r+` `associate-/r*` `distribute-lft-in` `flip3-+` `times-frac` `sqrt-div` `frac-add` `flip-+` `insert-posit16`
3×	`associate-l` `sqrt-prod` `div-inv`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `pow1/2` `div-exp` `associate-/r/` `-commutative` `associate-/l`

Calls

4 calls:

Slowest

20.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
12.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
4.0ms	(/ (* l 2) (/ x l))
3.0ms	(* (sqrt 2) t)

series295.0ms

Calls

4 calls:

Slowest

226.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
36.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
21.0ms	(* (sqrt 2) t)
12.0ms	(/ (* l 2) (/ x l))

simplify3.9s

Calls

45 calls:

Slowest

368.0ms	(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
348.0ms	(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
331.0ms	(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
257.0ms	(sqrt (- (* (/ (* l 2) (/ x l)) (/ (* l 2) (/ x l))) (* (* t (* t (+ 2 (/ 4 x)))) (* t (* t (+ 2 (/ 4 x)))))))
218.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

localize26.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
0.8b	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.2b	(* (cbrt (sqrt 2)) t)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/`
7×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-cube-cbrt`
6×	`add-log-exp`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `sqrt-div` `frac-add` `flip-+` `insert-posit16`
3×	`cbrt-prod` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow1/2` `associate-r`

Calls

4 calls:

Slowest

31.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
16.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
14.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
3.0ms	(* (cbrt (sqrt 2)) t)

series746.0ms

Calls

4 calls:

Slowest

444.0ms	(* (cbrt (sqrt 2)) t)
222.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
41.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
39.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify4.4s

Calls

41 calls:

Slowest

450.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
381.0ms	(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
347.0ms	(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
342.0ms	(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
281.0ms	(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
0.8b	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.4b	(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log`
18×	`add-cbrt-cube` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-*r/`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `sqrt-div` `frac-add` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-r` `associate-l` `*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow1/2`

Calls

4 calls:

Slowest

71.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
22.0ms	(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
8.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
7.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))

series755.0ms

Calls

4 calls:

Slowest

446.0ms	(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
225.0ms	(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
47.0ms	(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
37.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

simplify10.0s

Calls

56 calls:

Slowest

627.0ms	(+ (* (* l 2) (- 2 (/ 4 x))) (* (/ x l) (* t (* t (- (* 2 2) (* (/ 4 x) (/ 4 x)))))))
578.0ms	(* (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (* (* (cbrt (cbrt (sqrt 2))) t) (* (cbrt (cbrt (sqrt 2))) t)) (* (cbrt (cbrt (sqrt 2))) t)))
542.0ms	(* (* (sqrt 2) (sqrt 2)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (* (cbrt (cbrt (sqrt 2))) t) (* (cbrt (cbrt (sqrt 2))) t)) (* (cbrt (cbrt (sqrt 2))) t))))
349.0ms	(+ (log (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (log (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))))
343.0ms	(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.6b

regimes883.0ms

Accuracy

72% (7.1b remaining)

Error of 9.2b against oracle of 2.2b and baseline of 27.5b

bsearch1.3s

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.1s	10027×	body	80	nan
1.4s	836×	body	1280	valid
1.3s	1043×	body	640	valid
1.1s	5105×	body	80	valid
1.1s	621×	body	1280	nan
472.0ms	553×	body	640	nan
397.0ms	644×	body	320	valid
240.0ms	333×	body	320	nan
138.0ms	372×	body	160	valid
87.0ms	188×	body	160	nan