Details

sample241.0ms

Algorithm

intervals

Results

77.0ms	323×	body	80	nan
14.0ms	30×	body	1280	valid
14.0ms	162×	body	80	valid
11.0ms	34×	body	640	valid
8.0ms	17×	body	1280	nan
5.0ms	17×	body	640	nan
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid
2.0ms	5×	body	320	nan
1.0ms	8×	body	160	nan

simplify1.5s

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
10.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

88.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms	(* (sqrt 2.0) t)
46.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
80.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

661.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
74.0ms	(* (sqrt 2.0) t)
324.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.1s

Counts: 92 → 92

prune511.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.9b	(/ (pow l 2) x)
7.1b	(/ (pow t 2) x)
23.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

20.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
12.0ms	(/ (pow l 2) x)
14.0ms	(/ (pow t 2) x)
19.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
35.0ms	(/ (pow l 2) x)
41.0ms	(/ (pow t 2) x)
238.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify1.0s

Counts: 142 → 142

prune628.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
7.1b	(/ (pow t 2) x)
23.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `add-cbrt-cube` `associate-/l`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`associate-+r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

16.0ms	(* (sqrt 2.0) t)
29.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.0ms	(/ (pow t 2) x)
26.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sqrt 2.0) t)
89.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
31.0ms	(/ (pow t 2) x)
218.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify1.1s

Counts: 115 → 115

prune589.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
7.1b	(/ (pow t 2) x)
23.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`associate-r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+r+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 103

Calls

4 calls:

71.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
25.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.0ms	(/ (pow t 2) x)
27.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
107.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
33.0ms	(/ (pow t 2) x)
269.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify1.0s

Counts: 115 → 115

prune598.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

regimes697.0ms

Accuracy

77.7% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.0b

bsearch371.0ms

Steps

Iters	Range		Point
7	2.9198617186330072e+93	4.599804381208895e+95	6.11971881621691e+94
8	-1.618056145580231e+71	-2.1293241434994903e+67	-1.4042907669751023e+70

simplify656.0ms

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.2s	10293×	body	80	nan
709.0ms	5071×	body	80	valid
633.0ms	1041×	body	640	valid
584.0ms	848×	body	1280	valid
532.0ms	329×	body	320	nan
392.0ms	605×	body	1280	nan
387.0ms	679×	body	320	valid
324.0ms	583×	body	640	nan
176.0ms	361×	body	160	valid
33.0ms	160×	body	160	nan