Details

sample362.0ms

Algorithm: halfpoints

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	3509
8	2235
7	1201
6	423
5	176
4	113
3	80
2	48
1	30
0	16

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
58.4b	(- (exp x) (exp (- x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 103

Calls

4 calls:

9.0ms	(+ (exp x) (exp (- x)))
41.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
42.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
10.0ms	(- (exp x) (exp (- x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (exp x) (exp (- x)))
83.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
84.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify1.5s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	1811
1	516
0	200

prune743.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* 1/3 (* x x)) 2))
0.1b	(* 1/60 (pow x 5))
0.1b	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2) (sin y))
0.2b	(* 1/3 (* x x))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`associate-l`
21×	`add-exp-log`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
14×	`associate-r`
13×	`pow1`
10×	`times-frac`
9×	`prod-exp`
7×	`cbrt-unprod` `unswap-sqr`
5×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `distribute-lft-in` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

75.0ms	(* x (+ (* 1/3 (* x x)) 2))
8.0ms	(* 1/60 (pow x 5))
82.0ms	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2) (sin y))
13.0ms	(* 1/3 (* x x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* x (+ (* 1/3 (* x x)) 2))
59.0ms	(* 1/60 (pow x 5))
120.0ms	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2) (sin y))
46.0ms	(* 1/3 (* x x))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1956
1	540
0	195

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* x x))
0.2b	(* 1/3 (* x x))
0.4b	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
0.5b	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
14×	`sqrt-div` `associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
7×	`flip3-+` `sqrt-prod` `flip-+`
4×	`frac-times` `*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 95

Calls

4 calls:

27.0ms	(* 1/3 (* x x))
13.0ms	(* 1/3 (* x x))
121.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
84.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 1/3 (* x x))
32.0ms	(* 1/3 (* x x))
138.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
163.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

simplify2.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1734
1	410
0	142

prune888.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize196.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* x x))
0.3b	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2)) (sin y)))
0.4b	(/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2))
1.0b	(/ 1 (sqrt 2))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac` `add-exp-log`
49×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
34×	`add-cbrt-cube`
33×	`sqrt-prod`
25×	`associate-l`
23×	`prod-exp`
16×	`pow1`
13×	`div-exp` `cbrt-unprod`
12×	`associate-/r*`
7×	`cbrt-undiv`
6×	`pow-prod-down` `associate-/l*`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`associate-*l/` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

17.0ms	(* 1/3 (* x x))
87.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2)) (sin y)))
85.0ms	(/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2))
10.0ms	(/ 1 (sqrt 2))

series478.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* 1/3 (* x x))
278.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2)) (sin y)))
167.0ms	(/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) (sqrt 2))
0.0ms	(/ 1 (sqrt 2))

simplify2.0s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	2216
1	664
0	248

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes206.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample12.2s

Algorithm: halfpoints