Details

sample380.0ms

Algorithm: halfpoints

simplify935.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	935
5	233
4	120
3	84
2	48
1	30
0	16

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.2b

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))
58.2b	(- (exp x) (exp (- x)))

rewrite101.0ms

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)))
38.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
41.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
11.0ms	(- (exp x) (exp (- x)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (exp x) (exp (- x)))
64.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
85.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
44.0ms	(- (exp x) (exp (- x)))

simplify1.4s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2209
1	516
0	200

prune764.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize124.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-exp-log`
25×	`add-cbrt-cube`
20×	`pow1` `associate-l`
17×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-r` `prod-exp`
12×	`cbrt-unprod`
10×	`times-frac` `pow-prod-down`
6×	`unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `div-exp` `associate-*l/` `pow-exp` `div-inv`

Counts

4 → 101

Calls

4 calls:

18.0ms	(* 1/60 (pow x 5))
68.0ms	(* (* 1/3 (* x x)) x)
77.0ms	(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) 2) (sin y))
27.0ms	(* 1/3 (* x x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* 1/60 (pow x 5))
52.0ms	(* (* 1/3 (* x x)) x)
121.0ms	(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) 2) (sin y))
49.0ms	(* 1/3 (* x x))

simplify2.0s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	2741
1	472
0	180

prune991.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize155.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y))
0.4b	(* (/ 1 (sqrt 2)) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y)))
0.5b	(/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2))
1.0b	(/ 1 (sqrt 2))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `insert-posit16` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 186

Calls

4 calls:

66.0ms	(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y))
80.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y)))
119.0ms	(/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2))
11.0ms	(/ 1 (sqrt 2))

series631.0ms

Counts

4 → 10

Calls

4 calls:

180.0ms	(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y))
268.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2)) (sin y)))
183.0ms	(/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt 2))
0.0ms	(/ 1 (sqrt 2))

simplify3.3s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
2	4630
1	735
0	259

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize150.0ms

Local error

Found 4 expressions with local error:

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

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

276×	`add-exp-log`
152×	`prod-exp`
94×	`add-cbrt-cube`
90×	`times-frac`
84×	`sqrt-prod`
80×	`div-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
53×	`associate-l`
44×	`cbrt-unprod`
30×	`rec-exp` `1-exp`
24×	`cbrt-undiv`
23×	`pow1`
15×	`associate-/r*`
10×	`associate-*l/`
9×	`pow-prod-down`
8×	`pow-flip`
6×	`frac-times` `associate-r/` `associate-/l`
5×	`sqrt-pow1`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`pow1/2`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative` `inv-pow`

Counts

4 → 278

Calls

4 calls:

117.0ms	(* (/ 1 (sqrt (sqrt 2))) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt (sqrt 2))) (sin y)))
341.0ms	(* (/ 1 (sqrt 2)) (* (/ 1 (sqrt (sqrt 2))) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt (sqrt 2))) (sin y))))
5.0ms	(/ 1 (sqrt 2))
6.0ms	(/ 1 (sqrt (sqrt 2)))

series575.0ms

Counts

4 → 8

Calls

4 calls:

218.0ms	(* (/ 1 (sqrt (sqrt 2))) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt (sqrt 2))) (sin y)))
357.0ms	(* (/ 1 (sqrt 2)) (* (/ 1 (sqrt (sqrt 2))) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* (* 1/3 (* x x)) x))) (sqrt (sqrt 2))) (sin y))))
0.0ms	(/ 1 (sqrt 2))
0.0ms	(/ 1 (sqrt (sqrt 2)))

simplify2.2s

Counts

286 → 286

Iterations

Iter	Nodes
done	5001
1	1093
0	337

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes186.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample12.0s

Algorithm: halfpoints