Details

sample775.0ms

Algorithm: halfpoints

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
8	2000
7	1201
6	423
5	176
4	113
3	80
2	48
1	30
0	16

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize147.0ms

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))
57.5b	(- (exp x) (exp (- x)))

rewrite169.0ms

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)))
64.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
75.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
20.0ms	(- (exp x) (exp (- x)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (exp x) (exp (- x)))
98.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
115.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
54.0ms	(- (exp x) (exp (- x)))

simplify1.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	2024
3	2024
2	1811
1	516
0	200

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

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

rewrite263.0ms

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:

8.0ms	(* 1/60 (pow x 5))
36.0ms	(* x (* (* x x) 1/3))
203.0ms	(* (/ (+ (+ (+ x x) (* x (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2) (sin y))
15.0ms	(* (* x x) 1/3)

series284.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 1/60 (pow x 5))
75.0ms	(* x (* (* x x) 1/3))
114.0ms	(* (/ (+ (+ (+ x x) (* x (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2) (sin y))
30.0ms	(* (* x x) 1/3)

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	2001
3	2001
2	1407
1	439
0	182

prune2.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize175.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/3)
0.3b	(* (/ 1 (sqrt 2)) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
0.5b	(/ (sqrt 2) (sin y))
1.0b	(/ 1 (sqrt 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

215×	`times-frac`
184×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
110×	`add-cube-cbrt`
74×	`associate-r`
73×	`sqrt-prod`
54×	`add-exp-log`
34×	`add-cbrt-cube`
23×	`associate-l`
21×	`div-exp` `unswap-sqr`
15×	`prod-exp`
13×	`pow1`
11×	`cbrt-undiv`
9×	`associate-/r` `cbrt-unprod` `associate-/l`
7×	`div-inv`
4×	`rec-exp` `1-exp` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow-flip`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `associate-/r/` `inv-pow`

Counts

4 → 250

Calls

4 calls:

27.0ms	(* (* x x) 1/3)
47.0ms	(* (/ 1 (sqrt 2)) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
6.0ms	(/ (sqrt 2) (sin y))
5.0ms	(/ 1 (sqrt 2))

series397.0ms

Counts

4 → 10

Calls

4 calls:

44.0ms	(* (* x x) 1/3)
265.0ms	(* (/ 1 (sqrt 2)) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
88.0ms	(/ (sqrt 2) (sin y))
0.0ms	(/ 1 (sqrt 2))

simplify1.5s

Counts

260 → 260

Iterations

Iter	Nodes
done	2003
2	2003
1	1221
0	384

prune5.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize161.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
0.5b	(/ (sqrt 2) (sin y))
1.0b	(/ 1 (sqrt (sqrt 2)))
1.0b	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

1507×	`times-frac`
1334×	`sqrt-prod`
1069×	`add-sqr-sqrt`
690×	`*-un-lft-identity`
654×	`add-cube-cbrt`
283×	`associate-l`
92×	`unswap-sqr`
79×	`add-exp-log`
71×	`associate-r`
49×	`add-cbrt-cube`
42×	`div-exp`
40×	`associate-/l*`
31×	`div-inv`
23×	`cbrt-undiv`
21×	`associate-/r*`
20×	`pow1` `sqrt-pow1`
15×	`prod-exp`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
9×	`cbrt-unprod`
5×	`rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`inv-pow`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 930

Calls

4 calls:

61.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
6.0ms	(/ (sqrt 2) (sin y))
6.0ms	(/ 1 (sqrt (sqrt 2)))
11.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series358.0ms

Counts

4 → 8

Calls

4 calls:

303.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* (pow x 5) 1/60)) (/ (sqrt 2) (sin y))))
55.0ms	(/ (sqrt 2) (sin y))
0.0ms	(/ 1 (sqrt (sqrt 2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify1.7s

Counts

938 → 938

Iterations

Iter	Nodes
done	2000
1	2000
0	747

prune24.7s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes308.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample11.6s

Algorithm: halfpoints