Details

sample408.0ms

Algorithm: halfpoints

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4994
8	2879
7	1410
6	468
5	192
4	123
3	80
2	48
1	30
0	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize94.0ms

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))
58.5b	(- (exp x) (exp (- x)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`associate-l`
31×	`add-cube-cbrt`
29×	`times-frac`
14×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`fma-def` `fma-neg`
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 → 126

Calls

4 calls:

15.0ms	(+ (exp x) (exp (- x)))
82.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
65.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
26.0ms	(- (exp x) (exp (- x)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
86.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
106.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
46.0ms	(- (exp x) (exp (- x)))

simplify1.9s

Counts

138 → 138

Iterations

Iter	Nodes
done	5003
2	1872
1	582
0	232

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* (* 1/3 x) x) 2))
0.1b	(* (* 1/3 x) x)
0.1b	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* 1/3 x) x) 2))) 2) (sin y))
0.3b	(* 1/3 x)

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity` `add-cube-cbrt`
15×	`pow1`
12×	`associate-r`
10×	`times-frac`
7×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*r/`
1×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `flip3-+` `div-exp` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

79.0ms	(* x (+ (* (* 1/3 x) x) 2))
33.0ms	(* (* 1/3 x) x)
28.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* 1/3 x) x) 2))) 2) (sin y))
7.0ms	(* 1/3 x)

series331.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* x (+ (* (* 1/3 x) x) 2))
42.0ms	(* (* 1/3 x) x)
137.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* 1/3 x) x) 2))) 2) (sin y))
18.0ms	(* 1/3 x)

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5002
2	1540
1	456
0	173

prune987.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 x)
0.3b	(* 1/3 x)
0.4b	(* (* x (sqrt (+ (* (* 1/3 x) x) 2))) (sqrt (+ (* (* 1/3 x) x) 2)))
0.4b	(* x (sqrt (+ (* (* 1/3 x) x) 2)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`sqrt-div`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l` `associate-*r/`
7×	`flip3-+` `sqrt-prod` `flip-+`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 101

Calls

4 calls:

10.0ms	(* 1/3 x)
6.0ms	(* 1/3 x)
169.0ms	(* (* x (sqrt (+ (* (* 1/3 x) x) 2))) (sqrt (+ (* (* 1/3 x) x) 2)))
89.0ms	(* x (sqrt (+ (* (* 1/3 x) x) 2)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 1/3 x)
21.0ms	(* 1/3 x)
101.0ms	(* (* x (sqrt (+ (* (* 1/3 x) x) 2))) (sqrt (+ (* (* 1/3 x) x) 2)))
166.0ms	(* x (sqrt (+ (* (* 1/3 x) x) 2)))

simplify3.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
3	4959
2	1363
1	388
0	145

prune966.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

353×	`times-frac`
257×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
184×	`add-cube-cbrt`
109×	`sqrt-prod`
71×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube`
31×	`associate-/r*`
24×	`div-exp`
22×	`associate-l`
20×	`unswap-sqr`
14×	`cbrt-undiv`
12×	`prod-exp` `div-inv` `associate-/l*`
8×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-flip`
2×	`associate-/r/`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow`

Counts

4 → 345

Calls

4 calls:

13.0ms	(/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (/ (sqrt 2) (sin y)))
67.0ms	(* (/ 1 (sqrt 2)) (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (/ (sqrt 2) (sin y))))
19.0ms	(/ (sqrt 2) (sin y))
7.0ms	(/ 1 (sqrt 2))

series550.0ms

Counts

4 → 10

Calls

4 calls:

195.0ms	(/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (/ (sqrt 2) (sin y)))
296.0ms	(* (/ 1 (sqrt 2)) (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (/ (sqrt 2) (sin y))))
59.0ms	(/ (sqrt 2) (sin y))
0.0ms	(/ 1 (sqrt 2))

simplify2.8s

Counts

355 → 355

Iterations

Iter	Nodes
done	5001
2	4053
1	1340
0	437

prune3.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes247.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample12.4s

Algorithm: halfpoints