Details

sample394.0ms

Algorithm: halfpoints

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
8	2293
7	1238
6	470
5	194
4	122
3	78
2	46
1	30
0	16

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.8b

localize92.0ms

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))
57.8b	(- (exp x) (exp (- x)))

rewrite120.0ms

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:

10.0ms	(+ (exp x) (exp (- x)))
42.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
42.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
23.0ms	(- (exp x) (exp (- x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
61.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
89.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
40.0ms	(- (exp x) (exp (- x)))

simplify3.3s

Counts

138 → 138

Iterations

Iter	Nodes
3	5525
2	1754
1	580
0	232

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize129.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
35×	`associate-l`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`times-frac`
21×	`add-cbrt-cube` `add-exp-log`
15×	`pow1`
10×	`associate-r`
8×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 120

Calls

4 calls:

11.0ms	(* x (+ 2 (* 1/3 (* x x))))
41.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
12.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ 2 (* 1/3 (* x x))))) 2) (sin y))
17.0ms	(* 1/3 (* x x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* x (+ 2 (* 1/3 (* x x))))
60.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
97.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ 2 (* 1/3 (* x x))))) 2) (sin y))
32.0ms	(* 1/3 (* x x))

simplify671.0ms

Counts

132 → 132

Iterations

Iter	Nodes
2	2214
1	618
0	236

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
33×	`associate-l`
29×	`*-un-lft-identity`
28×	`add-cbrt-cube` `add-exp-log`
23×	`times-frac` `add-cube-cbrt`
22×	`pow1`
13×	`prod-exp` `cbrt-unprod`
11×	`pow-prod-down`
10×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 119

Calls

4 calls:

66.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
63.0ms	(* (* 1/3 (* x x)) x)
18.0ms	(* (/ (fma 1/60 (pow x 5) (+ (* 2 x) (* (* 1/3 (* x x)) x))) 2) (sin y))
13.0ms	(* 1/3 (* x x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
43.0ms	(* (* 1/3 (* x x)) x)
127.0ms	(* (/ (fma 1/60 (pow x 5) (+ (* 2 x) (* (* 1/3 (* x x)) x))) 2) (sin y))
32.0ms	(* 1/3 (* x x))

simplify5.5s

Counts

131 → 131

Iterations

Iter	Nodes
3	7212
2	1939
1	565
0	222

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize168.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (* (* x x) (* x (* x x))))
0.1b	(* x (* x x))
0.2b	(/ (fma x (fma (* 1/3 x) x 2) (* 1/60 (* (* x x) (* x (* x x))))) (/ 2 (sin y)))
0.3b	(* 1/3 x)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
53×	`add-sqr-sqrt`
50×	`*-un-lft-identity` `add-cube-cbrt`
49×	`pow1`
45×	`add-cbrt-cube` `add-exp-log`
26×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`associate-/r*`
9×	`associate-l`
5×	`associate-r` `pow-prod-up` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `-commutative` `associate-/l`
2×	`unswap-sqr`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `associate-/r/` `pow-sqr`

Counts

4 → 157

Calls

4 calls:

137.0ms	(* 1/60 (* (* x x) (* x (* x x))))
29.0ms	(* x (* x x))
15.0ms	(/ (fma x (fma (* 1/3 x) x 2) (* 1/60 (* (* x x) (* x (* x x))))) (/ 2 (sin y)))
12.0ms	(* 1/3 x)

series279.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* 1/60 (* (* x x) (* x (* x x))))
63.0ms	(* x (* x x))
122.0ms	(/ (fma x (fma (* 1/3 x) x 2) (* 1/60 (* (* x x) (* x (* x x))))) (/ 2 (sin y)))
27.0ms	(* 1/3 x)

simplify4.3s

Counts

169 → 169

Iterations

Iter	Nodes
3	7894
2	1868
1	666
0	276

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	25

end0.0ms

sample12.3s

Algorithm: halfpoints