Details

sample503.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize83.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
58.1b	(- (exp x) (exp (- x)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 108

Calls

3 calls:

39.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
36.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
12.0ms	(- (exp x) (exp (- x)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
80.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1726
1	545
0	217

prune661.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize106.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

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:

56.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
48.0ms	(* x (+ (* 1/3 (* x x)) 2))
12.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ (* 1/3 (* x x)) 2))) 2) (sin y))
14.0ms	(* 1/3 (* x x))

series378.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
133.0ms	(* x (+ (* 1/3 (* x x)) 2))
133.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ (* 1/3 (* x x)) 2))) 2) (sin y))
34.0ms	(* 1/3 (* x x))

simplify1.8s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	2379
1	645
0	236

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

35×	`associate-l`
34×	`add-sqr-sqrt`
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`
8×	`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:

71.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
52.0ms	(* x (* 1/3 (* x x)))
19.0ms	(* (/ (fma (pow x 5) 1/60 (+ (* x (* 1/3 (* x x))) (* x 2))) 2) (sin y))
18.0ms	(* 1/3 (* x x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
45.0ms	(* x (* 1/3 (* x x)))
132.0ms	(* (/ (fma (pow x 5) 1/60 (+ (* x (* 1/3 (* x x))) (* x 2))) 2) (sin y))
36.0ms	(* 1/3 (* x x))

simplify1.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1949
1	553
0	221

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-l`
6×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `unpow-prod-down` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 142

Calls

4 calls:

0.0ms	(fma (* x x) 1/3 2)
15.0ms	(* (pow x 5) 1/60)
9.0ms	(/ 2 (sin y))
22.0ms	(/ (fma (fma (* x x) 1/3 2) x (* (pow x 5) 1/60)) (/ 2 (sin y)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma (* x x) 1/3 2)
107.0ms	(* (pow x 5) 1/60)
27.0ms	(/ 2 (sin y))
103.0ms	(/ (fma (fma (* x x) 1/3 2) x (* (pow x 5) 1/60)) (/ 2 (sin y)))

simplify1.8s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	1770
1	574
0	247

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes223.0ms

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	32
1	32
0	25

end0.0ms

sample12.4s

Algorithm: halfpoints