Details

sample476.0ms

Algorithm: halfpoints

simplify4.4s

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize128.0ms

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)))

rewrite126.0ms

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:

48.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
53.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
23.0ms	(- (exp x) (exp (- x)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
128.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
62.0ms	(- (exp x) (exp (- x)))

simplify1.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1726
1	545
0	217

prune782.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize126.0ms

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))

rewrite141.0ms

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:

45.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
47.0ms	(* x (+ (* 1/3 (* x x)) 2))
21.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ (* 1/3 (* x x)) 2))) 2) (sin y))
27.0ms	(* 1/3 (* x x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
105.0ms	(* x (+ (* 1/3 (* x x)) 2))
117.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ (* 1/3 (* x x)) 2))) 2) (sin y))
37.0ms	(* 1/3 (* x x))

simplify1.9s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	2379
1	645
0	236

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize118.0ms

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

rewrite135.0ms

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:

41.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
63.0ms	(* (* 1/3 (* x x)) x)
14.0ms	(* (/ (fma (pow x 5) 1/60 (+ (* (* 1/3 (* x x)) x) (* 2 x))) 2) (sin y))
15.0ms	(* 1/3 (* x x))

series292.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
66.0ms	(* (* 1/3 (* x x)) x)
109.0ms	(* (/ (fma (pow x 5) 1/60 (+ (* (* 1/3 (* x x)) x) (* 2 x))) 2) (sin y))
49.0ms	(* 1/3 (* x x))

simplify1.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1954
1	567
0	222

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (fma (* 1/3 x) x 2))
0.1b	(/ 2 (sin y))
0.2b	(/ (fma (pow x 5) 1/60 (* x (fma (* 1/3 x) x 2))) (/ 2 (sin y)))
0.3b	(* 1/3 x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 147

Calls

4 calls:

16.0ms	(* x (fma (* 1/3 x) x 2))
9.0ms	(/ 2 (sin y))
15.0ms	(/ (fma (pow x 5) 1/60 (* x (fma (* 1/3 x) x 2))) (/ 2 (sin y)))
10.0ms	(* 1/3 x)

series326.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* x (fma (* 1/3 x) x 2))
16.0ms	(/ 2 (sin y))
164.0ms	(/ (fma (pow x 5) 1/60 (* x (fma (* 1/3 x) x 2))) (/ 2 (sin y)))
16.0ms	(* 1/3 x)

simplify2.1s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
2	1688
1	595
0	249

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes252.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample12.0s

Algorithm: halfpoints