Details

sample457.0ms

Algorithm: halfpoints

simplify6.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	48	11
3	83	11
4	127	11
5	200	11
6	373	11
7	608	11
8	1105	11
9	1521	11
10	1855	11
11	1939	11
12	1959	11
done	1959	11

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.2b	(- (exp x) (exp (- x)))

rewrite182.0ms

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-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `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` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 122

Calls

4 calls:

64.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
19.0ms	(+ (exp x) (exp (- x)))
76.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.0ms	(- (exp x) (exp (- x)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
41.0ms	(+ (exp x) (exp (- x)))
109.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
48.0ms	(- (exp x) (exp (- x)))

simplify1.7s

Counts

134 → 134

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	232	1903
1	565	1734
2	1576	1486
done	5001	1429

prune747.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
29×	`associate-l`
23×	`times-frac`
22×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `unswap-sqr`
3×	`fma-def`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef`

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
77.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
26.0ms	(+ (exp x) (exp (- x)))
19.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series351.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
99.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(+ (exp x) (exp (- x)))
135.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify1.2s

Counts

110 → 110

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	199	1796
1	481	1766
2	1469	1539
done	5000	1534

prune920.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 188

Calls

4 calls:

32.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
98.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
11.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
9.0ms	(/ 1 (sqrt 2.0))

series748.0ms

Counts

4 → 10

Calls

4 calls:

245.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
310.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
192.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.4s

Counts

198 → 198

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	254	4584
1	601	4231
2	1984	3619
done	5001	3595

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b	(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (* (sqrt 2.0) 2.0))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-l`
31×	`add-exp-log`
22×	`sqrt-prod` `add-cbrt-cube`
18×	`pow1`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`cbrt-prod` `pow-flip` `div-exp` `associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv` `pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`rec-exp` `cbrt-div` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `1-exp` `clear-num` `*-commutative` `pow-prod-up`
1×	`frac-times` `cube-unmult` `associate-*r/` `inv-pow`

Counts

4 → 152

Calls

4 calls:

28.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
85.0ms	(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
7.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
16.0ms	(/ 1 (* (sqrt 2.0) 2.0))

series1.1s

Counts

4 → 10

Calls

4 calls:

195.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
752.0ms	(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
163.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (* (sqrt 2.0) 2.0))

simplify1.6s

Counts

162 → 162

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	260	3780
1	594	3626
2	1776	3253
done	5000	3247

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	31
1	29	31
done	29	31

end0.0ms

sample12.1s

Algorithm: halfpoints