Details

sample356.0ms

Algorithm: halfpoints

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize81.0ms

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

rewrite224.0ms

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:

69.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
16.0ms	(+ (exp x) (exp (- x)))
101.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
34.0ms	(- (exp x) (exp (- x)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
24.0ms	(+ (exp x) (exp (- x)))
107.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
49.0ms	(- (exp x) (exp (- x)))

simplify1.5s

Counts

134 → 134

Iterations

Useful iterations: done (1.5s)

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

prune699.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

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))

rewrite138.0ms

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:

0.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
69.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
30.0ms	(+ (exp x) (exp (- x)))
35.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series311.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
78.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
24.0ms	(+ (exp x) (exp (- x)))
121.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify1.3s

Counts

110 → 110

Iterations

Useful iterations: done (1.3s)

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

prune889.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize85.0ms

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))

rewrite194.0ms

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:

47.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
109.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
12.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
12.0ms	(/ 1 (sqrt 2.0))

series752.0ms

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))
308.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
199.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.3s

Counts

198 → 198

Iterations

Useful iterations: done (1.3s)

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

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b	(* (pow 2.0 -1/2) (* (/ (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))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity` `times-frac`
36×	`add-cube-cbrt`
35×	`add-exp-log`
29×	`associate-l`
22×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`prod-exp`
7×	`cbrt-unprod`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `fma-def` `pow-exp` `associate-/l*` `unswap-sqr`
2×	`associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-*r/` `pow-prod-down` `clear-num` `sum-log` `flip-+` `distribute-lft-out` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
25.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
57.0ms	(* (pow 2.0 -1/2) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
13.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

series742.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
235.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
310.0ms	(* (pow 2.0 -1/2) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
172.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

simplify1.5s

Counts

145 → 145

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	248	3543
1	601	3435
2	1917	3088
done	5000	3086

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes206.0ms

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

sample9.2s

Algorithm: halfpoints