Details

sample323.0ms

Algorithm: halfpoints

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	7
1	47	7
2	84	7
3	131	7
4	223	7
5	466	7
6	1123	7
7	2244	7
8	5002	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize52.0ms

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))
58.1b	(- (exp x) (exp (- x)))

rewrite80.0ms

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:

28.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
6.0ms	(+ (exp x) (exp (- x)))
29.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
11.0ms	(- (exp x) (exp (- x)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
23.0ms	(+ (exp x) (exp (- x)))
82.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
39.0ms	(- (exp x) (exp (- x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	574	1243
1	2008	1013
2	5002	1009

prune477.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

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))

rewrite49.0ms

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)))
28.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
6.0ms	(+ (exp x) (exp (- x)))
9.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series235.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
63.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
22.0ms	(+ (exp x) (exp (- x)))
91.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	487	969
1	1911	846
2	5001	842

prune603.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

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))

rewrite60.0ms

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:

16.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
29.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
4.0ms	(/ 1 (sqrt 2.0))

series486.0ms

Counts

4 → 10

Calls

4 calls:

155.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
218.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
113.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	633	2260
1	3213	1931
2	5001	1821

prune891.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize76.0ms

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))

rewrite50.0ms

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-l/` `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×	`neg-sub0` `frac-times` `pow-neg` `*-commutative` `div-inv` `pow-sub`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-*r/` `pow-prod-down` `clear-num` `sum-log` `flip-+` `distribute-lft-out` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

6.0ms	(+ (exp x) (exp (- x)))
14.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
21.0ms	(* (pow 2.0 (- 1/2)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

series673.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (exp x) (exp (- x)))
303.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
226.0ms	(* (pow 2.0 (- 1/2)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
121.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	639	1818
1	2833	1620
2	5001	1614

prune782.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	29	17

end0.0ms

sample6.2s

Algorithm: halfpoints