Details

sample115.0ms

Algorithm: halfpoints

simplify60.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`associate-l`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out` `add-log-exp`
3×	`fma-def` `associate-r`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 54

Calls

2 calls:

5.0ms	(+ (exp x) (exp (- x)))
10.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))

series87.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (exp x) (exp (- x)))
64.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))

simplify167.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	286	487
1	1053	428
2	4913	426
3	5001	426

prune139.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	5	61

Merged error: 0.0b

Counts

61 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) (exp (- x))))
0.0b	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
0.0b	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
0.0b	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

153×	`sqrt-prod`
134×	`*-un-lft-identity`
126×	`times-frac`
95×	`add-sqr-sqrt`
92×	`add-cube-cbrt`
46×	`associate-l`
29×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*`
10×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-*l/` `flip-+` `div-inv`
2×	`sqrt-undiv` `frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-r` `-commutative` `hypot-def`

Counts

4 → 237

Calls

4 calls:

5.0ms	(sqrt (+ (exp x) (exp (- x))))
9.0ms	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
9.0ms	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
24.0ms	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (exp x) (exp (- x))))
128.0ms	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
121.0ms	(/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))
148.0ms	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	553	3691
1	2280	3146
2	5002	2985

prune517.0ms

Filtered

249 candidates to 136 candidates (54.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	248	6	254

Merged error: 0b

Counts

254 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (sqrt (+ (exp x) (exp (- x)))))
0.0b	(* (/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0))) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))
0.0b	(/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0)))
0.0b	(* (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt (+ (exp x) (exp (- x))))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

314×	`cbrt-prod`
193×	`*-un-lft-identity`
180×	`times-frac`
171×	`sqrt-prod`
161×	`add-sqr-sqrt`
139×	`add-cube-cbrt`
104×	`associate-l`
29×	`add-exp-log`
26×	`distribute-lft-out`
19×	`add-cbrt-cube`
16×	`pow1` `cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`associate-r` `prod-exp` `cbrt-unprod`
10×	`associate-/l*`
9×	`associate-/r*` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`pow1/3`
6×	`cbrt-undiv` `div-exp`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num`

Counts

4 → 337

Calls

4 calls:

5.0ms	(cbrt (sqrt (+ (exp x) (exp (- x)))))
33.0ms	(* (/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0))) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))
11.0ms	(/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0)))
16.0ms	(* (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt (+ (exp x) (exp (- x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (sqrt (+ (exp x) (exp (- x)))))
342.0ms	(* (/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0))) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))
394.0ms	(/ (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt 2.0)))
140.0ms	(* (cbrt (sqrt (+ (exp x) (exp (- x))))) (cbrt (sqrt (+ (exp x) (exp (- x))))))

simplify126.0ms

Algorithm

egg-herbie

Counts

349 → 349

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	814	6555
1	3425	6213
2	5001	6043

prune1.2s

Filtered

349 candidates to 202 candidates (57.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	349	6	355

Merged error: 0b

Counts

355 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.3b	(pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3)
0.5b	(cbrt (pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `associate-l`
15×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac`
9×	`pow1`
8×	`cbrt-prod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`pow-unpow` `fma-def` `associate-r` `associate-*l/` `pow-exp` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `flip3-+` `pow1/3` `sum-log` `*-commutative` `rem-cbrt-cube` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

5.0ms	(+ (exp x) (exp (- x)))
10.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
10.0ms	(pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3)
2.0ms	(cbrt (pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3))

series227.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (exp x) (exp (- x)))
57.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
82.0ms	(pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3)
62.0ms	(cbrt (pow (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	397	922
1	1744	884
2	5003	881

prune258.0ms

Filtered

113 candidates to 83 candidates (73.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	113	6	119

Merged error: 0b

Counts

119 → 6

regimes56.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample2.5s

Algorithm: halfpoints