Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	12	5
2	14	5
3	15	5
4	20	5
5	41	5
6	66	5
7	165	5
8	1123	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ 2.0 (+ (exp x) (exp (- x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `distribute-lft-out`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

10.0ms

(/ 2.0 (+ (exp x) (exp (- x))))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(/ 2.0 (+ (exp x) (exp (- x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	167	323
1	568	300
2	2220	299
3	5001	299

prune88.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
0.0b	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
0.0b	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
60×	`times-frac`
46×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
16×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

3 → 147

Calls

3 calls:

7.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
11.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
10.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

series155.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
41.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
78.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

simplify63.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	458	1568
1	1997	1458
2	5002	1442

prune272.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
0.0b	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))))
0.0b	(/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))
0.0b	(* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
116×	`*-un-lft-identity`
110×	`add-exp-log`
95×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
54×	`associate-r`
44×	`div-exp`
43×	`prod-exp`
32×	`add-cbrt-cube`
30×	`unpow-prod-down` `cube-prod`
25×	`distribute-lft-out`
20×	`associate-/r/`
15×	`associate-l` `associate-/l*` `unswap-sqr`
14×	`pow1` `flip3-+` `flip-+`
12×	`sqr-pow`
10×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp`
9×	`cube-mult` `unpow3` `cbrt-unprod`
8×	`pow-to-exp` `pow-exp`
6×	`pow-flip` `associate-r/` `associate-l/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div`
2×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow-sqr` `*-commutative` `pow-prod-up` `inv-pow`

Counts

4 → 270

Calls

4 calls:

19.0ms	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
63.0ms	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))))
11.0ms	(/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))
105.0ms	(* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
44.0ms	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))))
59.0ms	(/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x)))
99.0ms	(* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (/ (pow 2.0 3) (+ (exp (* -1 x)) (exp x))))

simplify147.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	934	3875
1	4929	3404
2	5001	3404

prune592.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))
0.0b	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
0.5b	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (pow 2.0 3)))
0.5b	(cbrt (+ (exp (* -1 x)) (exp x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
19×	`pow1`
17×	`add-exp-log`
13×	`add-sqr-sqrt` `flip3-+` `flip-+`
11×	`add-cube-cbrt` `add-cbrt-cube`
8×	`frac-times` `associate-/r/`
7×	`distribute-lft-out`
6×	`pow-flip` `swap-sqr`
5×	`cbrt-prod` `associate-*l/`
4×	`expm1-log1p-u` `associate-r/` `div-exp` `associate-r` `associate-l*` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow2` `rec-exp` `pow-plus` `pow1/3` `1-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `-commutative` `div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

28.0ms	(* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))
19.0ms	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
58.0ms	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (pow 2.0 3)))
3.0ms	(cbrt (+ (exp (* -1 x)) (exp x)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))
53.0ms	(/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x))))
185.0ms	(cbrt (* (/ 1 (* (+ (exp (* -1 x)) (exp x)) (+ (exp (* -1 x)) (exp x)))) (pow 2.0 3)))
125.0ms	(cbrt (+ (exp (* -1 x)) (exp x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	433	1329
1	1998	1111
2	5001	1060

prune341.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	18
1	21	18

end0.0ms

sample267.0ms

Algorithm

intervals

Results

177.0ms

8000×

body

valid