Details

sample19.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify212.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	12	5
2	14	5
3	15	5
4	20	5
5	40	5
6	61	5
7	150	5
8	1040	5
9	5002	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))))

rewrite11.0ms

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` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

10.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify67.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	163	311
1	549	289
2	2172	288
3	5001	288

prune72.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

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×	`pow-unpow` `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 → 141

Calls

3 calls:

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

series148.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
70.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
40.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	447	1530
1	1969	1425
2	5002	1411

prune242.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)))
0.6b	(* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3))
0.6b	(pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)
1.0b	(pow (sqrt 2.0) 3)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

182×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
120×	`times-frac`
106×	`unpow-prod-down` `cube-prod`
88×	`sqrt-prod`
76×	`add-cube-cbrt`
66×	`associate-r`
48×	`unswap-sqr`
28×	`add-exp-log`
24×	`distribute-lft-out`
18×	`associate-l` `sqr-pow`
13×	`pow-exp`
12×	`prod-exp`
10×	`add-cbrt-cube`
9×	`pow-to-exp`
8×	`associate-/r/`
7×	`pow1`
6×	`pow-unpow`
4×	`cube-mult` `pow-pow` `flip3-+` `unpow3` `div-exp` `flip-+` `div-inv` `add-log-exp`
3×	`cube-div` `rem-cube-cbrt`
2×	`associate-*r/` `pow-prod-down`
1×	`cbrt-undiv` `cbrt-prod` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 278

Calls

4 calls:

17.0ms	(cbrt (* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)))
81.0ms	(* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3))
13.0ms	(pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)
2.0ms	(pow (sqrt 2.0) 3)

series438.0ms

Counts

4 → 10

Calls

4 calls:

96.0ms	(cbrt (* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)))
170.0ms	(* (pow (sqrt 2.0) 3) (pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3))
171.0ms	(pow (/ (sqrt 2.0) (+ (exp (* -1 x)) (exp x))) 3)
0.0ms	(pow (sqrt 2.0) 3)

simplify172.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	715	3738
1	4138	3190
2	5001	3022

prune438.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	18	11

end0.0ms

sample281.0ms

Algorithm

intervals

Results

187.0ms

8000×

body

valid