Details

sample11.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify225.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

5.0ms	(+ (exp x) (exp (- x)))
6.0ms	(/ 2.0 (+ (exp x) (exp (- x))))

series61.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (exp x) (exp (- x)))
40.0ms	(/ 2.0 (+ (exp x) (exp (- x))))

simplify118.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	200	433
1	666	397
2	3139	394
3	5001	393

prune102.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	3	59

Merged error: 0b

Counts

59 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

8.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
4.0ms	(+ (exp (* -1 x)) (exp x))
8.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
6.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
20.0ms	(+ (exp (* -1 x)) (exp x))
35.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
39.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	475	1670
1	2035	1557
2	5002	1539

prune256.0ms

Filtered

176 candidates to 94 candidates (53.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	176	3	179

Merged error: 0b

Counts

179 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ 2.0 (+ (exp x) (exp (- x)))))
0.0b	(expm1 (log1p (/ 2.0 (+ (exp x) (exp (- x))))))
0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ 2.0 (+ (exp x) (exp (- x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u` `distribute-lft-out`
4×	`pow1` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `sum-log` `div-inv` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

1.0ms	(log1p (/ 2.0 (+ (exp x) (exp (- x)))))
1.0ms	(expm1 (log1p (/ 2.0 (+ (exp x) (exp (- x))))))
5.0ms	(+ (exp x) (exp (- x)))
10.0ms	(/ 2.0 (+ (exp x) (exp (- x))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(log1p (/ 2.0 (+ (exp x) (exp (- x)))))
180.0ms	(expm1 (log1p (/ 2.0 (+ (exp x) (exp (- x))))))
21.0ms	(+ (exp x) (exp (- x)))
37.0ms	(/ 2.0 (+ (exp x) (exp (- x))))

simplify183.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (175.0ms)

Iter	Nodes	Cost
0	285	645
1	897	583
2	4347	576
3	5001	575

prune175.0ms

Filtered

86 candidates to 65 candidates (75.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
0.0b	(+ (exp x) (exp (- x)))
0.5b	(* (sqrt 2.0) (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 125

Calls

3 calls:

7.0ms	(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
9.0ms	(+ (exp x) (exp (- x)))
30.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))

series195.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (sqrt 2.0) (+ (exp x) (exp (- x))))
22.0ms	(+ (exp x) (exp (- x)))
103.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (+ (exp x) (exp (- x)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	377	1293
1	1669	1171
2	5001	1140

prune222.0ms

Filtered

134 candidates to 87 candidates (64.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Merged error: 0b

Counts

137 → 3

regimes67.0ms

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	14	7
1	14	7

end0.0ms

sample269.0ms

Algorithm

intervals

Results

180.0ms

8000×

body

valid