Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	244×	body	80	valid
0.0ms	6×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	2560	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	4
1	11	4
2	11	4

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: 0.1b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

6.0ms

(+ x (/ (fabs (- y x)) 2.0))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	110
1	226	97
2	540	97
3	1522	97
4	5001	97

prune42.0ms

Filtered

20 candidates to 16 candidates (80.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Merged error: 0.0b

Counts

21 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

series97.0ms

Counts

1 → 3

Calls

1 calls:

97.0ms

(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	88	117
1	275	101
2	1326	95
3	5001	92

prune32.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	13	3	16

Merged error: 0.0b

Counts

16 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.1b	(pow (+ x (/ (fabs (- y x)) 2.0)) 3)
37.0b	(cbrt (pow (+ x (/ (fabs (- y x)) 2.0)) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
5×	`distribute-lft-out` `add-log-exp`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 73

Calls

3 calls:

6.0ms	(+ x (/ (fabs (- y x)) 2.0))
7.0ms	(pow (+ x (/ (fabs (- y x)) 2.0)) 3)
7.0ms	(cbrt (pow (+ x (/ (fabs (- y x)) 2.0)) 3))

series54.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ x (/ (fabs (- y x)) 2.0))
23.0ms	(pow (+ x (/ (fabs (- y x)) 2.0)) 3)
15.0ms	(cbrt (pow (+ x (/ (fabs (- y x)) 2.0)) 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	243	595
1	994	555
2	5002	549

prune131.0ms

Filtered

82 candidates to 49 candidates (59.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Merged error: 0.0b

Counts

85 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.1b	(pow (+ x (/ (fabs (- y x)) 2.0)) 2)
0.1b	(* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0)))
37.0b	(cbrt (* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cube-cbrt`
9×	`unpow-prod-down` `associate-l`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`unpow2`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `log1p-expm1-u` `distribute-lft-out` `unswap-sqr`
3×	`pow-unpow` `fma-def` `flip3-+` `prod-exp` `flip-+` `sqr-pow`
2×	`pow-to-exp` `cbrt-div` `pow3` `pow-exp`
1×	`+-commutative` `cbrt-prod` `distribute-rgt-in` `pow-pow` `distribute-lft-in` `pow-plus` `pow1/3` `sum-log` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

6.0ms	(+ x (/ (fabs (- y x)) 2.0))
7.0ms	(pow (+ x (/ (fabs (- y x)) 2.0)) 2)
14.0ms	(* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0)))
12.0ms	(cbrt (* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ x (/ (fabs (- y x)) 2.0))
17.0ms	(pow (+ x (/ (fabs (- y x)) 2.0)) 2)
21.0ms	(* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0)))
16.0ms	(cbrt (* (pow (+ x (/ (fabs (- y x)) 2.0)) 2) (+ x (/ (fabs (- y x)) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	336	926
1	1359	701
2	5002	680

prune186.0ms

Filtered

102 candidates to 68 candidates (66.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	102	4	106

Merged error: 0.0b

Counts

106 → 4

regimes57.0ms

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	8	4
1	8	4

end0.0ms

sample302.0ms

Algorithm

intervals

Results

150.0ms	7717×	body	80	valid
8.0ms	87×	body	1280	valid
6.0ms	87×	body	640	valid
6.0ms	50×	body	2560	valid
5.0ms	39×	body	320	valid
1.0ms	21×	body	160	valid