Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	243×	body	80	valid
0.0ms	4×	body	1280	valid
0.0ms	3×	body	2560	valid
0.0ms	3×	body	640	valid
0.0ms	3×	body	320	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

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))

simplify45.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (3.0ms)

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

prune43.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`sqrt-prod`
20×	`pow1`
15×	`add-cube-cbrt`
14×	`sqrt-div`
11×	`swap-sqr`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log` `hypot-def`
1×	`pow2` `rem-sqrt-square` `times-frac` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

13.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
6.0ms	(+ x (/ (fabs (- y x)) 2.0))
6.0ms	(+ x (/ (fabs (- y x)) 2.0))
47.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms	(+ x (/ (fabs (- y x)) 2.0))
16.0ms	(+ x (/ (fabs (- y x)) 2.0))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	287	1012
1	1177	904
2	5002	874

prune243.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
0.4b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
112×	`sqrt-prod`
91×	`sqrt-pow1`
69×	`pow1`
60×	`add-sqr-sqrt`
47×	`pow1/2`
42×	`*-un-lft-identity`
39×	`pow-prod-up`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
20×	`swap-sqr`
17×	`associate-l`
16×	`associate-*r/`
12×	`pow-prod-down`
11×	`add-exp-log` `associate-r` `pow-sqr` `add-cbrt-cube` `unswap-sqr`
10×	`associate-*l/`
9×	`distribute-lft-out`
4×	`expm1-log1p-u` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`pow2` `pow-plus` `rem-square-sqrt`

Counts

4 → 213

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
11.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
84.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
55.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
51.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
52.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	659	2854
1	2504	2480
2	5001	2438

prune443.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize8.0ms

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:

0.0ms

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

series105.0ms

Counts

1 → 3

Calls

1 calls:

105.0ms

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

simplify44.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (41.0ms)

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

prune30.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes61.0ms

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

152.0ms	7707×	body	80	valid
10.0ms	114×	body	1280	valid
5.0ms	75×	body	640	valid
5.0ms	44×	body	2560	valid
3.0ms	48×	body	320	valid
0.0ms	13×	body	160	valid