Details

sample12.0ms

Algorithm

intervals

Results

4.0ms	249×	body	80	valid
0.0ms	3×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	160	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: 0.0b

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:

15.0ms

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

simplify44.0ms

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

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

6.0ms	(+ x (/ (fabs (- y x)) 2.0))
11.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
11.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
47.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ x (/ (fabs (- y x)) 2.0))
46.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
43.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
19.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	287	1107
1	1125	1001
2	5002	967

prune255.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 219

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
11.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
94.0ms	(* (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
53.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
52.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
16.0ms	(* (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
45.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	678	2916
1	2646	2427
2	5001	2385

prune422.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.4b	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
17×	`associate-r`
14×	`sqrt-div`
13×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`unswap-sqr`
2×	`pow1/3` `associate-l/` `-commutative`

Counts

4 → 95

Calls

4 calls:

25.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
49.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
67.0ms	(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
51.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
49.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	680	2059
1	2634	1912
2	5002	1876

prune357.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes66.0ms

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

sample289.0ms

Algorithm

intervals

Results

146.0ms	7713×	body	80	valid
8.0ms	94×	body	1280	valid
5.0ms	49×	body	320	valid
5.0ms	74×	body	640	valid
5.0ms	46×	body	2560	valid
1.0ms	27×	body	160	valid