Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 21.3b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308

prune129.0ms

Filtered

53 candidates to 43 candidates (81.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0.6b

Counts

55 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
20.8b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 96

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
14.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
7.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
60.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
48.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	401	799
1	2118	704
2	5002	688

prune209.0ms

Filtered

105 candidates to 77 candidates (73.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot x y) 1))
0.0b	(* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y)))
0.0b	(/ (+ x y) (hypot x y))
0.2b	(* (- x y) (* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
91×	`prod-exp`
61×	`add-cbrt-cube`
51×	`div-exp`
42×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`times-frac`
30×	`1-exp`
26×	`add-cube-cbrt`
24×	`cbrt-unprod`
17×	`cbrt-undiv` `associate-r`
15×	`rec-exp`
14×	`pow1`
12×	`associate-l`
10×	`frac-times`
7×	`associate-r/` `distribute-lft-out` `associate-/l`
6×	`associate-*l/`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `flip3--` `associate-/r*` `flip--` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`flip3-+` `flip-+` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

5.0ms	(/ 1 (* (hypot x y) 1))
14.0ms	(* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y)))
5.0ms	(/ (+ x y) (hypot x y))
16.0ms	(* (- x y) (* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1 (* (hypot x y) 1))
70.0ms	(* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y)))
83.0ms	(/ (+ x y) (hypot x y))
92.0ms	(* (- x y) (* (/ 1 (* (hypot x y) 1)) (/ (+ x y) (hypot x y))))

simplify75.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	718	1570
1	3718	1258
2	5001	1227

prune296.0ms

Filtered

202 candidates to 103 candidates (51.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	203	5	208

Merged error: 0b

Counts

208 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x y)
0.0b	(* (/ (+ x y) (hypot x y)) (- x y))
0.0b	(/ (* (/ (+ x y) (hypot x y)) (- x y)) (* (hypot x y) 1))
0.0b	(/ (+ x y) (hypot x y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
41×	`add-exp-log` `add-sqr-sqrt`
34×	`add-cube-cbrt`
32×	`add-cbrt-cube`
26×	`times-frac`
18×	`prod-diff`
16×	`associate-l`
14×	`div-exp` `prod-exp`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
7×	`associate-/l/` `distribute-lft-out`
6×	`pow1`
5×	`associate-r` `associate-/l*`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-r/` `associate-/r` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`1-exp` `div-inv`
2×	`sub-neg` `frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`hypot-udef` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

1.0ms	(hypot x y)
12.0ms	(* (/ (+ x y) (hypot x y)) (- x y))
13.0ms	(/ (* (/ (+ x y) (hypot x y)) (- x y)) (* (hypot x y) 1))
5.0ms	(/ (+ x y) (hypot x y))

series297.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot x y)
84.0ms	(* (/ (+ x y) (hypot x y)) (- x y))
85.0ms	(/ (* (/ (+ x y) (hypot x y)) (- x y)) (* (hypot x y) 1))
85.0ms	(/ (+ x y) (hypot x y))

simplify74.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	634	1331
1	3378	1028
2	5001	1028

prune280.0ms

Filtered

157 candidates to 101 candidates (64.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	157	5	162

Merged error: 0b

Counts

162 → 5

regimes53.0ms

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	15	8
1	17	8
2	17	8

end0.0ms

sample505.0ms

Algorithm

intervals

Results

245.0ms	8000×	body	80	valid
112.0ms	8000×	pre	80	true