Details

sample15.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	14	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: 4.1b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

4.1b	(/ (+ x y) (- 1.0 (/ y z)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
29×	`times-frac`
13×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`distribute-lft-out`
6×	`associate-/r*`
5×	`distribute-lft-out--`
4×	`associate-/l*`
3×	`add-exp-log` `add-cbrt-cube`
2×	`associate-/r/` `associate-/l/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 52

Calls

1 calls:

11.0ms

(/ (+ x y) (- 1.0 (/ y z)))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(/ (+ x y) (- 1.0 (/ y z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	208	432
1	632	414
2	1909	414
3	5002	414

prune109.0ms

Filtered

55 candidates to 37 candidates (67.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	7	56

Merged error: 3.1b

Counts

56 → 7

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ 1 (- 1.0 (/ y z)))
3.7b	(* (+ x y) (/ 1 (- 1.0 (/ y z))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
45×	`times-frac`
41×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-r`
15×	`add-exp-log`
14×	`difference-of-squares`
9×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/r*`
5×	`pow1`
4×	`div-exp` `associate-l` `prod-exp` `associate-/r/`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `rec-exp` `flip3--` `flip3-+` `1-exp` `associate-*l/` `flip--` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `distribute-lft-out` `inv-pow`

Counts

2 → 101

Calls

2 calls:

8.0ms	(/ 1 (- 1.0 (/ y z)))
17.0ms	(* (+ x y) (/ 1 (- 1.0 (/ y z))))

series96.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ 1 (- 1.0 (/ y z)))
53.0ms	(* (+ x y) (/ 1 (- 1.0 (/ y z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	351	684
1	1631	607
2	5001	557

prune161.0ms

Filtered

107 candidates to 63 candidates (58.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Merged error: 3.1b

Counts

114 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ x y) (sqrt (- 1.0 (/ y z))))
0.1b	(* (/ 1 (sqrt (- 1.0 (/ y z)))) (/ (+ x y) (sqrt (- 1.0 (/ y z)))))
2.2b	(sqrt (- 1.0 (/ y z)))
2.2b	(sqrt (- 1.0 (/ y z)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

178×	`add-sqr-sqrt`
135×	`times-frac`
132×	`*-un-lft-identity`
95×	`sqrt-prod`
60×	`add-cube-cbrt`
42×	`associate-r`
33×	`associate-l`
28×	`add-exp-log` `difference-of-squares`
19×	`distribute-lft-out`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
14×	`distribute-lft-out--`
10×	`sqrt-div`
9×	`div-exp` `associate-/r*`
8×	`pow1` `prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip-+`

Counts

4 → 223

Calls

4 calls:

12.0ms	(/ (+ x y) (sqrt (- 1.0 (/ y z))))
47.0ms	(* (/ 1 (sqrt (- 1.0 (/ y z)))) (/ (+ x y) (sqrt (- 1.0 (/ y z)))))
9.0ms	(sqrt (- 1.0 (/ y z)))
10.0ms	(sqrt (- 1.0 (/ y z)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (+ x y) (sqrt (- 1.0 (/ y z))))
120.0ms	(* (/ 1 (sqrt (- 1.0 (/ y z)))) (/ (+ x y) (sqrt (- 1.0 (/ y z)))))
80.0ms	(sqrt (- 1.0 (/ y z)))
83.0ms	(sqrt (- 1.0 (/ y z)))

simplify94.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	699	2537
1	3933	2267
2	5001	2145

prune436.0ms

Filtered

235 candidates to 142 candidates (60.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	235	7	242

Merged error: 3.1b

Counts

242 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
0.1b	(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
8.3b	(sqrt (/ y z))
8.3b	(sqrt (/ y z))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

628×	`*-un-lft-identity`
620×	`times-frac`
560×	`add-sqr-sqrt`
375×	`sqrt-prod`
176×	`add-cube-cbrt`
172×	`distribute-lft-out`
162×	`difference-of-squares`
54×	`distribute-lft-out--`
30×	`associate-/l*`
28×	`associate-/r/`
16×	`associate-/r*` `div-inv`
14×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `rem-sqrt-square` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 443

Calls

4 calls:

35.0ms	(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
14.0ms	(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
3.0ms	(sqrt (/ y z))
3.0ms	(sqrt (/ y z))

series716.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
171.0ms	(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
46.0ms	(sqrt (/ y z))
55.0ms	(sqrt (/ y z))

simplify156.0ms

Algorithm

egg-herbie

Counts

455 → 455

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	925	8802
1	4028	8195
2	5001	8165

prune625.0ms

Filtered

455 candidates to 186 candidates (40.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	455	0	455
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	455	7	462

Merged error: 3.1b

Counts

462 → 7

regimes113.0ms

Accuracy

0% (1.8b remaining)

Error of 7.3b against oracle of 5.5b and baseline of 7.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample370.0ms

Algorithm

intervals

Results

206.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid