Details

sample29.0ms

Algorithm

intervals

Results

15.0ms

453×

body

valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 26.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.9b	(- (+ (* x x) (* y y)) (* z z))
24.4b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

817×	`*-un-lft-identity`
337×	`associate-l`
335×	`add-sqr-sqrt`
228×	`times-frac`
211×	`distribute-lft-out`
154×	`distribute-lft-out--`
137×	`add-cube-cbrt`
120×	`prod-diff`
117×	`swap-sqr`
87×	`associate-r`
70×	`difference-of-squares`
43×	`*-commutative` `unswap-sqr`
19×	`associate-/l*`
15×	`fma-def`
12×	`associate-/r*`
10×	`add-log-exp`
8×	`add-exp-log` `fma-neg` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `+-commutative` `flip3--` `diff-log` `div-exp` `associate--l+` `sum-log` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 472

Calls

3 calls:

21.0ms	(+ (* x x) (* y y))
31.0ms	(- (+ (* x x) (* y y)) (* z z))
51.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series167.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
46.0ms	(- (+ (* x x) (* y y)) (* z z))
92.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify191.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	1018	5363
1	4243	4308
2	5001	4295

prune581.0ms

Filtered

481 candidates to 136 candidates (28.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	474	7	481
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	474	8	482

Merged error: 0b

Counts

482 → 8

localize15.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (+ (fabs z) (hypot x y)) (/ (- (/ (hypot x y) y) (/ (fabs z) y)) 2.0))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

270×	`associate-/l/`
243×	`frac-sub`
227×	`add-sqr-sqrt`
216×	`frac-times`
209×	`*-un-lft-identity`
200×	`associate-/l*`
195×	`associate-/r*`
150×	`add-cube-cbrt`
109×	`flip3-+` `flip-+`
108×	`associate-*r/`
97×	`times-frac`
63×	`frac-2neg`
58×	`clear-num`
40×	`associate-r`
25×	`distribute-lft-out--`
24×	`difference-of-squares`
21×	`sub-div`
13×	`div-inv`
6×	`add-exp-log` `distribute-rgt-out--` `add-cbrt-cube`
4×	`associate-l`
3×	`pow1` `flip3--` `un-div-inv` `flip--`
2×	`associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-prod-down` `*-commutative` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 390

Calls

1 calls:

73.0ms

(* (+ (fabs z) (hypot x y)) (/ (- (/ (hypot x y) y) (/ (fabs z) y)) 2.0))

series433.0ms

Counts

1 → 3

Calls

1 calls:

432.0ms

(* (+ (fabs z) (hypot x y)) (/ (- (/ (hypot x y) y) (/ (fabs z) y)) 2.0))

simplify194.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 1 (104.0ms)

Iter	Nodes	Cost
0	2463	8047
1	5003	7974

prune1.3s

Filtered

393 candidates to 253 candidates (64.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	391	2	393
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	397	4	401

Merged error: 0b

Counts

401 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y)))
0.1b	(/ (+ (fabs z) (hypot x y)) (/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

936×	`times-frac`
934×	`*-un-lft-identity`
740×	`add-sqr-sqrt`
558×	`associate-/r/`
526×	`associate-/r*`
500×	`add-cube-cbrt`
486×	`frac-sub`
334×	`associate-/l*`
131×	`distribute-lft-out`
123×	`frac-2neg`
111×	`clear-num`
80×	`distribute-lft-out--` `difference-of-squares`
47×	`div-inv`
42×	`sub-div`
20×	`distribute-rgt-out--`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3-+` `flip-+`

Counts

2 → 845

Calls

2 calls:

33.0ms	(/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y)))
55.0ms	(/ (+ (fabs z) (hypot x y)) (/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y))))

series429.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y)))
326.0ms	(/ (+ (fabs z) (hypot x y)) (/ 2.0 (- (/ (hypot x y) y) (/ (fabs z) y))))

simplify242.0ms

Algorithm

egg-herbie

Counts

851 → 851

Iterations

Useful iterations: 1 (87.0ms)

Iter	Nodes	Cost
0	2911	15939
1	5002	15816

prune2.1s

Filtered

851 candidates to 483 candidates (56.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	851	0	851
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	851	4	855

Merged error: 0b

Counts

855 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ (fabs z) (hypot x y)) y)
0.0b	(/ 2.0 (- (hypot x y) (fabs z)))
0.2b	(/ (/ (+ (fabs z) (hypot x y)) y) (/ 2.0 (- (hypot x y) (fabs z))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

882×	`times-frac`
609×	`*-un-lft-identity`
467×	`add-sqr-sqrt`
355×	`add-cube-cbrt`
71×	`distribute-lft-out`
56×	`distribute-lft-out--` `difference-of-squares`
47×	`associate-/r/`
42×	`div-inv`
37×	`associate-/r*`
30×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
18×	`flip3--` `flip--`
16×	`associate-/l/`
10×	`cbrt-undiv` `div-exp`
5×	`frac-2neg` `clear-num`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+`

Counts

3 → 490

Calls

3 calls:

7.0ms	(/ (+ (fabs z) (hypot x y)) y)
6.0ms	(/ 2.0 (- (hypot x y) (fabs z)))
30.0ms	(/ (/ (+ (fabs z) (hypot x y)) y) (/ 2.0 (- (hypot x y) (fabs z))))

series568.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (+ (fabs z) (hypot x y)) y)
93.0ms	(/ 2.0 (- (hypot x y) (fabs z)))
357.0ms	(/ (/ (+ (fabs z) (hypot x y)) y) (/ 2.0 (- (hypot x y) (fabs z))))

simplify159.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 1 (69.0ms)

Iter	Nodes	Cost
0	1899	8986
1	5001	8834

prune1.5s

Filtered

499 candidates to 322 candidates (64.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	498	1	499
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	499	4	503

Merged error: 0b

Counts

503 → 4

regimes145.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms

sample888.0ms

Algorithm

intervals

Results

554.0ms

13684×

body

valid