Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1343	7
7	5001	7

prune8.0ms

Filtered

1 candidates to 0 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: 18.6b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite15.0ms

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` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series15.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify98.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune135.0ms

Filtered

48 candidates to 39 candidates (18.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Merged error: 0.4b

Counts

49 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(- (pow y 2) (pow x 2))
18.4b	(/ (- (pow y 2) (pow x 2)) (neg (+ (* x x) (* y y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

272×	`add-sqr-sqrt`
210×	`times-frac`
192×	`difference-of-squares`
128×	`*-un-lft-identity`
120×	`unpow-prod-down`
96×	`unpow2` `sqr-pow`
80×	`add-cube-cbrt`
66×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
24×	`distribute-lft-out--`
22×	`neg-mul-1`
21×	`associate-/l*`
10×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 299

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
7.0ms	(- (pow y 2) (pow x 2))
20.0ms	(/ (- (pow y 2) (pow x 2)) (neg (+ (* x x) (* y y))))

series22.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
6.0ms	(- (pow y 2) (pow x 2))
11.0ms	(/ (- (pow y 2) (pow x 2)) (neg (+ (* x x) (* y y))))

simplify92.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	1047	4137
1	2707	3719
2	5002	3716

prune747.0ms

Filtered

308 candidates to 121 candidates (60.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	308	5	313

Merged error: 0.4b

Counts

313 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
17.9b	(sqrt (+ (* x x) (* y y)))
17.9b	(sqrt (+ (* x x) (* y y)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
96×	`times-frac`
95×	`*-un-lft-identity`
57×	`add-cube-cbrt` `sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `associate-/r/` `distribute-lft-out`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 183

Calls

4 calls:

30.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
8.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
12.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
6.0ms	(sqrt (+ (* x x) (* y y)))
6.0ms	(sqrt (+ (* x x) (* y y)))

simplify73.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	628	2483
1	2598	2290
2	5001	2205

prune798.0ms

Filtered

195 candidates to 125 candidates (35.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Merged error: 0.4b

Counts

200 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.2b	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
18.1b	(/ (+ x y) (+ (pow x 2) (pow y 2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
41×	`times-frac`
32×	`add-sqr-sqrt`
31×	`distribute-lft-out`
26×	`associate-r`
25×	`add-cube-cbrt`
20×	`unpow-prod-down`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 109

Calls

3 calls:

7.0ms	(+ (pow x 2) (pow y 2))
18.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
13.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

series23.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (pow x 2) (pow y 2))
10.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
7.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	390	902
1	1953	823
2	5002	822

prune300.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	118	5	123

Merged error: 0.4b

Counts

123 → 5

regimes111.0ms

Accuracy

78.4% (4.3b remaining)

Error of 4.8b against oracle of 0.5b and baseline of 20.5b

bsearch131.0ms

Steps

Iters	Range	Point
9	1.7814796083688998e-166	2.2989197778650966e-159	1.365744097418829e-159
10	-1.2266878854493793e-157	-1.5070288184943165e-173	-2.548773784153301e-161
9	-1.9206346708680486e+155	-6.967955356982681e+149	-7.618433636602945e+149

Iters

Range

Point

1.7814796083688998e-166

2.2989197778650966e-159

1.365744097418829e-159

-1.2266878854493793e-157

-1.5070288184943165e-173

-2.548773784153301e-161

-1.9206346708680486e+155

-6.967955356982681e+149

-7.618433636602945e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	38	16
2	38	16

end0.0ms

sample656.0ms

Algorithm

intervals

Results

295.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

sample27.0ms

simplify59.0ms

prune8.0ms

localize9.0ms

rewrite15.0ms

series15.0ms

simplify98.0ms

prune135.0ms

localize10.0ms

rewrite48.0ms

series22.0ms

simplify92.0ms

prune747.0ms

localize11.0ms

rewrite55.0ms

series34.0ms

simplify73.0ms

prune798.0ms

localize9.0ms

rewrite42.0ms

series23.0ms

simplify55.0ms

prune300.0ms

regimes111.0ms

bsearch131.0ms

simplify2.0ms

end0.0ms

sample656.0ms

Profiling