Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	40	9
2	78	9
3	134	9
4	200	9
5	233	9
6	239	9
7	239	9

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: 30.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.3b	(- (* x x) (* (* y 4.0) y))
30.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

881×	`add-sqr-sqrt`
677×	`*-un-lft-identity`
630×	`associate-l`
330×	`prod-diff`
282×	`unswap-sqr`
233×	`add-cube-cbrt`
216×	`times-frac`
165×	`difference-of-squares`
162×	`associate-r`
156×	`distribute-lft-out`
105×	`swap-sqr`
87×	`*-commutative`
66×	`distribute-lft-out--`
24×	`associate-/l*`
15×	`fma-def` `fma-neg`
9×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 682

Calls

3 calls:

24.0ms	(+ (* x x) (* (* y 4.0) y))
38.0ms	(- (* x x) (* (* y 4.0) y))
81.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series175.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* x x) (* (* y 4.0) y))
48.0ms	(- (* x x) (* (* y 4.0) y))
79.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify234.0ms

Algorithm

egg-herbie

Counts

691 → 691

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	1208	11295
1	3628	8413
2	5001	8270

prune357.0ms

Filtered

691 candidates to 133 candidates (19.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	686	5	691
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	687	5	692

Merged error: 0.2b

Counts

692 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
3.1b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
16.9b	(/ (fma x x (* (* y 4.0) y)) y)
18.5b	(/ (fma x x (* (* y 4.0) y)) x)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
227×	`add-sqr-sqrt`
199×	`add-cube-cbrt` `*-un-lft-identity`
42×	`associate-r` `associate-l`
38×	`associate-/r*`
27×	`associate-/l*`
25×	`add-exp-log` `add-cbrt-cube`
21×	`div-inv`
18×	`associate-/r/`
14×	`*-commutative` `unswap-sqr`
11×	`cbrt-undiv` `div-exp`
6×	`frac-2neg` `clear-num`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 348

Calls

4 calls:

7.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
14.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
3.0ms	(/ (fma x x (* (* y 4.0) y)) y)
4.0ms	(/ (fma x x (* (* y 4.0) y)) x)

series282.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
63.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
73.0ms	(/ (fma x x (* (* y 4.0) y)) y)
82.0ms	(/ (fma x x (* (* y 4.0) y)) x)

simplify103.0ms

Algorithm

egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	1331	4109
1	5002	3910

prune692.0ms

Filtered

360 candidates to 264 candidates (73.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	360	5	365

Merged error: 0.2b

Counts

365 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (* x x) (* (* y 4.0) y))
28.3b	(sqrt (* (* y 4.0) y))
28.3b	(sqrt (* (* y 4.0) y))
30.0b	(/ (- (* x x) (* (* y 4.0) y)) (* (hypot x (sqrt (* (* y 4.0) y))) (hypot x (sqrt (* (* y 4.0) y)))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

1337×	`add-sqr-sqrt`
552×	`associate-l`
549×	`*-un-lft-identity`
428×	`unswap-sqr`
360×	`times-frac`
345×	`add-cube-cbrt`
330×	`prod-diff`
255×	`difference-of-squares`
246×	`associate-r`
195×	`swap-sqr`
133×	`*-commutative`
102×	`distribute-lft-out--`
44×	`sqrt-prod`
24×	`associate-/l*`
16×	`pow1`
15×	`fma-neg` `associate-/r*`
9×	`add-exp-log` `add-cbrt-cube`
6×	`rem-sqrt-square` `sqrt-pow1` `pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `pow1/2` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 874

Calls

4 calls:

32.0ms	(- (* x x) (* (* y 4.0) y))
9.0ms	(sqrt (* (* y 4.0) y))
13.0ms	(sqrt (* (* y 4.0) y))
61.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (hypot x (sqrt (* (* y 4.0) y))) (hypot x (sqrt (* (* y 4.0) y)))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* x x) (* (* y 4.0) y))
38.0ms	(sqrt (* (* y 4.0) y))
43.0ms	(sqrt (* (* y 4.0) y))
246.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (hypot x (sqrt (* (* y 4.0) y))) (hypot x (sqrt (* (* y 4.0) y)))))

simplify210.0ms

Algorithm

egg-herbie

Counts

886 → 886

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	1811	17707
1	5001	14325

prune715.0ms

Filtered

886 candidates to 220 candidates (24.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	883	3	886
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	884	7	891

Merged error: 0.2b

Counts

891 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (* (* y 4.0) y))
28.3b	(sqrt (* (* y 4.0) y))
28.3b	(sqrt (* (* y 4.0) y))
28.3b	(sqrt (* (* y 4.0) y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
76×	`add-sqr-sqrt`
60×	`associate-l`
28×	`pow1` `unswap-sqr`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
12×	`rem-sqrt-square` `sqrt-pow1` `pow-prod-down`
8×	`*-commutative`
4×	`add-exp-log` `expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

9.0ms	(sqrt (* (* y 4.0) y))
9.0ms	(sqrt (* (* y 4.0) y))
10.0ms	(sqrt (* (* y 4.0) y))
9.0ms	(sqrt (* (* y 4.0) y))

series165.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (* (* y 4.0) y))
43.0ms	(sqrt (* (* y 4.0) y))
39.0ms	(sqrt (* (* y 4.0) y))
44.0ms	(sqrt (* (* y 4.0) y))

simplify142.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 4 (46.0ms)

Iter	Nodes	Cost
0	117	720
1	352	712
2	730	676
3	988	676
4	1593	672
5	2293	672
6	5002	672

prune506.0ms

Filtered

164 candidates to 116 candidates (70.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	164	7	171

Merged error: 0.2b

Counts

171 → 7

regimes183.0ms

Accuracy

72.4% (5.3b remaining)

Error of 5.6b against oracle of 0.3b and baseline of 19.4b

bsearch115.0ms

Steps

Iters	Range		Point
8	1.2626065079888024e+147	2.8939171912899624e+150	2.285909953188242e+150
9	-3.483124212075601e+151	-3.32688586057143e+142	-3.406491123882815e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	39
1	40	39

end0.0ms

sample394.0ms

Algorithm

intervals

Results

255.0ms

8000×

body

valid