Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify28.0ms

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 (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: 32.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.5b	(- (* x x) (* (* y 4.0) y))
31.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite208.0ms

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))
33.0ms	(- (* x x) (* (* y 4.0) y))
85.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x x) (* (* y 4.0) y))
48.0ms	(- (* x x) (* (* y 4.0) y))
75.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify226.0ms

Algorithm

egg-herbie

Counts

691 → 691

Iterations

Useful iterations: 2 (123.0ms)

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

prune347.0ms

Filtered

691 candidates to 133 candidates (80.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	687	4	691
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	688	4	692

Merged error: 0.1b

Counts

692 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.1b

Counts

4 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

29.5b	(sqrt (* (* y 4.0) y))
29.5b	(sqrt (* (* y 4.0) y))
30.0b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.0b	(sqrt (+ (* x x) (* (* y 4.0) y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
62×	`sqrt-prod`
50×	`unswap-sqr`
48×	`associate-l`
40×	`*-un-lft-identity`
30×	`hypot-def`
18×	`pow1`
16×	`add-cube-cbrt`
12×	`associate-r` `distribute-lft-out`
10×	`*-commutative`
8×	`rem-sqrt-square` `sqrt-pow1`
6×	`swap-sqr` `pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+`

Counts

4 → 152

Calls

4 calls:

9.0ms	(sqrt (* (* y 4.0) y))
9.0ms	(sqrt (* (* y 4.0) y))
25.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
28.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (* (* y 4.0) y))
38.0ms	(sqrt (* (* y 4.0) y))
63.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
65.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))

simplify97.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	196	700
1	688	672
2	2077	638
3	5002	638

prune361.0ms

Filtered

164 candidates to 112 candidates (31.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	164	4	168

Merged error: 0.1b

Counts

168 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
0.0b	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
2.5b	(- (* x x) (* (* y 4.0) y))
31.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

1754×	`add-sqr-sqrt`
1522×	`*-un-lft-identity`
1212×	`associate-l`
648×	`times-frac`
605×	`unswap-sqr`
444×	`exp-prod`
438×	`distribute-lft-out`
435×	`difference-of-squares`
330×	`prod-diff`
298×	`add-cube-cbrt`
223×	`log-pow`
174×	`distribute-lft-out--`
159×	`associate-r`
156×	`swap-sqr`
140×	`*-commutative`
24×	`associate-/l*`
15×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-log-exp`
6×	`associate-/r/` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `flip3-+` `div-sub` `flip-+` `div-inv`
2×	`flip3--` `exp-diff` `rem-log-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `clear-num` `rem-exp-log`

Counts

4 → 1119

Calls

4 calls:

81.0ms	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
85.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
36.0ms	(- (* x x) (* (* y 4.0) y))
79.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
70.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
44.0ms	(- (* x x) (* (* y 4.0) y))
74.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify265.0ms

Algorithm

egg-herbie

Counts

1131 → 1131

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	1309	14528
1	3750	11475
2	5001	11230

prune905.0ms

Filtered

1131 candidates to 213 candidates (81.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1131	0	1131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1131	4	1135

Merged error: 0.1b

Counts

1135 → 4

regimes171.0ms

Accuracy

63.4% (11.5b remaining)

Error of 11.8b against oracle of 0.3b and baseline of 31.6b

bsearch97.0ms

Steps

Iters	Range		Point
6	2.2093669181297253e+294	1.836560188400803e+295	1.8120705214528157e+295
7	2.9008814709843022e-137	1.2899744278765863e-135	2.947283386563354e-137
7	2.5693603695882933e-220	6.955914094663762e-219	1.5854439680855296e-219
8	4.910861076357373e-302	3.884159237172627e-299	5.7821985637581754e-301

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	50
1	35	50

end0.0ms

sample370.0ms

Algorithm

intervals

Results

237.0ms

8000×

body

valid