Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify57.0ms

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	1355	7
7	5001	7

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: 18.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite19.0ms

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))
15.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
58.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

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

prune286.0ms

Filtered

48 candidates to 39 candidates (81.3%)

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: 0.1b

Counts

49 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
17.3b	(sqrt (+ (* x x) (* y y)))
17.3b	(sqrt (+ (* x x) (* y y)))

rewrite59.0ms

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:

9.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
34.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
63.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
35.0ms	(sqrt (+ (* x x) (* y y)))
42.0ms	(sqrt (+ (* x x) (* y y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	628	2483
1	2598	2290
2	5002	2205

prune317.0ms

Filtered

195 candidates to 124 candidates (63.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	195	5	200

Merged error: 0.1b

Counts

200 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
18.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`unpow-prod-down` `cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `times-frac` `add-cbrt-cube`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `associate-/r*` `flip--` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
14.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
74.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
75.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
58.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	494	1238
1	2872	1167
2	5001	1161

prune191.0ms

Filtered

128 candidates to 78 candidates (60.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	128	5	133

Merged error: 0.1b

Counts

133 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

18.1b	(cbrt (+ (* x x) (* y y)))
18.1b	(cbrt (+ (* x x) (* y y)))
18.1b	(cbrt (+ (* x x) (* y y)))
18.2b	(/ (* (- x y) (+ x y)) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
16×	`add-exp-log`
12×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`cbrt-prod`
8×	`frac-times` `associate-/r/` `associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
17.0ms	(/ (* (- x y) (+ x y)) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ (* x x) (* y y)))
91.0ms	(cbrt (+ (* x x) (* y y)))
87.0ms	(cbrt (+ (* x x) (* y y)))
179.0ms	(/ (* (- x y) (+ x y)) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	461	1021
1	2241	901
2	5001	891

prune209.0ms

Filtered

88 candidates to 74 candidates (84.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Merged error: 0.1b

Counts

93 → 5

regimes82.0ms

Accuracy

78% (4.2b remaining)

Error of 4.6b against oracle of 0.4b and baseline of 19.6b

bsearch105.0ms

Steps

Iters	Range	Point
9	5.979285330824152e-167	9.2325914621024e-162	8.686820838206432e-162
8	-2.756316178715079e-152	-1.7585719377007754e-156	-3.152838097076862e-156
10	-4.706237202987014e+161	-4.262486889663285e+150	-1.2571453085126962e+152

Iters

Range

Point

5.979285330824152e-167

9.2325914621024e-162

8.686820838206432e-162

-2.756316178715079e-152

-1.7585719377007754e-156

-3.152838097076862e-156

-4.706237202987014e+161

-4.262486889663285e+150

-1.2571453085126962e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	18
1	31	18

end0.0ms

sample506.0ms

Algorithm

intervals

Results

245.0ms	8000×	body	80	valid
117.0ms	8000×	pre	80	true