Details

sample25.0ms

Algorithm

intervals

Results

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

simplify60.0ms

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

prune3.0ms

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: 20.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

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)))

series19.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (* x x) (* y y))
10.0ms	(/ (* (- 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

prune265.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 0.5b

Counts

49 → 6

localize11.0ms

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)))))
19.1b	(sqrt (+ (* x x) (* y y)))
19.1b	(sqrt (+ (* x x) (* y y)))

rewrite61.0ms

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:

8.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
36.0ms	(* (/ (- 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)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify77.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (52.0ms)

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

prune144.0ms

Filtered

124 candidates to 195 candidates (-57.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	195	6	201

Merged error: 0.5b

Counts

201 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
0.0b	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
19.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
7.0ms	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
3.0ms	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
16.0ms	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
22.0ms	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	427	896
1	2457	791
2	5003	778

prune155.0ms

Filtered

77 candidates to 98 candidates (-27.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	98	6	104

Merged error: 0.5b

Counts

104 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.1b	(sqrt (+ (* x x) (* y y)))
19.1b	(sqrt (+ (* x x) (* y y)))
19.2b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
7×	`flip3-+` `flip-+`
6×	`pow1` `times-frac` `sqrt-div` `associate-/r*` `add-log-exp`
4×	`frac-times`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `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

4 → 78

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
6.0ms	(sqrt (+ (* x x) (* y y)))
6.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	345	684
1	1862	623
2	5001	616

prune98.0ms

Filtered

71 candidates to 90 candidates (-26.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	90	6	96

Merged error: 0.5b

Counts

96 → 6

regimes176.0ms

Accuracy

77.9% (4.4b remaining)

Error of 4.8b against oracle of 0.4b and baseline of 20.2b

bsearch77.0ms

Steps

Iters	Range		Point
10	1.211779747825994e-162	8.485300749516754e-149	1.2367394671873183e-162
8	1.1002355988166576e-179	1.9074193437639713e-175	1.8726660580882805e-175
9	-4.640980256977705e-167	-7.244607658235542e-175	-4.55507949107551e-167
8	-1.0234011842733718e-159	-5.745295285057345e-164	-5.841240397320597e-164
11	-5.400427999982575e+167	-1.3370939268532223e+147	-8.159830827848389e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample665.0ms

Algorithm

intervals

Results

288.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

sample25.0ms

simplify60.0ms

prune3.0ms

localize8.0ms

rewrite16.0ms

series19.0ms

simplify42.0ms

prune265.0ms

localize11.0ms

rewrite61.0ms

series35.0ms

simplify77.0ms

prune144.0ms

localize15.0ms

rewrite28.0ms

series54.0ms

simplify56.0ms

prune155.0ms

localize13.0ms

rewrite25.0ms

series30.0ms

simplify45.0ms

prune98.0ms

regimes176.0ms

bsearch77.0ms

simplify1.0ms

end0.0ms

sample665.0ms

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