Details

sample24.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify62.0ms

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: 16.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
16.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
8.0ms	(* (- x y) (+ x y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
41.0ms	(* (- x y) (+ x y))
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify82.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	419	577
1	2448	504
2	5003	497

prune142.0ms

Filtered

82 candidates to 62 candidates (75.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.2b

Counts

83 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x y) y)
0.0b	(+ (* (- x y) x) (* (- x y) y))
0.0b	(* (- x y) x)
16.4b	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

6.0ms	(* (- x y) y)
7.0ms	(+ (* (- x y) x) (* (- x y) y))
6.0ms	(* (- x y) x)
14.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (- x y) y)
29.0ms	(+ (* (- x y) x) (* (- x y) y))
37.0ms	(* (- x y) x)
49.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

simplify68.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	471	916
1	2250	809
2	5001	803

prune188.0ms

Filtered

111 candidates to 82 candidates (73.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Merged error: 0.2b

Counts

115 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
16.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
16.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
16.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

8.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
57.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
60.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
61.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	318	1178
1	1586	1021
2	5001	985

prune311.0ms

Filtered

123 candidates to 104 candidates (84.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Merged error: 0.2b

Counts

128 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

9.5b	(/ (cbrt (+ (* (- x y) x) (* (- x y) y))) (+ (* x x) (* y y)))
16.7b	(cbrt (+ (* (- x y) x) (* (- x y) y)))
16.7b	(cbrt (+ (* (- x y) x) (* (- x y) y)))
16.7b	(cbrt (+ (* (- x y) x) (* (- x y) y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`associate-*l/`
28×	`cbrt-prod`
24×	`cbrt-div`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
16×	`flip3--` `frac-add` `flip--`
7×	`distribute-lft-out` `associate-/l*`
6×	`add-exp-log` `associate-/l/`
5×	`flip3-+` `add-cbrt-cube` `flip-+`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 105

Calls

4 calls:

13.0ms	(/ (cbrt (+ (* (- x y) x) (* (- x y) y))) (+ (* x x) (* y y)))
7.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))
7.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))
7.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (cbrt (+ (* (- x y) x) (* (- x y) y))) (+ (* x x) (* y y)))
103.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))
105.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))
103.0ms	(cbrt (+ (* (- x y) x) (* (- x y) y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	439	1705
1	1599	1638
2	5002	1621

prune356.0ms

Filtered

117 candidates to 111 candidates (94.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	117	5	122

Merged error: 0.2b

Counts

122 → 5

regimes103.0ms

Accuracy

77.2% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 20.6b

bsearch84.0ms

Steps

Iters	Range	Point
6	2.698812869835215e-164	2.0725235958992727e-163	2.0406396431233693e-163
9	-1.4486783208235192e-156	-9.630569927619713e-165	-1.3530299398450909e-158
8	-2.6676859741206384e+154	-1.133666398063141e+151	-1.2400159933984513e+152

Iters

Range

Point

2.698812869835215e-164

2.0725235958992727e-163

2.0406396431233693e-163

-1.4486783208235192e-156

-9.630569927619713e-165

-1.3530299398450909e-158

-2.6676859741206384e+154

-1.133666398063141e+151

-1.2400159933984513e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	35
1	36	35

end0.0ms

sample620.0ms

Algorithm

intervals

Results

312.0ms	8000×	body	80	valid
154.0ms	8000×	pre	80	true

Details

sample24.0ms

simplify62.0ms

prune2.0ms

localize9.0ms

rewrite26.0ms

series132.0ms

simplify82.0ms

prune142.0ms

localize10.0ms

rewrite37.0ms

series151.0ms

simplify68.0ms

prune188.0ms

localize13.0ms

rewrite47.0ms

series354.0ms

simplify50.0ms

prune311.0ms

localize15.0ms

rewrite37.0ms

series486.0ms

simplify56.0ms

prune356.0ms

regimes103.0ms

bsearch84.0ms

simplify1.0ms

end0.0ms

sample620.0ms

Profiling