Details

analyze14.0ms

Algorithm

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

sample26.0ms

Algorithm

intervals

Results

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

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune8.0ms

Filtered

1 candidates to 1 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: 18.9b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
19.0b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite27.0ms

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:

9.0ms	(* (- x y) (+ x y))
4.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series22.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (- x y) (+ x y))
5.0ms	(+ (* x x) (* y y))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5602	1026

prune91.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Merged error: 0.3b

Counts

84 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3))
0.0b	(pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3)
0.1b	(* (/ (+ x y) (+ (* x x) (* y y))) (- x y))
18.5b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-l`
17×	`add-exp-log` `add-cbrt-cube`
10×	`cube-div`
9×	`pow1`
8×	`cbrt-prod`
7×	`distribute-lft-out`
6×	`frac-times` `flip3--` `associate-*r/` `flip--`
5×	`cbrt-div` `associate-r`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `associate-l/` `pow-exp` `associate-/r` `flip-+` `rem-cube-cbrt`
2×	`cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `div-inv` `associate-/l/` `unswap-sqr` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `pow1/3` `clear-num` `*-commutative` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 131

Calls

4 calls:

3.0ms	(cbrt (pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3))
15.0ms	(pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3)
15.0ms	(* (/ (+ x y) (+ (* x x) (* y y))) (- x y))
8.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3))
13.0ms	(pow (* (/ (+ x y) (+ (* x x) (* y y))) (- x y)) 3)
10.0ms	(* (/ (+ x y) (+ (* x x) (* y y))) (- x y))
7.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify33.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5092	2340

prune164.0ms

Filtered

102 candidates to 143 candidates (-40.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	143	5	148

Merged error: 0.3b

Counts

148 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(- (* x x) (* y y))
19.0b	(/ (- (* x x) (* y y)) (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
4×	`associate-/l*`
3×	`pow1` `associate-/r*`
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 → 59

Calls

3 calls:

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

series20.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
5.0ms	(- (* x x) (* y y))
9.0ms	(/ (- (* x x) (* y y)) (+ (* x x) (* y y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5201	1044

prune69.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 0.3b

Counts

73 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
18.5b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
15.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
8.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series22.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
7.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5317	1452

prune74.0ms

Filtered

69 candidates to 98 candidates (-42.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	98	5	103

Merged error: 0.3b

Counts

103 → 5

regimes110.0ms

Accuracy

78.3% (4.3b remaining)

Error of 4.8b against oracle of 0.4b and baseline of 20.5b

bsearch33.0ms

Steps

Iters	Range	Point
8	6.33830383506783e-172	1.99495145509404e-169	1.9735231634376482e-169
6	-9.671282779081546e-161	-1.575773035466551e-161	-1.5937452839923381e-161
7	-2.02585762581295e+154	-7.771465008136436e+152	-1.3297178600730637e+154

Iters

Range

Point

6.33830383506783e-172

1.99495145509404e-169

1.9735231634376482e-169

-9.671282779081546e-161

-1.575773035466551e-161

-1.5937452839923381e-161

-2.02585762581295e+154

-7.771465008136436e+152

-1.3297178600730637e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample594.0ms

Algorithm

intervals

Results

309.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

analyze14.0ms

sample26.0ms

simplify120.0ms

prune8.0ms

localize9.0ms

rewrite27.0ms

series22.0ms

simplify40.0ms

prune91.0ms

localize12.0ms

rewrite46.0ms

series43.0ms

simplify33.0ms

prune164.0ms

localize7.0ms

rewrite17.0ms

series20.0ms

simplify48.0ms

prune69.0ms

localize9.0ms

rewrite29.0ms

series22.0ms

simplify41.0ms

prune74.0ms

regimes110.0ms

bsearch33.0ms

simplify1.0ms

end0.0ms

sample594.0ms

Profiling