Details

sample53.0ms

Algorithm

intervals

Results

22.0ms	56×	body	1280	valid
8.0ms	33×	body	640	valid
7.0ms	131×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

prune3.0ms

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (cos y)) (* z (sin y)))
0.1b	(* x (cos y))
0.1b	(* z (sin y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

2×	`*-commutative`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

3 → 5

Calls

3 calls:

4.0ms	(+ (* x (cos y)) (* z (sin y)))
2.0ms	(* x (cos y))
3.0ms	(* z (sin y))

series143.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* x (cos y)) (* z (sin y)))
35.0ms	(* x (cos y))
42.0ms	(* z (sin y))

simplify223.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	56
1	196	56
2	549	56
3	1033	56
4	1803	56
5	4032	56
6	5001	56

prune23.0ms

Filtered

14 candidates to 8 candidates (57.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.1b

Counts

15 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
2.4b	(+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
38.4b	(/ (+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `flip3-+` `flip-+`
2×	`+-commutative` `associate-r/` `associate-l` `associate-/r/` `sum-cubes` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv` `associate-/l*`

Counts

4 → 28

Calls

4 calls:

14.0ms	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
7.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
6.0ms	(+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
20.0ms	(/ (+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
106.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
174.0ms	(+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
189.0ms	(/ (+ (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	276	542
1	1193	527
2	5001	519

prune141.0ms

Filtered

40 candidates to 29 candidates (72.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	37	5	42

Merged error: 0.1b

Counts

42 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
38.4b	(/ (* (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

8×	`flip3-+` `flip-+` `associate-/l/`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
5×	`*-commutative`
4×	`frac-times` `associate-+l+` `associate-l`
2×	`flip3--` `associate-l/` `associate-/r/` `flip--` `associate-/l`
1×	`+-commutative` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 40

Calls

4 calls:

15.0ms	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
7.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
7.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
36.0ms	(/ (* (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
107.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
106.0ms	(* (* z (sin y)) (- (* z (sin y)) (* x (cos y))))
79.0ms	(/ (* (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (- (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	321	903
1	1640	830
2	5001	804

prune213.0ms

Filtered

52 candidates to 39 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	53	4	57

Merged error: 0.1b

Counts

57 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2)))
2.1b	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
2.1b	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
28.9b	(/ (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
4×	`associate-+l+` `associate-r/` `associate-l` `-commutative`
3×	`flip3-+` `flip-+`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`+-commutative` `frac-2neg` `*-inverses` `clear-num` `div-inv`

Counts

4 → 33

Calls

4 calls:

13.0ms	(+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2)))
8.0ms	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
8.0ms	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
31.0ms	(/ (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2)))
153.0ms	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
158.0ms	(* (* (sin y) z) (- (* (sin y) z) (* x (cos y))))
4.0ms	(/ (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (+ (* (* (sin y) z) (- (* (sin y) z) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	189	546
1	850	491
2	5002	473

prune138.0ms

Filtered

45 candidates to 27 candidates (60.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	42	7	49

Merged error: 0.1b

Counts

49 → 7

regimes172.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

609.0ms	1497×	body	1280	valid
332.0ms	1267×	body	640	valid
226.0ms	4256×	body	80	valid
114.0ms	657×	body	320	valid
38.0ms	323×	body	160	valid