Details

Time bar (total: 4.8s)

sample54.0ms

Algorithm
intervals
Results
23.0ms56×body1280valid
8.0ms33×body640valid
7.0ms131×body80valid
4.0ms22×body320valid
2.0ms14×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1115

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
2×*-commutative
1×+-commutative flip3-+ flip-+
Counts
3 → 5
Calls
3 calls:
4.0ms
(+ (* x (sin y)) (* z (cos y)))
2.0ms
(* z (cos y))
6.0ms
(* x (sin y))

series147.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(+ (* x (sin y)) (* z (cos y)))
35.0ms
(* z (cos y))
38.0ms
(* x (sin y))

simplify223.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06758
119858
255158
3103558
4180558
5403458
6500158

prune29.0ms

Filtered
14 candidates to 9 candidates (64.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New13114
Fresh000
Picked011
Done000
Total13215

Merged error: 0.1b

Counts
15 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* x (sin y)) 3)
1.0b
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
2.3b
(+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3))
38.8b
(/ (+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3)) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-+l+ flip3-+ flip-+
2×+-commutative distribute-rgt-in sub-neg unpow-prod-down distribute-lft-in associate-/r/ sum-cubes associate-/l/
1×pow-to-exp frac-2neg unpow3 clear-num *-commutative div-inv associate-/l* sqr-pow
Counts
4 → 24
Calls
4 calls:
3.0ms
(pow (* x (sin y)) 3)
15.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
7.0ms
(+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3))
20.0ms
(/ (+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3)) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (* x (sin y)) 3)
105.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
166.0ms
(+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3))
224.0ms
(/ (+ (pow (* x (sin y)) 3) (pow (* z (cos y)) 3)) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0266476
11146466
25002456

prune141.0ms

Filtered
36 candidates to 28 candidates (77.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New33336
Fresh000
Picked101
Done011
Total34438

Merged error: 0.1b

Counts
38 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
2.3b
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
8.9b
(* (pow x 3) (pow (sin y) 3))
38.8b
(/ (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
5×pow-prod-down
4×associate-+l+ flip3-+ flip-+ sqr-pow
2×+-commutative distribute-rgt-in pow-to-exp sub-neg distribute-lft-in unpow3 associate-*r* associate-*l* associate-/r/ sum-cubes associate-/l/
1×frac-2neg prod-exp clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 27
Calls
4 calls:
21.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
11.0ms
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
4.0ms
(* (pow x 3) (pow (sin y) 3))
25.0ms
(/ (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

series567.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
167.0ms
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
73.0ms
(* (pow x 3) (pow (sin y) 3))
221.0ms
(/ (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0295537
11335512
25001496

prune165.0ms

Filtered
39 candidates to 30 candidates (76.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New38139
Fresh112
Picked101
Done011
Total40343

Merged error: 0.1b

Counts
43 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
2.3b
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
8.9b
(* (pow x 3) (pow (sin y) 3))
38.8b
(* (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (/ 1 (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
7×flip3-+ flip-+
6×frac-times
5×associate-*r* pow-prod-down
4×associate-+l+ clear-num sqr-pow
3×frac-2neg associate-*r/ associate-*l*
2×+-commutative distribute-rgt-in pow-to-exp sub-neg distribute-lft-in unpow3 associate-*l/ associate-/r/ un-div-inv sum-cubes *-commutative
1×prod-exp div-inv unswap-sqr
Counts
4 → 37
Calls
4 calls:
15.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
11.0ms
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
4.0ms
(* (pow x 3) (pow (sin y) 3))
25.0ms
(* (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (/ 1 (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))
167.0ms
(+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3)))
68.0ms
(* (pow x 3) (pow (sin y) 3))
229.0ms
(* (+ (* (pow x 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow z 3))) (/ 1 (+ (* (* z (cos y)) (- (* z (cos y)) (* x (sin y)))) (* (* x (sin y)) (* x (sin y))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0341795
11751746
25002729

prune202.0ms

Filtered
49 candidates to 35 candidates (71.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New49049
Fresh011
Picked011
Done011
Total49352

Merged error: 0.1b

Counts
52 → 3

regimes98.0ms

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)

IterNodesCost
0115
1115

end0.0ms

sample1.6s

Algorithm
intervals
Results
628.0ms1497×body1280valid
329.0ms1267×body640valid
234.0ms4256×body80valid
117.0ms656×body320valid
42.0ms324×body160valid