Details

Time bar (total: 3.9s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

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: 40.2b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u fma-def associate-/r* sum-log log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 76
Calls
3 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series254.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
53.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
166.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify125.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
0272784
11063695
24582674
35001673

prune231.0ms

Filtered
85 candidates to 71 candidates (83.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New79685
Fresh000
Picked101
Done000
Total80686

Merged error: 17.3b

Counts
86 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (* z z))
0.1b
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
37.3b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×sqrt-pow1 pow-prod-down
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 45
Calls
3 calls:
1.0ms
(fma y y (* z z))
3.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
3.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series269.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(fma y y (* z z))
60.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
176.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0137272
1541235
22831235
35001235

prune109.0ms

Filtered
54 candidates to 37 candidates (68.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New54054
Fresh055
Picked011
Done000
Total54660

Merged error: 17.3b

Counts
60 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y y (* z z))
0.1b
(/ 1 (/ 3.0 (fma x x (fma y y (* z z)))))
0.4b
(/ 3.0 (fma x x (fma y y (* z z))))
37.3b
(sqrt (/ 1 (/ 3.0 (fma x x (fma y y (* z z))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
98×add-sqr-sqrt
91×*-un-lft-identity
89×add-cube-cbrt
44×sqrt-prod
17×add-exp-log
16×associate-/r*
11×add-cbrt-cube
10×div-inv
8×div-exp
7×pow1
6×associate-/l*
5×rem-sqrt-square
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1
2×rec-exp pow-flip frac-2neg 1-exp clear-num associate-/r/ inv-pow
1×pow1/2 sqrt-div fma-udef
Counts
4 → 180
Calls
4 calls:
1.0ms
(fma y y (* z z))
6.0ms
(/ 1 (/ 3.0 (fma x x (fma y y (* z z)))))
5.0ms
(/ 3.0 (fma x x (fma y y (* z z))))
7.0ms
(sqrt (/ 1 (/ 3.0 (fma x x (fma y y (* z z))))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma y y (* z z))
61.0ms
(/ 1 (/ 3.0 (fma x x (fma y y (* z z)))))
61.0ms
(/ 3.0 (fma x x (fma y y (* z z))))
177.0ms
(sqrt (/ 1 (/ 3.0 (fma x x (fma y y (* z z))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04541885
118151694
250031513

prune310.0ms

Filtered
192 candidates to 102 candidates (53.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1920192
Fresh044
Picked011
Done011
Total1926198

Merged error: 17.3b

Counts
198 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
152×sqrt-prod
124×add-sqr-sqrt
84×times-frac
55×*-un-lft-identity
47×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
11×pow1
9×sqrt-div
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down div-inv
2×flip3-+ flip-+ hypot-def
1×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 166
Calls
4 calls:
7.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
26.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
169.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify71.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04033047
113642901
250012851

prune435.0ms

Filtered
178 candidates to 119 candidates (66.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1780178
Fresh033
Picked011
Done022
Total1786184

Merged error: 17.3b

Counts
184 → 6

regimes382.0ms

Accuracy

54.1% (9.0b remaining)

Error of 26.9b against oracle of 17.9b and baseline of 37.5b

bsearch110.0ms

Steps
ItersRangePoint
9
3.49360888869625e+131
3.351355619502645e+138
4.9296672245653324e+135
7
-5.530494810296786e-229
-3.8841983415636587e-231
-4.6992675325234154e-229
6
-2.612645209590514e-104
-5.091613400763011e-105
-5.1573652837714696e-105
4
-2.515916130415698e+129
-1.8012913134826672e+129
-2.0469435943033968e+129

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13717
23717

end0.0ms

sample454.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid