Details

Time bar (total: 5.5s)

sample18.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

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: 37.6b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 58
Calls
2 calls:
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series213.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify99.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0223655
1877586
23651577
35001577

prune197.0ms

Filtered
64 candidates to 55 candidates (85.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New57764
Fresh000
Picked101
Done000
Total58765

Merged error: 17.4b

Counts
65 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.7b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
532×times-frac
424×sqrt-prod
295×add-sqr-sqrt
274×add-cube-cbrt *-un-lft-identity
33×sqrt-div
28×associate-/r/
24×associate-/r*
16×flip3-+ flip-+
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×hypot-def associate-/l/
1×frac-2neg clear-num
Counts
4 → 397
Calls
4 calls:
18.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
25.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
8.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
184.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
95.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify147.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
086711029
1365810267
250019988

prune823.0ms

Filtered
409 candidates to 203 candidates (49.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New4072409
Fresh246
Picked101
Done000
Total4106416

Merged error: 17.4b

Counts
416 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
34.7b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square hypot-def associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 116
Calls
4 calls:
9.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
16.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
9.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series900.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
451.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
124.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify62.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
02581610
16861532
221711508
350011493

prune378.0ms

Filtered
128 candidates to 92 candidates (71.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1280128
Fresh055
Picked011
Done000
Total1286134

Merged error: 17.4b

Counts
134 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
75×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
25×associate-*l*
16×sqrt-div
12×unswap-sqr
11×pow1
9×associate-*r*
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×pow-prod-down
2×frac-times associate-*r/ hypot-def div-inv
1×sqrt-unprod associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 140
Calls
4 calls:
7.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
20.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
166.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify138.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03542242
111632177
247692159
350012159

prune443.0ms

Filtered
152 candidates to 109 candidates (71.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1520152
Fresh044
Picked011
Done011
Total1526158

Merged error: 17.4b

Counts
158 → 6

regimes354.0ms

Accuracy

64.5% (6.7b remaining)

Error of 24.8b against oracle of 18.1b and baseline of 37.1b

bsearch87.0ms

Steps
ItersRangePoint
8
4.6926641391142656e+86
5.0018524994459073e+89
2.1452959828457685e+89
10
-1.7063783991581126e+128
-7.490667611783549e+116
-1.0510217824479294e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03325
13925
23925

end0.0ms

sample452.0ms

Algorithm
intervals
Results
281.0ms8000×body80valid