Details

Time bar (total: 4.8s)

sample17.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0136
1206
2226
3226

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity sum-log
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
3 → 39
Calls
3 calls:
28.0ms
(+ (+ (* x x) (* y y)) (* z z))
7.0ms
(+ (* x x) (* y y))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
27.0ms
(+ (* x x) (* y y))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify83.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0209340
1959320
23316316
35001315

prune114.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
5.9b
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod
4×add-exp-log flip3-+ sqrt-div sum-log add-cbrt-cube flip-+
3×log-pow
2×+-commutative log-div sqrt-pow1 pow1/2 exp-diff
1×rem-sqrt-square associate-+l+ rem-exp-log
Counts
4 → 61
Calls
4 calls:
28.0ms
(+ (+ (* x x) (* y y)) (* z z))
7.0ms
(+ (* x x) (* y y))
24.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(+ (* x x) (* y y))
102.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify92.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0256553
11030528
23452509
35001501

prune172.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×pow-unpow sqrt-prod
6×cbrt-prod sqrt-div
5×add-log-exp
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube
3×unpow-prod-down rem-sqrt-square pow-pow flip3-+ log-pow flip-+
1×pow-to-exp exp-prod exp-to-pow pow-exp sqr-pow
Counts
4 → 70
Calls
4 calls:
8.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
379.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
107.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
01901221
15591124
219881118
350011114

prune285.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

localize31.0ms

Local error

Found 4 expressions with local error:

6.0b
(pow (pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt 1/2)) (cbrt (log (+ (+ (* x x) (* y y)) (* z z)))))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b
(log (+ (+ (* x x) (* y y)) (* z z)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×unpow-prod-down
8×pow1
7×pow-unpow
6×add-exp-log sqrt-prod
4×cbrt-prod sqrt-div pow-exp add-cbrt-cube add-log-exp
3×log-prod flip3-+ flip-+
2×pow-to-exp rem-sqrt-square log-div sqrt-pow1 pow1/2 log-pow sqr-pow
1×pow-pow rem-log-exp
Counts
4 → 71
Calls
4 calls:
8.0ms
(pow (pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt 1/2)) (cbrt (log (+ (+ (* x x) (* y y)) (* z z)))))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms
(log (+ (+ (* x x) (* y y)) (* z z)))

series1.0s

Counts
4 → 12
Calls
4 calls:
743.0ms
(pow (pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt 1/2)) (cbrt (log (+ (+ (* x x) (* y y)) (* z z)))))
108.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
108.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
68.0ms
(log (+ (+ (* x x) (* y y)) (* z z)))

simplify73.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
02941494
17611427
226071425
350011421

prune357.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

regimes425.0ms

Accuracy

63.8% (6.9b remaining)

Error of 25.0b against oracle of 18.1b and baseline of 37.2b

bsearch54.0ms

Steps
ItersRangePoint
8
2.714157836303516e+105
1.0348580530422823e+110
5.252172480184968e+109
9
-2.7274666728390567e+99
-3.9023604287691996e+93
-9.459978473614104e+97

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample444.0ms

Algorithm
intervals
Results
218.0ms8000×body80valid