Details

Time bar (total: 3.9s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

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:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series166.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(+ (* x x) (* y y))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify87.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0209340
1959320
23316316
35001315

prune129.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.5b
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
14.0ms
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
70.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
107.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify52.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02511459
110021362
250011331

prune288.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.3b

localize15.0ms

Local error

Found 4 expressions with local error:

28.7b
(cbrt (+ (* x x) (* y y)))
28.7b
(cbrt (+ (* x x) (* y y)))
28.7b
(cbrt (+ (* x x) (* y y)))
33.6b
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
2.0ms
(cbrt (+ (* x x) (* y y)))
2.0ms
(cbrt (+ (* x x) (* y y)))
2.0ms
(cbrt (+ (* x x) (* y y)))
56.0ms
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (+ (* x x) (* y y)))
94.0ms
(cbrt (+ (* x x) (* y y)))
95.0ms
(cbrt (+ (* x x) (* y y)))
108.0ms
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify72.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0201739
1622690
22121690
35003689

prune223.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.3b

localize20.0ms

Local error

Found 4 expressions with local error:

33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify98.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 4 (92.0ms)

IterNodesCost
090572
1275552
2951552
33615552
45002548

prune280.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 16.3b

regimes394.0ms

Accuracy

55.3% (8.6b remaining)

Error of 27.0b against oracle of 18.4b and baseline of 37.8b

bsearch110.0ms

Steps
ItersRangePoint
9
4.425494315758786e+67
1.2216548257337095e+75
1.199826361110612e+75
9
5.3983651447771314e+42
4.003892320803535e+50
5.4695075101521495e+42
9
2.116861950278137e-44
1.6968575466374542e-37
1.4232710093281964e-37
5
-3.768557111860464e+133
-1.2841116935308668e+133
-2.016424411749676e+133

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
12713

end0.0ms

sample423.0ms

Algorithm
intervals
Results
248.0ms8000×body80valid