Details

Time bar (total: 3.6s)

sample28.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite47.0ms

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×rem-sqrt-square 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 → 54
Calls
2 calls:
31.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series217.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
168.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify95.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0214630
1835578
23408576
35001574

prune171.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
9×sqrt-div
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×frac-times associate-*l/ add-log-exp
1×rem-sqrt-square sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 64
Calls
2 calls:
38.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series266.0ms

Counts
2 → 6
Calls
2 calls:
166.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify69.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0235788
1772762
22635738
35001725

prune176.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×flip3-+ flip-+ associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 78
Calls
2 calls:
22.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series332.0ms

Counts
2 → 6
Calls
2 calls:
228.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
103.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
02111118
16251058
222891035
350011035

prune184.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ z (sqrt 3.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
3.0ms
(/ z (sqrt 3.0))

series55.0ms

Counts
1 → 3
Calls
1 calls:
55.0ms
(/ z (sqrt 3.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 4 (43.0ms)

IterNodesCost
0103217
1273207
2729197
32027197
45001196

prune66.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.2b

regimes731.0ms

Accuracy

48.4% (13.6b remaining)

Error of 26.0b against oracle of 12.4b and baseline of 38.7b

bsearch168.0ms

Steps
ItersRangePoint
8
1.615910537420553e+115
8.280947652240643e+119
2.751658734007154e+118
6
7.0711602144254375e-276
4.3595580037837793e-275
2.3864141824080956e-275
7
-6.663366823115115e-209
-6.756501829647374e-211
-6.0707960974712676e-210
8
-2.1540843402859687e+101
-1.5690527451835986e+98
-5.787460784782642e+99

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05140
15340
25340

end0.0ms

sample732.0ms

Algorithm
intervals
Results
566.0ms8000×body80valid