Details

Time bar (total: 13.6s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33012
done3012

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 90
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series315.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x x) (* y y))
39.0ms
(+ (+ (* x x) (* y y)) (* z z))
64.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
182.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.2s

Counts
102 → 102
Iterations

Useful iterations: 3 (817.0ms)

IterNodesCost
01471805
13441579
211471360
345231348
done50011348

prune355.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b
(sqrt (fma z z (fma x x (* y y))))
35.2b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
508×times-frac
400×sqrt-prod
286×add-sqr-sqrt
266×add-cube-cbrt *-un-lft-identity
22×associate-/r*
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
5×sqrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×frac-2neg clear-num hypot-def
Counts
4 → 368
Calls
4 calls:
29.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
34.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y))))))
111.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
121.0ms
(sqrt (fma z z (fma x x (* y y))))
161.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (fma z z (fma x x (* y y)))))))

simplify1.1s

Counts
380 → 380
Iterations

Useful iterations: 2 (423.0ms)

IterNodesCost
047117645
183814758
2268413110
done500013110

prune780.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* y y))
0.2b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
35.2b
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l*
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod fma-udef
Counts
4 → 158
Calls
4 calls:
0.0ms
(fma x x (* y y))
3.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
45.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
8.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
43.0ms
(fma x x (* y y))
159.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
388.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
410.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

simplify1.9s

Counts
170 → 170
Iterations

Useful iterations: 3 (709.0ms)

IterNodesCost
02143977
13483796
28113605
322763601
done50003601

prune665.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* y y))
0.2b
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
0.2b
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
35.2b
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
526×times-frac
405×sqrt-prod
296×add-sqr-sqrt
279×add-cube-cbrt *-un-lft-identity
25×associate-/l*
16×div-inv
12×associate-/r*
11×add-exp-log add-cbrt-cube
7×rem-sqrt-square
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×sqrt-pow1 pow1/2 sqrt-div fma-udef associate-/l/
Counts
4 → 383
Calls
4 calls:
0.0ms
(fma x x (* y y))
7.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
12.0ms
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
23.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

series696.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma x x (* y y))
157.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
228.0ms
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
271.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

simplify2.1s

Counts
395 → 395
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
044412046
175711015
2146510399
3385310231
done500010231

prune791.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.1b

regimes222.0ms

Accuracy

38.9% (19.2b remaining)

Error of 25.8b against oracle of 6.6b and baseline of 38.1b

bsearch92.0ms

Steps
ItersRangePoint
9
6.367322558950871e+56
2.9131270869485945e+65
2.8539710068846394e+65
8
-6.818135621868607e+134
-9.818251175618728e+131
-2.2291282360035104e+133

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02843
13343
done3343

end0.0ms

sample432.0ms

Algorithm
intervals
Results
265.0ms8000×body80valid