Details

Time bar (total: 15.0s)

sample48.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
12.0ms256×body80nan

simplify59.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01114
12212
24411
36411
46911
57011
done7011

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ (* x y) (* x z))
1.4b
(+ (+ (* x y) (* x z)) (* y z))
19.5b
(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
6×add-sqr-sqrt
5×add-cube-cbrt fma-def *-un-lft-identity
4×pow1 sum-log
3×add-exp-log expm1-log1p-u flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative sqrt-div distribute-lft-out
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
3 → 51
Calls
3 calls:
15.0ms
(+ (* x y) (* x z))
57.0ms
(+ (+ (* x y) (* x z)) (* y z))
54.0ms
(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series258.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ (* x y) (* x z))
34.0ms
(+ (+ (* x y) (* x z)) (* y z))
176.0ms
(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify914.0ms

Counts
60 → 60
Iterations

Useful iterations: done (912.0ms)

IterNodesCost
092853
1275652
21070584
done5001573

prune216.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (fma x z (* y (+ z x)))))
0.5b
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
19.5b
(sqrt (fma x z (* y (+ z x))))
19.5b
(sqrt (fma x z (* y (+ z x))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square log1p-expm1-u add-log-exp
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
3.0ms
(sqrt (sqrt (fma x z (* y (+ z x)))))
28.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
2.0ms
(sqrt (fma x z (* y (+ z x))))
2.0ms
(sqrt (fma x z (* y (+ z x))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(sqrt (sqrt (fma x z (* y (+ z x)))))
136.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (sqrt (sqrt (fma x z (* y (+ z x))))))
131.0ms
(sqrt (fma x z (* y (+ z x))))
143.0ms
(sqrt (fma x z (* y (+ z x))))

simplify1.5s

Counts
140 → 140
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01252876
12771784
211381641
done50001603

prune369.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (* (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) (sqrt (sqrt (sqrt (fma x z (* y (+ z x))))))))
19.5b
(sqrt (fma x z (* y (+ z x))))
19.5b
(sqrt (fma x z (* y (+ z x))))
19.5b
(sqrt (fma x z (* y (+ z x))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
141×sqrt-pow1
66×pow1
51×pow1/2
50×pow-prod-up
24×sqrt-prod
19×add-sqr-sqrt
11×pow-prod-down
10×add-cube-cbrt *-un-lft-identity pow-sqr
9×add-exp-log associate-*l* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square swap-sqr prod-exp cbrt-unprod unswap-sqr
2×sqrt-unprod
1×associate-*r* *-commutative
Counts
4 → 112
Calls
4 calls:
109.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (* (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) (sqrt (sqrt (sqrt (fma x z (* y (+ z x))))))))
2.0ms
(sqrt (fma x z (* y (+ z x))))
2.0ms
(sqrt (fma x z (* y (+ z x))))
2.0ms
(sqrt (fma x z (* y (+ z x))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (sqrt (sqrt (fma x z (* y (+ z x))))) (* (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) (sqrt (sqrt (sqrt (fma x z (* y (+ z x))))))))
127.0ms
(sqrt (fma x z (* y (+ z x))))
118.0ms
(sqrt (fma x z (* y (+ z x))))
119.0ms
(sqrt (fma x z (* y (+ z x))))

simplify2.7s

Counts
124 → 124
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01292636
13231274
27701118
336711090
done50001078

prune499.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 20.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3) (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))))
0.7b
(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
19.5b
(sqrt (fma x z (* y (+ z x))))
19.5b
(sqrt (fma x z (* y (+ z x))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
204×sqrt-prod
106×add-sqr-sqrt
40×unpow-prod-down cube-prod unswap-sqr
30×associate-*l*
28×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×pow1 sqrt-pow1
10×add-exp-log
7×pow-pow add-cbrt-cube
6×sqr-pow
5×pow1/2
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp rem-sqrt-square unpow3 pow-exp
1×pow-plus *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 178
Calls
4 calls:
95.0ms
(* (pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3) (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))))
14.0ms
(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
3.0ms
(sqrt (fma x z (* y (+ z x))))
3.0ms
(sqrt (fma x z (* y (+ z x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3) (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))))
496.0ms
(pow (sqrt (sqrt (sqrt (fma x z (* y (+ z x)))))) 3)
178.0ms
(sqrt (fma x z (* y (+ z x))))
175.0ms
(sqrt (fma x z (* y (+ z x))))

simplify2.0s

Counts
190 → 190
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02065420
16043876
223513677
done50003279

prune708.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 20.5b

regimes376.0ms

Accuracy

0% (0.1b remaining)

Error of 20.2b against oracle of 20.1b and baseline of 20.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11714
done1714

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s8064×body80nan
693.0ms8000×body80valid