Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C

Details

Time bar (total: 1.4s)

analyze10.0ms (0.8%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
75%74.9%25%0.1%0%0%0%5
75%74.9%25%0.1%0%0%0%6
87.5%87.4%12.5%0.1%0%0%0%7
87.5%87.4%12.5%0.1%0%0%0%8
93.8%93.7%6.2%0.1%0%0%0%9
93.8%93.7%6.2%0.1%0%0%0%10
96.9%96.8%3.1%0.1%0%0%0%11
96.9%96.8%3.1%0.1%0%0%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample976.0ms (71.8%)

Results
878.0ms7204×body256valid
88.0ms1052×body256infinite
Bogosity

preprocess26.0ms (1.9%)

Algorithm
2×egg-herbie
Rules
8×associate-/r*
4×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0926
11526
21926
022
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(/.f64 x (*.f64 y 2))
(/.f64 y (*.f64 x 2))
Outputs
(/.f64 x (*.f64 y 2))
(/.f64 y (*.f64 x 2))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify12.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
4×associate-/r*
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11013
21213
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 x (*.f64 y 2))
Outputs
(/.f64 x (*.f64 y 2))

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Accurracy
99.6%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(/.f64 x (*.f64 y 2))
▶99.6%
(/.f64 x (*.f64 y 2))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize23.0ms (1.7%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓99.6%
(/.f64 x (*.f64 y 2))
Compiler

Compiled 14 to 9 computations (35.7% saved)

series3.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
(/.f64 x (*.f64 y 2))
1.0ms
x
@inf
(/.f64 x (*.f64 y 2))
1.0ms
x
@0
(/.f64 x (*.f64 y 2))
0.0ms
y
@inf
(/.f64 x (*.f64 y 2))
0.0ms
x
@-inf
(/.f64 x (*.f64 y 2))

rewrite62.0ms (4.6%)

Algorithm
1×batch-egg-rewrite
Rules
1558×pow1
1444×add-exp-log
1444×log1p-expm1-u
1444×expm1-log1p-u
1414×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
114713
2191213
Stop Event
1×node limit
Counts
1 → 37
Calls
Call 1
Inputs
(/.f64 x (*.f64 y 2))
Outputs
(-.f64 (+.f64 1 (*.f64 x (/.f64 1/2 y))) 1)
(*.f64 x (/.f64 1/2 y))
(*.f64 (*.f64 x (/.f64 1/2 y)) 1)
(*.f64 1 (*.f64 x (/.f64 1/2 y)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1/2 y)))
(*.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1/2 y)))
(*.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) (sqrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (neg.f64 x) (/.f64 1 (*.f64 y -2)))
(*.f64 (/.f64 1/2 y) x)
(*.f64 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (*.f64 y 2)))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (*.f64 y 2)))
(*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))
(*.f64 (/.f64 1 y) (/.f64 x 2))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 x (cbrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 y 2))) (/.f64 x (sqrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 2) (/.f64 (cbrt.f64 x) y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (*.f64 y 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 (sqrt.f64 x) 2) (/.f64 (sqrt.f64 x) y))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (*.f64 y 2))))
(pow.f64 (*.f64 x (/.f64 1/2 y)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 3)
(pow.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) 2)
(pow.f64 (/.f64 y (/.f64 x 2)) -1)
(neg.f64 (/.f64 x (*.f64 y -2)))
(sqrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (/.f64 1/2 y))))
(exp.f64 (log.f64 (*.f64 x (/.f64 1/2 y))))
(log1p.f64 (expm1.f64 (*.f64 x (/.f64 1/2 y))))

simplify51.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
1064×fma-def
808×log-prod
736×distribute-lft-in
730×log-div
524×cube-div
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097841
1236841
2789841
33622841
Stop Event
1×node limit
Counts
61 → 38
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(-.f64 (+.f64 1 (*.f64 x (/.f64 1/2 y))) 1)
(*.f64 x (/.f64 1/2 y))
(*.f64 (*.f64 x (/.f64 1/2 y)) 1)
(*.f64 1 (*.f64 x (/.f64 1/2 y)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1/2 y)))
(*.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1/2 y)))
(*.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) (sqrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (neg.f64 x) (/.f64 1 (*.f64 y -2)))
(*.f64 (/.f64 1/2 y) x)
(*.f64 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (*.f64 y 2)))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (*.f64 y 2)))
(*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))
(*.f64 (/.f64 1 y) (/.f64 x 2))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 x (cbrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 y 2))) (/.f64 x (sqrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 2) (/.f64 (cbrt.f64 x) y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (*.f64 y 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (*.f64 y 2))))
(*.f64 (/.f64 (sqrt.f64 x) 2) (/.f64 (sqrt.f64 x) y))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (*.f64 y 2))))
(pow.f64 (*.f64 x (/.f64 1/2 y)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 3)
(pow.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) 2)
(pow.f64 (/.f64 y (/.f64 x 2)) -1)
(neg.f64 (/.f64 x (*.f64 y -2)))
(sqrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (/.f64 1/2 y))))
(exp.f64 (log.f64 (*.f64 x (/.f64 1/2 y))))
(log1p.f64 (expm1.f64 (*.f64 x (/.f64 1/2 y))))
Outputs
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(-.f64 (+.f64 1 (*.f64 x (/.f64 1/2 y))) 1)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 (*.f64 x (/.f64 1/2 y)) 1)
(*.f64 1/2 (/.f64 x y))
(*.f64 1 (*.f64 x (/.f64 1/2 y)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1/2 y)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 2) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 1/2 (/.f64 x y))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1/2 y)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) (sqrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 1/2 (/.f64 x y))
(*.f64 (neg.f64 x) (/.f64 1 (*.f64 y -2)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1/2 y) x)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (*.f64 y 2)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (*.f64 y 2)))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1 y) (/.f64 x 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 x (cbrt.f64 (*.f64 y 2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 y 2))) (/.f64 x (sqrt.f64 (*.f64 y 2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 2) (/.f64 (cbrt.f64 x) y))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (cbrt.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (*.f64 y 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (*.f64 y 2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (sqrt.f64 x) 2) (/.f64 (sqrt.f64 x) y))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 y 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (*.f64 y 2))))
(*.f64 1/2 (/.f64 x y))
(pow.f64 (*.f64 x (/.f64 1/2 y)) 1)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 x (/.f64 1/2 y))) 3)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3) 1/3)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 y))) 2)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (/.f64 y (/.f64 x 2)) -1)
(*.f64 1/2 (/.f64 x y))
(neg.f64 (/.f64 x (*.f64 y -2)))
(*.f64 1/2 (/.f64 x y))
(sqrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 2))
(*.f64 1/2 (/.f64 x y))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 x (/.f64 1/2 y)) 3))
(*.f64 1/2 (/.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 1/2 (/.f64 x y))
(exp.f64 (log.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 1/2 (/.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 x (/.f64 1/2 y))))
(*.f64 1/2 (/.f64 x y))

eval8.0ms (0.6%)

Compiler

Compiled 373 to 249 computations (33.2% saved)

prune6.0ms (0.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New37138
Fresh000
Picked101
Done000
Total38139
Accurracy
100.0%
Counts
39 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (/.f64 x y) 1/2)
▶100.0%
(*.f64 (/.f64 x y) 1/2)
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize76.0ms (5.6%)

Compiler

Compiled 14 to 7 computations (50% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Accurracy
100.0%
Counts
1 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (/.f64 x y) 1/2)
Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes12.0ms (0.9%)

Accuracy

Total -0.2b remaining (-∞%)

Threshold costs -0.2b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 (/.f64 x y) 1/2)
(/.f64 x (*.f64 y 2))
Outputs
(*.f64 (/.f64 x y) 1/2)
Calls

4 calls:

4.0ms
y
3.0ms
(*.f64 y 2)
3.0ms
x
2.0ms
(/.f64 x (*.f64 y 2))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(/.f64 x (*.f64 y 2))
100.0%1(*.f64 y 2)
Compiler

Compiled 30 to 21 computations (30% saved)

simplify4.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
1813
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 x y) 1/2)
Outputs
(*.f64 (/.f64 x y) 1/2)
Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness63.0ms (4.6%)

Rules
1558×pow1
1444×add-exp-log
1444×log1p-expm1-u
1444×expm1-log1p-u
1414×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
114713
2191213
Stop Event
1×node limit
Compiler

Compiled 24 to 14 computations (41.7% saved)

end25.0ms (1.8%)

Compiler

Compiled 28 to 20 computations (28.6% saved)

Profiling

Loading profile data...