The quadratic formula (r2)

Time bar (total: 5.4s)

analyze130.0ms (2.4%)

Memory
-13.9MiB live, 53.9MiB allocated
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
0%0%99.9%0.1%0%0%0%3
25%25%74.9%0.1%0%0%0%4
37.5%37.4%62.4%0.1%0%0%0%5
37.5%37.4%62.4%0.1%0%0%0%6
40%37.4%56.2%0.1%0%6.2%0%7
48.3%45.2%48.4%0.1%0%6.2%0%8
53%48.4%42.9%0.1%0%8.6%0%9
58.1%50.3%36.3%0.1%0%13.3%0%10
66.1%56.8%29.1%0.1%0%14%0%11
70.4%58.8%24.7%0.1%0%16.4%0%12
Compiler

Compiled 40 to 31 computations (22.5% saved)

sample4.9s (92.5%)

Memory
-81.6MiB live, 1 608.7MiB allocated
Samples
967.0ms1 960×2valid-baseline
488.0ms5 501×0valid-baseline
459.0ms5 501×0valid-rival
420.0ms5 501×0valid-sollya
399.0ms1 960×2valid-rival
274.0ms1 960×2valid-sollya
242.0ms793×1valid-baseline
117.0ms793×1valid-rival
75.0ms793×1valid-sollya
0.0ms1×0valid-rival+baseline-real
Precisions
Click to see Rival histograms. Total time spent on operations: 783.0ms
ival-mult: 283.0ms (36.2% of total)
ival-sub: 119.0ms (15.2% of total)
ival-div: 115.0ms (14.7% of total)
ival-sqrt: 115.0ms (14.7% of total)
ival-neg: 72.0ms (9.2% of total)
adjust: 57.0ms (7.3% of total)
ival-true: 9.0ms (1.1% of total)
...in/eval/compile.rkt:76:19: 8.0ms (1% of total)
ival-assert: 4.0ms (0.5% of total)
Precisions
Click to see Base histograms. Total time spent on operations: 1.1s
ival-mult: 507.0ms (44.8% of total)
ival-sub: 193.0ms (17.1% of total)
ival-sqrt: 156.0ms (13.8% of total)
ival-div: 146.0ms (12.9% of total)
ival-neg: 97.0ms (8.6% of total)
const: 31.0ms (2.7% of total)
Bogosity

preprocess240.0ms (4.5%)

Memory
-6.7MiB live, 25.7MiB allocated
Algorithm
1×egg-herbie
Rules
1 892×fmm-def
379×fma-define
366×sub-neg
364×div-sub
282×associate-/r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
067779
1216723
2635691
32137671
45143671
56383671
66739671
76871671
86910671
97064671
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 a) c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a (neg.f64 c)))))) (*.f64 #s(literal 2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 a) c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a))))
(neg.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a)))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a (neg.f64 c)))))) (*.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (*.f64 a a) (*.f64 #s(literal 4 binary64) (*.f64 b c))))) (*.f64 #s(literal 2 binary64) b))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 c a))))) (*.f64 #s(literal 2 binary64) c))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (*.f64 c c) (*.f64 #s(literal 4 binary64) (*.f64 a b))))) (*.f64 #s(literal 2 binary64) a))
Outputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) c) a)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) c) a)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 a) c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (*.f64 b b) (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal 1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) c) a)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) (*.f64 a #s(literal -2 binary64)))
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) (/.f64 #s(literal -1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a (neg.f64 c)))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (*.f64 b b) (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 a) c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (*.f64 b b) (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) c) a)))) (*.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal -2 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) a))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) a) #s(literal 1/2 binary64))
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a (neg.f64 c)))))) (*.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (*.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (*.f64 b b) (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal 1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (*.f64 a a) (*.f64 #s(literal 4 binary64) (*.f64 b c))))) (*.f64 #s(literal 2 binary64) b))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (+.f64 (*.f64 a a) (*.f64 #s(literal -4 binary64) (*.f64 b c))))) (*.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (*.f64 (*.f64 #s(literal -4 binary64) b) c)))) (*.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (*.f64 c (*.f64 b #s(literal -4 binary64)))))) (*.f64 b #s(literal 2 binary64)))
(/.f64 (/.f64 (+.f64 a (sqrt.f64 (fma.f64 a a (*.f64 c (*.f64 b #s(literal -4 binary64)))))) #s(literal -2 binary64)) b)
(*.f64 (/.f64 #s(literal -1/2 binary64) b) (+.f64 a (sqrt.f64 (fma.f64 a a (*.f64 c (*.f64 b #s(literal -4 binary64)))))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 c a))))) (*.f64 #s(literal 2 binary64) c))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 #s(literal 4 binary64) c) a)))) (*.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 #s(literal -4 binary64) a))))) (*.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 c #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (*.f64 c #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1/2 binary64) c) (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (*.f64 c c) (*.f64 #s(literal 4 binary64) (*.f64 a b))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (+.f64 (*.f64 c c) (*.f64 #s(literal -4 binary64) (*.f64 b a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 c c (*.f64 (*.f64 #s(literal -4 binary64) a) b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 c c (*.f64 b (*.f64 a #s(literal -4 binary64)))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (/.f64 (+.f64 c (sqrt.f64 (fma.f64 c c (*.f64 b (*.f64 a #s(literal -4 binary64)))))) #s(literal -2 binary64)) a)
(*.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 c (sqrt.f64 (fma.f64 c c (*.f64 b (*.f64 a #s(literal -4 binary64)))))))
Compiler

Compiled 20 to 14 computations (30% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
49.4%
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
Compiler

Compiled 40 to 28 computations (30% saved)

simplify4.0ms (0.1%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
1×egg-herbie
Rules
14×*-commutative
14×+-commutative
13×sub-neg
11×neg-sub0
11×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02169
13569
25269
37469
48969
510469
611169
711469
811569
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
Outputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 a #s(literal 2 binary64)))

soundness0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Stop Event
1×fuel
Compiler

Compiled 20 to 14 computations (30% saved)

preprocess26.0ms (0.5%)

Memory
3.2MiB live, 34.4MiB allocated
Compiler

Compiled 170 to 98 computations (42.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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