Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

Time bar (total: 2.7s)

analyze3.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
Operation ival-sqrt, time spent: 1.0ms, 83.0% of total-time
Operation ival-sub, time spent: 0.0ms, 0.0% of total-time
Operation ival-mult, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.1s (41.9%)

Results
1.1s8255×256valid
0.0ms5×256invalid
0.0ms1×256valid
Precisions
Click to see histograms. Total time spent on operations: 312.0ms
Operation ival-sqrt, time spent: 154.0ms, 49.0% of total-time
Operation ival-mult, time spent: 87.0ms, 28.0% of total-time
Operation ival-sub, time spent: 57.0ms, 18.0% of total-time
Operation const, time spent: 14.0ms, 4.0% of total-time
Bogosity

preprocess344.0ms (12.8%)

Algorithm
1×egg-herbie
Rules
1234×sub-neg
1188×fma-define
1138×distribute-lft-out
868×associate-+r+
798×fma-neg
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f64 (-.f64 1 (*.f64 x x)))
00-0-x
00-0-(*.f64 x x)
00-0-(-.f64 1 (*.f64 x x))
00-0-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01596
13696
25696
310296
414996
523496
636796
764196
8124196
9211296
10475196
11646996
12723696
13753496
14759096
15762296
16789696
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x))))
(neg.f64 (sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))))
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(neg.f64 (sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))))
(neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(neg.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) 1)))
Symmetry

(abs x)

Compiler

Compiled 43 to 23 computations (46.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
Operation ival-sqrt, time spent: 7.0ms, 38.0% of total-time
Operation ival-sub, time spent: 6.0ms, 33.0% of total-time
Operation ival-mult, time spent: 4.0ms, 22.0% of total-time
Operation const, time spent: 1.0ms, 5.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
▶100.0%
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize160.0ms (5.9%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(-.f64 1 (*.f64 x x))
Compiler

Compiled 33 to 16 computations (51.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
Operation composed, time spent: 8.0ms, 28.0% of total-time
Operation ival-sqrt, time spent: 7.0ms, 25.0% of total-time
Operation ival-mult, time spent: 6.0ms, 21.0% of total-time
Operation ival-sub, time spent: 3.0ms, 11.0% of total-time
Operation ival-add, time spent: 3.0ms, 11.0% of total-time
Operation const, time spent: 1.0ms, 4.0% of total-time
Operation ival-neg, time spent: 1.0ms, 4.0% of total-time

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(-.f64 1 (*.f64 x x))
1.0ms
x
@0
(-.f64 1 (*.f64 x x))
1.0ms
x
@-inf
(-.f64 1 (*.f64 x x))

rewrite269.0ms (10%)

Algorithm
1×batch-egg-rewrite
Rules
566×unpow-prod-down
346×log1p-expm1-u
346×expm1-log1p-u
330×add-exp-log
330×cbrt-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
18616
2100916
Stop Event
1×node limit
Counts
1 → 62
Calls
Call 1
Inputs
(-.f64 1 (*.f64 x x))
Outputs
(+.f64 1 (neg.f64 (pow.f64 x 2)))
(+.f64 0 (-.f64 1 (pow.f64 x 2)))
(+.f64 (neg.f64 (pow.f64 x 2)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(*.f64 1 (-.f64 1 (pow.f64 x 2)))
(*.f64 (-.f64 1 (pow.f64 x 2)) 1)
(*.f64 (-.f64 1 (pow.f64 x 2)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2) (cbrt.f64 (-.f64 1 (pow.f64 x 2))))
(*.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (sqrt.f64 (-.f64 1 (pow.f64 x 2))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (pow.f64 x 2)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))))
(/.f64 1 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (pow.f64 x 2)) 2)) (-.f64 1 (neg.f64 (pow.f64 x 2))))
(/.f64 (+.f64 1 (*.f64 -1 (pow.f64 x 6))) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (pow.f64 x 2)) 2) (neg.f64 (pow.f64 x 2)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 6)))) (cbrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 4)))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (-.f64 1 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 3)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (pow.f64 x 2))))
(pow.f64 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))) -1)
(pow.f64 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))) (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2))
(log.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))
(cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (-.f64 1 (pow.f64 x 2))))
(exp.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) 2))
(fma.f64 1 (neg.f64 (pow.f64 x 2)) 1)
(fma.f64 x (neg.f64 x) 1)
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (neg.f64 (pow.f64 (cbrt.f64 x) 2)) 1)
(fma.f64 (neg.f64 x) x 1)
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 x 2))) 2) (cbrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (pow.f64 x 2))) (sqrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(fma.f64 -1 (pow.f64 x 2) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2) 1)
(fma.f64 (*.f64 (neg.f64 x) 1) x 1)
(fma.f64 (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1)
(fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) 1)

simplify78.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
930×fma-define
784×fma-neg
618×cancel-sign-sub-inv
518×unswap-sqr
440×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01682029
13911894
210871882
344241882
Stop Event
1×node limit
Counts
74 → 73
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (pow.f64 x 2)))
(+.f64 0 (-.f64 1 (pow.f64 x 2)))
(+.f64 (neg.f64 (pow.f64 x 2)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(*.f64 1 (-.f64 1 (pow.f64 x 2)))
(*.f64 (-.f64 1 (pow.f64 x 2)) 1)
(*.f64 (-.f64 1 (pow.f64 x 2)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2) (cbrt.f64 (-.f64 1 (pow.f64 x 2))))
(*.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (sqrt.f64 (-.f64 1 (pow.f64 x 2))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (pow.f64 x 2)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))))
(/.f64 1 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (pow.f64 x 2)) 2)) (-.f64 1 (neg.f64 (pow.f64 x 2))))
(/.f64 (+.f64 1 (*.f64 -1 (pow.f64 x 6))) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (pow.f64 x 2)) 2) (neg.f64 (pow.f64 x 2)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 6)))) (cbrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 4)))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (-.f64 1 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 3)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (pow.f64 x 2))))
(pow.f64 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))) -1)
(pow.f64 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))) (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2))
(log.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))
(cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (-.f64 1 (pow.f64 x 2))))
(exp.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) 2))
(fma.f64 1 (neg.f64 (pow.f64 x 2)) 1)
(fma.f64 x (neg.f64 x) 1)
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (neg.f64 (pow.f64 (cbrt.f64 x) 2)) 1)
(fma.f64 (neg.f64 x) x 1)
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 x 2))) 2) (cbrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (pow.f64 x 2))) (sqrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(fma.f64 -1 (pow.f64 x 2) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2) 1)
(fma.f64 (*.f64 (neg.f64 x) 1) x 1)
(fma.f64 (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1)
(fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) 1)
Outputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 1 (neg.f64 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 0 (-.f64 1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 (neg.f64 (pow.f64 x 2)) 1)
(-.f64 1 (pow.f64 x 2))
(+.f64 (log.f64 (E.f64)) (neg.f64 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 1 (pow.f64 x 2))
(*.f64 1 (-.f64 1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(*.f64 (-.f64 1 (pow.f64 x 2)) 1)
(-.f64 1 (pow.f64 x 2))
(*.f64 (-.f64 1 (pow.f64 x 2)) (log.f64 (E.f64)))
(-.f64 1 (pow.f64 x 2))
(*.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2))
(-.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 2) (cbrt.f64 (-.f64 1 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(*.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (sqrt.f64 (-.f64 1 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (pow.f64 x 2)))
(-.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 3))
(-.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3)) 1/3))
(-.f64 1 (pow.f64 x 2))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))))
(-.f64 1 (pow.f64 x 2))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (pow.f64 x 2)) (cbrt.f64 (-.f64 1 (pow.f64 x 2)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))))
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 1 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (fma.f64 x x 1)))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (pow.f64 x 2)) 2)) (-.f64 1 (neg.f64 (pow.f64 x 2))))
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (+.f64 1 (*.f64 -1 (pow.f64 x 6))) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (pow.f64 x 2)) 2) (neg.f64 (pow.f64 x 2)))))
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 6)))) (cbrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 x 6)) (pow.f64 (-.f64 1 (pow.f64 x 2)) 2))) (cbrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) (-.f64 1 (pow.f64 x 4)))) (cbrt.f64 (fma.f64 x x 1)))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 x 4)) (pow.f64 (-.f64 1 (pow.f64 x 2)) 2))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (-.f64 1 (pow.f64 x 2)) 1)
(-.f64 1 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 3)
(-.f64 1 (pow.f64 x 2))
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2) 1/2)
(-.f64 1 (pow.f64 x 2))
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3) 1/3)
(-.f64 1 (pow.f64 x 2))
(pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 2)
(-.f64 1 (pow.f64 x 2))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(pow.f64 (/.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4))) (-.f64 1 (pow.f64 x 6))) -1)
(*.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(pow.f64 (/.f64 (fma.f64 x x 1) (-.f64 1 (pow.f64 x 4))) -1)
(*.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))) (sqrt.f64 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 2))
(-.f64 1 (pow.f64 x 2))
(log.f64 (exp.f64 (-.f64 1 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3))
(-.f64 1 (pow.f64 x 2))
(expm1.f64 (log1p.f64 (-.f64 1 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(log1p.f64 (expm1.f64 (-.f64 1 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(exp.f64 (log1p.f64 (neg.f64 (pow.f64 x 2))))
(-.f64 1 (pow.f64 x 2))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 3))
(-.f64 1 (pow.f64 x 2))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (pow.f64 x 2)))) 1/3))
(-.f64 1 (pow.f64 x 2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) 2))
(-.f64 1 (pow.f64 x 2))
(fma.f64 1 (neg.f64 (pow.f64 x 2)) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 x (neg.f64 x) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (neg.f64 (pow.f64 (cbrt.f64 x) 2)) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (neg.f64 x) x 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 x 2))) 2) (cbrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (sqrt.f64 (neg.f64 (pow.f64 x 2))) (sqrt.f64 (neg.f64 (pow.f64 x 2))) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 -1 (pow.f64 x 2) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (*.f64 (neg.f64 x) 1) x 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1)
(-.f64 1 (pow.f64 x 2))
(fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) 1)
(-.f64 1 (pow.f64 x 2))

eval25.0ms (0.9%)

Compiler

Compiled 936 to 780 computations (16.7% saved)

prune11.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New72173
Fresh000
Picked022
Done000
Total72375
Accuracy
100.0%
Counts
75 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
✓100.0%
(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶99.0%
(sqrt.f64 1)
Compiler

Compiled 17 to 13 computations (23.5% saved)

localize23.0ms (0.8%)

Compiler

Compiled 5 to 5 computations (0% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
Operation ival-sqrt, time spent: 4.0ms, 96.0% of total-time
Operation const, time spent: 1.0ms, 24.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033
Accuracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
✓100.0%
(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓99.0%
(sqrt.f64 1)
Compiler

Compiled 32 to 24 computations (25% saved)

regimes9.0ms (0.3%)

Counts
3 → 1
Calls
Call 1
Inputs
(sqrt.f64 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
Outputs
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
Calls

4 calls:

3.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms
(-.f64 1 (*.f64 x x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (-.f64 1 (*.f64 x x)))
100.0%1(-.f64 1 (*.f64 x x))
100.0%1(*.f64 x x)
Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes10.0ms (0.4%)

Counts
2 → 1
Calls
Call 1
Inputs
(sqrt.f64 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Calls

4 calls:

4.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
3.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(-.f64 1 (*.f64 x x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (-.f64 1 (*.f64 x x)))
100.0%1(-.f64 1 (*.f64 x x))
100.0%1(*.f64 x x)
Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes2.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 1)
Outputs
(sqrt.f64 1)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.0%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×sub-neg
6×+-commutative
4×*-commutative
4×neg-sub0
4×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01547
12747
23347
33647
43747
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 1)
Outputs
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 1)
1
Compiler

Compiled 16 to 12 computations (25% saved)

soundness585.0ms (21.7%)

Rules
1234×sub-neg
1188×fma-define
1138×distribute-lft-out
868×associate-+r+
798×fma-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01596
13696
25696
310296
414996
523496
636796
764196
8124196
9211296
10475196
11646996
12723696
13753496
14759096
15762296
16789696
Stop Event
1×node limit
Compiler

Compiled 35 to 20 computations (42.9% saved)

end0.0ms (0%)

preprocess38.0ms (1.4%)

Remove

(abs x)

Compiler

Compiled 98 to 70 computations (28.6% saved)

Profiling

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