Expanding a square

Details

Time bar (total: 2.1s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 11 to 9 computations (18.2% saved)

sample827.0ms (39.7%)

Results
297.0ms2017×body1024valid
217.0ms2965×body256valid
148.0ms2010×body256infinite
114.0ms1048×body512valid
41.0ms216×body2048valid
Bogosity

preprocess77.0ms (3.7%)

Algorithm
2×egg-herbie
Rules
1906×fma-def
1604×fma-neg
1178×distribute-lft-in
1078×associate--r-
1078×distribute-neg-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721
12519
25813
313813
458313
5203713
6545613
7783113
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(*.f64 x (-.f64 x -2))
Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify70.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
1906×fma-def
1604×fma-neg
1178×distribute-lft-in
1078×associate--r-
1078×distribute-neg-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0721
12519
25813
313813
458313
5203713
6545613
7783113
Stop Event
1×node limit
Counts
1 → 5
Calls
Call 1
Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(*.f64 x (-.f64 x -2))

eval1.0ms (0%)

Compiler

Compiled 35 to 25 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New415
Fresh101
Picked000
Done000
Total516
Accurracy
100.0%
Counts
6 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 x (-.f64 x -2))
▶100.0%
(*.f64 x (-.f64 x -2))
Compiler

Compiled 12 to 8 computations (33.3% saved)

localize18.0ms (0.9%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(*.f64 x (-.f64 x -2))
Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite52.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
1366×pow1
1274×add-exp-log
1274×log1p-expm1-u
1274×expm1-log1p-u
1252×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
113313
2167413
Stop Event
1×node limit
Counts
1 → 17
Calls
Call 1
Inputs
(*.f64 x (-.f64 x -2))
Outputs
(+.f64 (*.f64 x x) (*.f64 x 2))
(+.f64 (*.f64 x x) (*.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))

simplify55.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
1670×fma-def
1268×log-prod
724×*-commutative
646×distribute-lft-out
640×associate-*r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
058451
1134443
2398435
32440431
45933431
Stop Event
1×node limit
Counts
29 → 29
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 x x) (*.f64 x 2))
(+.f64 (*.f64 x x) (*.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 x x) (*.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 x x) (*.f64 2 x))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (*.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))

eval5.0ms (0.3%)

Compiler

Compiled 254 to 169 computations (33.5% saved)

prune13.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New26329
Fresh000
Picked011
Done000
Total26430
Accurracy
100.0%
Counts
30 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(+.f64 (*.f64 x x) (*.f64 x 2))
▶45.6%
(+.f64 x x)
✓100.0%
(*.f64 x (-.f64 x -2))
▶56.0%
(*.f64 x x)
▶100.0%
(+.f64 (*.f64 x x) (*.f64 x 2))
▶45.6%
(+.f64 x x)
✓100.0%
(*.f64 x (-.f64 x -2))
▶56.0%
(*.f64 x x)
Compiler

Compiled 44 to 26 computations (40.9% saved)

localize27.0ms (1.3%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(+.f64 (*.f64 x x) (*.f64 x 2))
Compiler

Compiled 25 to 10 computations (60% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 (*.f64 x x) (*.f64 x 2))
0.0ms
x
@-inf
(+.f64 (*.f64 x x) (*.f64 x 2))
0.0ms
x
@inf
(+.f64 (*.f64 x x) (*.f64 x 2))

rewrite54.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
1580×pow1
1474×add-exp-log
1472×log1p-expm1-u
1472×expm1-log1p-u
1448×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
115413
2205613
Stop Event
1×node limit
Counts
1 → 39
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 x 2))
Outputs
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 x 2))) (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 x 2))))
(*.f64 x (+.f64 x 2))
(*.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 1 (*.f64 x (+.f64 x 2)))
(*.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x 2)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))
(*.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(*.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (/.f64 1 (*.f64 x (-.f64 x 2))))
(*.f64 (+.f64 x 2) x)
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (*.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (-.f64 (*.f64 x 2) (*.f64 x x)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x x (*.f64 x 2))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x 2))
(fma.f64 1 (*.f64 x 2) (*.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))

simplify56.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
1186×fma-neg
928×div-sub
820×times-frac
632×fma-def
580×log-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01021157
12841107
2995981
35227981
Stop Event
1×node limit
Counts
51 → 55
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 x 2))) (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 x 2))))
(*.f64 x (+.f64 x 2))
(*.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 1 (*.f64 x (+.f64 x 2)))
(*.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x 2)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))
(*.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(*.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (/.f64 1 (*.f64 x (-.f64 x 2))))
(*.f64 (+.f64 x 2) x)
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (*.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (-.f64 (*.f64 x 2) (*.f64 x x)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x x (*.f64 x 2))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x 2))
(fma.f64 1 (*.f64 x 2) (*.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))
Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(-.f64 (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 x 2))) (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(*.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(*.f64 1 (*.f64 x (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(*.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(*.f64 x (+.f64 2 x))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(*.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(*.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x (*.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (*.f64 x x) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(*.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (/.f64 1 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(*.f64 (+.f64 x 2) x)
(*.f64 x (+.f64 2 x))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x (*.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (*.f64 x x) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 1 (/.f64 (*.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x (*.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (*.f64 x x) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x (*.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (*.f64 x x) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x (*.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (*.f64 x 4) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (*.f64 x x) (*.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (-.f64 (*.f64 x 2) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) 4)) (*.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(fma.f64 x x (*.f64 x 2))
(*.f64 x (+.f64 2 x))
(fma.f64 x 2 (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 1 (*.f64 x x) (*.f64 x 2))
(*.f64 x (+.f64 2 x))
(fma.f64 1 (*.f64 x 2) (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (*.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (+.f64 x x))
(fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))
(*.f64 x (+.f64 2 x))

eval12.0ms (0.6%)

Compiler

Compiled 671 to 447 computations (33.4% saved)

prune79.0ms (3.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New55055
Fresh000
Picked033
Done011
Total55459
Accurracy
100.0%
Counts
59 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(+.f64 (*.f64 x x) (*.f64 x 2))
✓45.6%
(+.f64 x x)
✓100.0%
(*.f64 x (-.f64 x -2))
✓56.0%
(*.f64 x x)
Compiler

Compiled 50 to 29 computations (42% saved)

regimes12.0ms (0.6%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x (-.f64 x -2))
(+.f64 (*.f64 x x) (*.f64 x 2))
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
Outputs
(+.f64 (*.f64 x x) (*.f64 x 2))
Calls

4 calls:

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

Compiled 52 to 34 computations (34.6% saved)

regimes4.0ms (0.2%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x (-.f64 x -2))
Outputs
(*.f64 x (-.f64 x -2))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
Compiler

Compiled 14 to 7 computations (50% saved)

regimes9.0ms (0.4%)

Counts
2 → 3
Calls
Call 1
Inputs
(*.f64 x x)
(+.f64 x x)
Outputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x x)
Calls

1 calls:

8.0ms
x
Results
AccuracySegmentsBranch
96.9%3x
Compiler

Compiled 9 to 4 computations (55.6% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
56.0%1x
Compiler

Compiled 6 to 3 computations (50% saved)

bsearch26.0ms (1.2%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
13.0ms
9.175958657278557e-5
6.694290637606029
13.0ms
-2.6533865485472115
-4.440363095029017e-7
Results
23.0ms288×body256valid
Compiler

Compiled 194 to 119 computations (38.7% saved)

simplify5.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
6×+-commutative
6×*-commutative
4×sub-neg
2×neg-mul-1
2×if-if-or-not
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01878
12978
23478
33678
43778
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 x 2))
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (*.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (*.f64 x x)))
(*.f64 x x)
Outputs
(+.f64 (*.f64 x x) (*.f64 x 2))
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (*.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (*.f64 x x)))
(*.f64 x x)
Compiler

Compiled 36 to 20 computations (44.4% saved)

soundness354.0ms (17%)

Rules
1906×fma-def
1670×fma-def
1670×fma-def
1604×fma-neg
1366×pow1
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0721
12519
25813
313813
458313
5203713
6545613
7783113
0613
113313
2167413
058451
1134443
2398435
32440431
45933431
058451
1134443
2398435
32440431
45933431
Stop Event
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 177 to 128 computations (27.7% saved)

end321.0ms (15.4%)

Compiler

Compiled 86 to 46 computations (46.5% saved)

Profiling

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