Details

Time bar (total: 1.3s)

analyze10.0ms (0.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%50%50%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
25%0%75%13
25%0%75%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample886.0ms (65.8%)

Results
874.0ms8256×body128valid
0.0msbody128invalid
Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess36.0ms (2.7%)

Algorithm
egg-herbie
Rules
1-exp_binary64
rules-20_binary64
rules-21_binary64
rules-52_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21311
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0.5%)

Algorithm
egg-herbie
Rules
1-exp_binary64
rules-20_binary64
rules-21_binary64
rules-52_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21311
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 31 to 22 computations (29% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series7.0ms (0.6%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
2.0ms
x
@0
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
1.0ms
x
@inf
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite35.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
659×rules-40_binary64
659×rules-41_binary64
659×rules-42_binary64
659×rules-43_binary64
614×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11629
219949
Stop Event
node limit
Counts
1 → 34
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 (sqrt.f64 x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 (sqrt.f64 (+.f64 x -1)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 (sqrt.f64 x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 (sqrt.f64 (+.f64 x -1)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x -1)) (/.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 1 (sqrt.f64 (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) (+.f64 (*.f64 x (+.f64 x -1)) (+.f64 0 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) (+.f64 (*.f64 x (+.f64 x -1)) (-.f64 0 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x -1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify33.0ms (2.5%)

Algorithm
egg-herbie
Rules
234×rules-4_binary64
218×rules-21_binary64
217×rules-6-rev_binary64
204×rules-12-rev_binary64
186×rules-5-rev_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01834
15034
216434
369032
4472431
Stop Event
node limit
Counts
38 → 41
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(-.f64 (-.f64 x 1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (fma.f64 x 1/2 1/8) (/.f64 1/16 x)) x))
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))

prune24.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh000
Picked101
Done000
Total40242
Error
0b
Counts
42 → 2
Alt Table
StatusErrorProgram
0.2b
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))
30.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 441 to 329 computations (25.4% saved)

localize6.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)

series2.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)
1.0ms
x
@-inf
(/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)
1.0ms
x
@inf
(/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)

rewrite33.0ms (2.5%)

Algorithm
batch-egg-rewrite
Rules
770×rules-40_binary64
770×rules-41_binary64
770×rules-42_binary64
770×rules-43_binary64
74×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
117310
2217710
Stop Event
node limit
Counts
1 → 29
Calls
Call 1
Inputs
(/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 0 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (/.f64 1/16 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/16 x))) 2) (/.f64 (cbrt.f64 (+.f64 1/8 (/.f64 1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/16 x))) (/.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/8 (/.f64 1/16 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))))))

simplify32.0ms (2.4%)

Algorithm
egg-herbie
Rules
466×rules-20_binary64
452×rules-23-rev_binary64
362×fma-def_binary64
304×rules-14-rev_binary64
271×rules-13_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
014132
133132
290132
3286132
41701105
54284105
Stop Event
node limit
Counts
41 → 34
Calls
Call 1
Inputs
(/.f64 1/16 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(/.f64 1/8 x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(/.f64 1/8 x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
Outputs
(/.f64 1/16 (pow.f64 x 2))
(/.f64 1/16 (*.f64 x x))
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(/.f64 1/8 x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(/.f64 1/8 x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)
(+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 (-.f64 (/.f64 1/16 x) -1/8) x)

prune22.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New34034
Fresh011
Picked011
Done000
Total34236
Error
0b
Counts
36 → 2
Alt Table
StatusErrorProgram
0.2b
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))
30.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 534 to 415 computations (22.3% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
28.7b
(sqrt.f64 (*.f64 x (+.f64 x -1)))

series4.0ms (0.3%)

Counts
1 → 8
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@0
(sqrt.f64 (*.f64 x (+.f64 x -1)))
1.0ms
x
@-inf
(sqrt.f64 (*.f64 x (+.f64 x -1)))
1.0ms
x
@inf
(sqrt.f64 (*.f64 x (+.f64 x -1)))

rewrite41.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
632×rules-40_binary64
632×rules-41_binary64
632×rules-42_binary64
632×rules-43_binary64
590×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11459
218279
Stop Event
node limit
Counts
1 → 35
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 0 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) (cbrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) (pow.f64 (-.f64 (*.f64 x x) x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2) (+.f64 (-.f64 (*.f64 x x) x) (+.f64 0 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2) (+.f64 (-.f64 (*.f64 x x) x) (-.f64 0 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 (*.f64 x x) x) 1/4) (pow.f64 (-.f64 (*.f64 x x) x) 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) x)) 1/2))))))

simplify17.0ms (1.3%)

Algorithm
egg-herbie
Rules
275×rules-4_binary64
267×rules-6-rev_binary64
237×rules-12-rev_binary64
206×rules-6_binary64
202×rules-11_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02371
15870
219270
384666
Stop Event
node limit
Counts
43 → 48
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(*.f64 -1 x)
(-.f64 1/2 x)
(-.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))) x)
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))) x)
Outputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (-.f64 x 1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(/.f64 (-.f64 (fma.f64 (-.f64 x 1/2) x -1/8) (/.f64 1/16 x)) x)
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(-.f64 1/2 x)
(-.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))) x)
(-.f64 (/.f64 1/8 x) (-.f64 x 1/2))
(-.f64 1/2 (-.f64 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))) x)
(-.f64 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))) (-.f64 x 1/2))
(-.f64 (/.f64 1/8 x) (-.f64 (-.f64 x 1/2) (/.f64 1/16 (*.f64 x x))))
(+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 x 1/2)))
(/.f64 (-.f64 (/.f64 1/16 x) (fma.f64 (-.f64 x 1/2) x -1/8)) x)

prune39.0ms (2.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New48048
Fresh000
Picked011
Done011
Total48250
Error
0b
Counts
50 → 2
Alt Table
StatusErrorProgram
0.2b
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))
30.8b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 497 to 211 computations (57.5% saved)

regimes61.0ms (4.5%)

Accuracy

Total 0.3b remaining (99.5%)

Threshold costs 0.3b (99.5%)

Counts
35 → 1
Compiler

Compiled 652 to 476 computations (27% saved)

simplify1.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
Stop Event
saturated
Calls
Call 1
Inputs
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))
Outputs
(-.f64 x (+.f64 1/2 (/.f64 (+.f64 1/8 (/.f64 1/16 x)) x)))

end42.0ms (3.1%)

Stop Event
done
Compiler

Compiled 43 to 32 computations (25.6% saved)

Profiling

Loading profile data...