Details

Time bar (total: 1.2s)

analyze4.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample735.0ms (60.2%)

Results
723.0ms8256×body128valid

preprocess16.0ms (1.3%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*r*_binary64
associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1109
2119
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Outputs
(sqrt.f64 (*.f64 (*.f64 2 x) x))
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.5%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*r*_binary64
associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1109
2119
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Outputs
(sqrt.f64 (*.f64 (*.f64 2 x) x))
(sqrt.f64 (*.f64 2 (*.f64 x x)))

eval0.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
30.2b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
30.2b
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
28.9b
(sqrt.f64 (*.f64 (*.f64 2 x) x))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite30.0ms (2.5%)

Algorithm
batch-egg-rewrite
Rules
527×pow1_binary64
488×add-log-exp_binary64
488×log1p-expm1-u_binary64
488×expm1-log1p-u_binary64
477×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11226
213746
Stop Event
node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))))

simplify11.0ms (0.9%)

Algorithm
egg-herbie
Rules
38×fma-def_binary64
sub-neg_binary64
+-commutative_binary64
*-commutative_binary64
distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0780
11280
22580
32980
43380
55180
67380
78480
89680
912180
Stop Event
saturated
Counts
36 → 26
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

eval6.0ms (0.5%)

Compiler

Compiled 208 to 159 computations (23.6% saved)

prune13.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New21526
Fresh000
Picked011
Done000
Total21627
Error
0.2b
Counts
27 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
30.2b
(sqrt.f64 (*.f64 (*.f64 2 x) x))
0.5b
(fabs.f64 (*.f64 (sqrt.f64 2) x))
30.6b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
30.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
30.5b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
30.3b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
Compiler

Compiled 103 to 81 computations (21.4% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (sqrt.f64 2) x)

series1.0ms (0.1%)

Counts
1 → 0
Calls

3 calls:

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

rewrite27.0ms (2.2%)

Algorithm
batch-egg-rewrite
Rules
417×pow1_binary64
386×add-log-exp_binary64
386×log1p-expm1-u_binary64
386×expm1-log1p-u_binary64
378×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11006
210756
Stop Event
node limit
Counts
1 → 13
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))))

simplify6.0ms (0.5%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
13 → 13
Calls
Call 1
Inputs
Outputs

eval3.0ms (0.3%)

Compiler

Compiled 105 to 91 computations (13.3% saved)

prune9.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New11213
Fresh134
Picked011
Done011
Total12719
Error
0.2b
Counts
19 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
30.2b
(sqrt.f64 (*.f64 (*.f64 2 x) x))
0.5b
(fabs.f64 (*.f64 (sqrt.f64 2) x))
1.4b
(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
30.6b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
30.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
30.5b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
42.9b
(fabs.f64 (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 x 3))))
Compiler

Compiled 121 to 98 computations (19% saved)

localize7.0ms (0.6%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (sqrt.f64 2) x)
0.6b
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
0.7b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)

series6.0ms (0.5%)

Counts
2 → 0
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
2.0ms
x
@0
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
1.0ms
x
@inf
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
1.0ms
x
@-inf
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
1.0ms
x
@inf
(cbrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite37.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
575×pow1_binary64
543×add-log-exp_binary64
542×log1p-expm1-u_binary64
542×expm1-log1p-u_binary64
530×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
116814
2157814
Stop Event
node limit
Counts
2 → 54
Calls
Call 1
Inputs
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) (*.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) 3) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) 3) (pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1/3) (pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))))

simplify6.0ms (0.5%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
54 → 54
Calls
Call 1
Inputs
Outputs

eval21.0ms (1.7%)

Compiler

Compiled 776 to 636 computations (18% saved)

prune30.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New64367
Fresh314
Picked101
Done022
Total68674
Error
0.0b
Counts
74 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
30.2b
(sqrt.f64 (*.f64 (*.f64 2 x) x))
0.5b
(fabs.f64 (*.f64 (sqrt.f64 2) x))
1.4b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
2.6b
(fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3) 3))
30.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
0.4b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
Compiler

Compiled 99 to 82 computations (17.2% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(*.f64 x (pow.f64 2 1/4))
0.3b
(*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))

series51.0ms (4.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
33.0ms
x
@0
(*.f64 x (pow.f64 2 1/4))
15.0ms
x
@-inf
(*.f64 x (pow.f64 2 1/4))
1.0ms
x
@inf
(*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
0.0ms
x
@inf
(*.f64 x (pow.f64 2 1/4))
0.0ms
x
@0
(*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))

rewrite43.0ms (3.6%)

Algorithm
batch-egg-rewrite
Rules
610×pow1_binary64
566×add-log-exp_binary64
566×log1p-expm1-u_binary64
566×expm1-log1p-u_binary64
68×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0720
114813
2160913
Stop Event
node limit
Counts
2 → 28
Calls
Call 1
Inputs
(*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 x (pow.f64 2 1/4))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 1/4) 3) (pow.f64 (*.f64 x (pow.f64 2 1/4)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x (pow.f64 2 1/4)) 3) (pow.f64 (pow.f64 2 1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (pow.f64 2 1/4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (pow.f64 2 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (pow.f64 2 1/4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (pow.f64 2 1/4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (sqrt.f64 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (pow.f64 2 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (pow.f64 2 1/4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (pow.f64 2 1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 1/4) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (pow.f64 2 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (pow.f64 2 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (pow.f64 2 1/4))))))))

simplify63.0ms (5.1%)

Algorithm
egg-herbie
Rules
733×sqr-pow_binary64
435×associate-*l*_binary64
362×unswap-sqr_binary64
313×pow-sqr_binary64
256×cube-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08156
114156
223156
342156
499156
5305156
61146156
71839156
81929156
92064156
102223156
112457156
122779156
133200156
143700156
154295156
Stop Event
node limit
Counts
52 → 31
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 (pow.f64 2 1/4) x)
Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) x)
(*.f64 x (pow.f64 2 1/4))

eval9.0ms (0.8%)

Compiler

Compiled 332 to 297 computations (10.5% saved)

prune24.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New31031
Fresh033
Picked011
Done022
Total31637
Error
0.0b
Counts
37 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
30.2b
(sqrt.f64 (*.f64 (*.f64 2 x) x))
0.5b
(fabs.f64 (*.f64 (sqrt.f64 2) x))
1.4b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
2.6b
(fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3) 3))
30.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
0.4b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
Compiler

Compiled 56 to 46 computations (17.9% saved)

regimes23.0ms (1.9%)

Accuracy

Total -52.4b remaining (-13018.1%)

Threshold costs -52.4b (-13018.1%)

Counts
11 → 1
Calls
Call 1
Inputs
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
(fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3) 3))
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
(fabs.f64 (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 x 3))))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(sqrt.f64 (*.f64 (*.f64 2 x) x))
Outputs
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
Results
TimeErrorSegmentsBranch
6.0ms0.4b1x
8.0ms0.4b1(sqrt.f64 (*.f64 (*.f64 2 x) x))
5.0ms0.4b1(*.f64 (*.f64 2 x) x)
Compiler

Compiled 115 to 91 computations (20.9% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
fabs-mul_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11315
21715
Stop Event
saturated
Calls
Call 1
Inputs
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
Outputs
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
(fabs.f64 (*.f64 (pow.f64 2 1/4) (*.f64 x (pow.f64 2 1/4))))

end17.0ms (1.4%)

Stop Event
fuel
Compiler

Compiled 22 to 20 computations (9.1% saved)

Profiling

Loading profile data...