Details

Time bar (total: 1.8s)

analyze3.0ms (0.2%)

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
Compiler

Compiled 8 to 6 computations (25% saved)

sample1.2s (66.5%)

Results
1.2s8251×body64valid
1.0msbody128valid
0.0msbody64invalid

preprocess21.0ms (1.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
069
199
2129
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Outputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
069
199
2129
Stop Event
saturated
Counts
1 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Outputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
30.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
30.1b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
29.0b
(sqrt.f64 (*.f64 2 (*.f64 x x)))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite45.0ms (2.5%)

Algorithm
batch-egg-rewrite
Rules
503×pow1_binary64
486×add-sqr-sqrt_binary64
466×add-log-exp_binary64
466×log1p-expm1-u_binary64
466×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11226
213636
Stop Event
node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (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 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(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 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 x) 1/2) (sqrt.f64 x))))) (#(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 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 fabs.f64 (*.f64 x (sqrt.f64 2)))))) (#(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 x (sqrt.f64 2)) 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))))))))

simplify22.0ms (1.2%)

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))

prune19.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New22426
Fresh000
Picked011
Done000
Total22527
Error
0.2b
Counts
27 → 5
Alt Table
StatusErrorProgram
0.4b
(fabs.f64 (*.f64 x (sqrt.f64 2)))
34.6b
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
30.1b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
34.4b
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
46.4b
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
Compiler

Compiled 278 to 219 computations (21.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.4b
(*.f64 x (sqrt.f64 2))

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite37.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
417×pow1_binary64
403×add-sqr-sqrt_binary64
395×*-un-lft-identity_binary64
386×add-log-exp_binary64
386×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11006
210756
Stop Event
node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 x (sqrt.f64 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.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 (*.f64 2 (*.f64 x x)) 1/2)))) (#(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 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.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 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))))))))

simplify7.0ms (0.4%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0572
1672
Stop Event
saturated
Counts
27 → 16
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)
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)

prune16.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New14216
Fresh033
Picked011
Done011
Total14721
Error
0.1b
Counts
21 → 7
Alt Table
StatusErrorProgram
34.6b
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
1.5b
(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
46.4b
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
42.1b
(fabs.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3)))
0.4b
(fabs.f64 (*.f64 x (sqrt.f64 2)))
30.1b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
34.4b
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
Compiler

Compiled 246 to 202 computations (17.9% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.4b
(*.f64 x (sqrt.f64 2))
0.6b
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
0.7b
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

series7.0ms (0.4%)

Counts
2 → 0
Calls

6 calls:

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

rewrite41.0ms (2.3%)

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 → 52
Calls
Call 1
Inputs
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 2)) (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 (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) (cbrt.f64 (*.f64 2 (*.f64 x 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 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(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 (*.f64 x (sqrt.f64 2)) 1/6) (*.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 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 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) 3) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))))) (#(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 (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 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))))) (#(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 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (*.f64 x (sqrt.f64 2)) 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 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 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 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) (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 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 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 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 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 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))))))

simplify6.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
52 → 52
Calls
Call 1
Inputs
Outputs

prune52.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New64468
Fresh314
Picked101
Done022
Total68775
Error
0.0b
Counts
75 → 7
Alt Table
StatusErrorProgram
1.4b
(fabs.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (sqrt.f64 2))))
0.4b
(fabs.f64 (*.f64 x (sqrt.f64 2)))
1.4b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
0.4b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
30.1b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
34.4b
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
1.7b
(fabs.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)) 3))
Compiler

Compiled 922 to 749 computations (18.8% saved)

localize5.0ms (0.3%)

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))

series41.0ms (2.3%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
38.0ms
x
@0
(*.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
@-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))

rewrite49.0ms (2.8%)

Algorithm
batch-egg-rewrite
Rules
610×pow1_binary64
566×add-log-exp_binary64
566×log1p-expm1-u_binary64
566×expm1-log1p-u_binary64
554×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0720
114813
2160913
Stop Event
node limit
Counts
2 → 22
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 (+.f64 1 (*.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 cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 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 (+.f64 1 (*.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 cbrt.f64 (pow.f64 (*.f64 x (pow.f64 2 1/4)) 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))))))))

simplify130.0ms (7.3%)

Algorithm
egg-herbie
Rules
1333×sqr-pow_binary64
715×pow-sqr_binary64
530×cube-prod_binary64
477×fabs-mul_binary64
435×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08156
114156
223156
342156
499156
5305156
61146156
71839156
81929156
92064156
102223156
112457156
122779156
133200156
143700156
154295156
165015156
175338156
185626156
195850156
206032156
216116156
227056156
Stop Event
node limit
Counts
46 → 25
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))

prune25.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New25025
Fresh044
Picked011
Done022
Total25732
Error
0.0b
Counts
32 → 7
Alt Table
StatusErrorProgram
1.4b
(fabs.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (sqrt.f64 2))))
0.4b
(fabs.f64 (*.f64 x (sqrt.f64 2)))
1.4b
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
0.4b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
30.1b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
34.4b
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
1.7b
(fabs.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)) 3))
Compiler

Compiled 317 to 275 computations (13.2% saved)

regimes25.0ms (1.4%)

Accuracy

Total -52.8b remaining (-11746.4%)

Threshold costs -52.8b (-11746.4%)

Counts
11 → 1
Calls
Call 1
Inputs
(fabs.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (sqrt.f64 2))))
(fabs.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
(fabs.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)) 3))
(fabs.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3))
(fabs.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3)))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Outputs
(fabs.f64 (*.f64 (*.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4)))
Results
7.0ms0.4bx
5.0ms0.4b(sqrt.f64 (*.f64 2 (*.f64 x x)))
6.0ms0.4b(*.f64 2 (*.f64 x x))
5.0ms0.4b(*.f64 x x)
Compiler

Compiled 116 to 88 computations (24.1% saved)

simplify2.0ms (0.1%)

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))))

end18.0ms (1%)

Stop Event
fuel
Compiler

Compiled 22 to 20 computations (9.1% saved)

Profiling

Loading profile data...