Details

Time bar (total: 1.2s)

analyze4.0ms (0.3%)

Algorithm
1×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 10 to 5 computations (50% saved)

sample661.0ms (53.3%)

Results
649.0ms8256×body128valid
Compiler

Compiled 20 to 10 computations (50% saved)

preprocess13.0ms (1.1%)

Algorithm
2×egg-herbie
Rules
2×*-commutative_binary64
2×associate-*r*_binary64
2×count-2_binary64
1×associate-*l*_binary64
1×distribute-rgt-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054
1114
2144
3174
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)
Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify9.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
2×associate-*r*_binary64
2×count-2_binary64
1×associate-*l*_binary64
1×distribute-rgt-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054
1114
2144
3174
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.1b
(hypot.f64 x x)
Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(hypot.f64 x x)

series3.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

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

rewrite25.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
271×pow1_binary64
260×add-sqr-sqrt_binary64
255×*-un-lft-identity_binary64
249×add-log-exp_binary64
249×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
1604
26954
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) (cbrt.f64 (exp.f64 (hypot.f64 x x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x x)))))))

simplify10.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0780
11280
22580
32980
43380
55180
67380
78480
89680
912180
Stop Event
1×saturated
Counts
32 → 23
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))

prune20.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New18523
Fresh000
Picked011
Done000
Total18624
Error
0.0b
Counts
24 → 6
Alt Table
StatusErrorProgram
▶0.5b
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓0.1b
(hypot.f64 x x)
43.3b
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
1.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
34.3b
(*.f64 (sqrt.f64 2) (neg.f64 x))
28.6b
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 242 to 121 computations (50% saved)

localize4.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 x x)
✓0.1b
(sqrt.f64 (hypot.f64 x x))
✓0.5b
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series5.0ms (0.4%)

Counts
2 → 0
Calls

6 calls:

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

rewrite30.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
416×pow1_binary64
386×add-log-exp_binary64
386×log1p-expm1-u_binary64
386×expm1-log1p-u_binary64
376×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
112510
2112610
Stop Event
1×node limit
Counts
2 → 38
Calls
Call 1
Inputs
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (hypot.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/4) (*.f64 (pow.f64 (hypot.f64 x x) 1/4) (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/4)) (pow.f64 (hypot.f64 x x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (hypot.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 1/2) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x x)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))))))))

simplify6.0ms (0.5%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
38 → 38
Calls
Call 1
Inputs
Outputs

prune38.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New59261
Fresh134
Picked011
Done011
Total60767
Error
0.0b
Counts
67 → 7
Alt Table
StatusErrorProgram
✓0.5b
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓0.1b
(hypot.f64 x x)
34.3b
(*.f64 (sqrt.f64 2) (neg.f64 x))
2.0b
(pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3) 2)
1.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
28.6b
(*.f64 (sqrt.f64 2) x)
▶0.9b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
Compiler

Compiled 690 to 343 computations (50.3% saved)

localize7.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓0.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓0.6b
(cbrt.f64 (hypot.f64 x x))
✓0.6b
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))

series45.0ms (3.6%)

Counts
4 → 24
Calls

12 calls:

TimeVariablePointExpression
24.0ms
x
@0
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
9.0ms
x
@-inf
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
7.0ms
x
@inf
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
1.0ms
x
@0
(cbrt.f64 (hypot.f64 x x))
1.0ms
x
@inf
(cbrt.f64 (hypot.f64 x x))

rewrite41.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
537×pow1_binary64
499×add-log-exp_binary64
499×log1p-expm1-u_binary64
499×expm1-log1p-u_binary64
484×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0854
115726
2180626
Stop Event
1×node limit
Counts
4 → 72
Calls
Call 1
Inputs
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
(cbrt.f64 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (hypot.f64 x x) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (hypot.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/6) (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (hypot.f64 x x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6) (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 2))))))))

simplify34.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
517×fma-def_binary64
490×div-sub_binary64
360×fma-neg_binary64
228×associate-*l*_binary64
219×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
024272
154272
2110248
3236200
4597196
51400196
63678196
Stop Event
1×node limit
Counts
96 → 80
Calls
Call 1
Inputs
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 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 -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
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(*.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 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))

prune41.0ms (3.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New79180
Fresh044
Picked011
Done022
Total79887
Error
0b
Counts
87 → 8
Alt Table
StatusErrorProgram
✓0.5b
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓0.1b
(hypot.f64 x x)
34.3b
(*.f64 (sqrt.f64 2) (neg.f64 x))
2.0b
(pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3) 2)
▶0.9b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
1.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
28.6b
(*.f64 (sqrt.f64 2) x)
✓0.9b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
Compiler

Compiled 1361 to 493 computations (63.8% saved)

localize6.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓0.3b
(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓0.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
0.6b
(cbrt.f64 (hypot.f64 x x))

series3.0ms (0.2%)

Counts
3 → 24
Calls

9 calls:

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

rewrite38.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
543×pow1_binary64
505×add-log-exp_binary64
505×log1p-expm1-u_binary64
505×expm1-log1p-u_binary64
489×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0844
116120
2189220
Stop Event
1×node limit
Counts
3 → 47
Calls
Call 1
Inputs
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (*.f64 x (+.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (hypot.f64 x x) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) (sqrt.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 x x) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (hypot.f64 x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 x x) 1/6)))))))

simplify35.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
517×fma-def_binary64
479×div-sub_binary64
355×fma-neg_binary64
230×associate-*l*_binary64
220×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
024272
154272
2110248
3236200
4598196
51397196
63677196
Stop Event
1×node limit
Counts
71 → 55
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))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 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 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 1 x)))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/6) (pow.f64 x 1/6))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/6)
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1/6)

prune39.0ms (3.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New1050105
Fresh044
Picked011
Done033
Total1058113
Error
0b
Counts
113 → 8
Alt Table
StatusErrorProgram
✓0.5b
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓0.1b
(hypot.f64 x x)
34.3b
(*.f64 (sqrt.f64 2) (neg.f64 x))
2.0b
(pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3) 2)
✓0.9b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
1.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
28.6b
(*.f64 (sqrt.f64 2) x)
✓0.9b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
Compiler

Compiled 1820 to 601 computations (67% saved)

regimes37.0ms (3%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Counts
21 → 1
Compiler

Compiled 226 to 77 computations (65.9% saved)

simplify1.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
(hypot.f64 x x)

end82.0ms (6.6%)

Stop Event
1×fuel
Compiler

Compiled 84 to 48 computations (42.9% saved)

Profiling

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