Details

Time bar (total: 2.2s)

analyze5.0ms (0.2%)

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
Compiler

Compiled 10 to 5 computations (50% saved)

sample859.0ms (38.7%)

Results
846.0ms8256×body256valid
0.0ms4×body256invalid

preprocess13.0ms (0.6%)

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 10 to 5 computations (50% saved)

simplify8.0ms (0.4%)

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)

eval0.0ms (0%)

Compiler

Compiled 12 to 5 computations (58.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Compiled 4 to 2 computations (50% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(hypot.f64 x x)
Compiler

Compiled 5 to 2 computations (60% saved)

series3.0ms (0.1%)

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)

rewrite98.0ms (4.4%)

Algorithm
1×batch-egg-rewrite
Rules
356×log1p-udef_binary64
279×associate-*r*_binary64
271×pow1_binary64
259×associate-*l*_binary64
259×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
1604
26964
378794
Stop Event
1×node limit
Counts
1 → 103
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 0 0)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 0 0)) 2))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (+.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (*.f64 x (cbrt.f64 x)) (*.f64 x (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (pow.f64 1 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cbrt.f64 x)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (pow.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (*.f64 x (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 0 0)) 3) 1) (+.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) (+.f64 1 (+.f64 1 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) 1) (+.f64 (+.f64 1 (/.f64 0 0)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (/.f64 0 0)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x (cbrt.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x x))))))

simplify13.0ms (0.6%)

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
115 → 105
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))

eval22.0ms (1%)

Compiler

Compiled 899 to 665 computations (26% saved)

prune16.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1005105
Fresh000
Picked011
Done000
Total1006106
Error
0.1b
Counts
106 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.1b
(hypot.f64 x x)
▶60.7b
(*.f64 (*.f64 x x) 2)
▶29.4b
(*.f64 (sqrt.f64 2) x)
▶33.7b
(*.f64 (sqrt.f64 2) (neg.f64 x))
▶64.0b
(/.f64 0 0)
▶30.0b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 62 to 46 computations (25.8% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiled 9 to 7 computations (22.2% saved)

series2.0ms (0.1%)

Counts
1 → 0
Calls

3 calls:

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

rewrite38.0ms (1.7%)

Algorithm
1×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
1×node limit
Counts
1 → 15
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))))) (#(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 (*.f64 2 (*.f64 x x)) 1/2)))) (#(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 expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))) (#(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)))))))

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
15 → 15
Calls
Call 1
Inputs
Outputs

localize2.0ms (0.1%)

Compiler

Compiled 5 to 5 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (*.f64 x x) 2)
Compiler

Compiled 11 to 5 computations (54.5% saved)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite39.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
423×pow1_binary64
409×add-sqr-sqrt_binary64
402×*-un-lft-identity_binary64
390×add-log-exp_binary64
390×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
211247
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) 2)))))))

simplify166.0ms (7.5%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
558×fabs-mul_binary64
523×pow-sqr_binary64
445×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0584
11184
22284
34384
410584
532984
6125984
7213284
8229684
9248084
10268884
11298484
12337984
13386084
14442684
15511884
16595184
17634384
18663184
19691184
20698584
21701984
22796084
Stop Event
1×node limit
Counts
28 → 18
Calls
Call 1
Inputs
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
Outputs
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.5b
(*.f64 (sqrt.f64 2) (neg.f64 x))
Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite38.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
450×pow1_binary64
437×add-sqr-sqrt_binary64
428×*-un-lft-identity_binary64
418×add-log-exp_binary64
417×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068
11256
214736
Stop Event
1×node limit
Counts
1 → 13
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (neg.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 2) x))))) (#(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 neg.f64 (*.f64 (sqrt.f64 2) x))))) (#(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 expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))) (#(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)))))))

simplify12.0ms (0.5%)

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
0796
11296
22596
32996
43396
55196
67396
78496
89696
912196
Stop Event
1×saturated
Counts
25 → 15
Calls
Call 1
Inputs
(*.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))
(*.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))
(*.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 -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))
(*.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))
(*.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))

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 18 to 5 computations (72.2% saved)

series4.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@0
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
2.0ms
x
@-inf
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms
x
@inf
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite39.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
417×pow1_binary64
408×prod-diff_binary64
401×add-sqr-sqrt_binary64
394×add-log-exp_binary64
393×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11294
218204
Stop Event
1×node limit
Counts
1 → 38
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) 0) (/.f64 (*.f64 x x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (*.f64 2 (pow.f64 x 3))) (*.f64 (fma.f64 x x 0) (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)))))

simplify20.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
248×fma-def_binary64
22×distribute-rgt-in_binary64
21×associate-*l*_binary64
21×sub-neg_binary64
19×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012100
121100
253100
3104100
4119100
5167100
6239100
7276100
8322100
9499100
10527100
Stop Event
1×saturated
Counts
50 → 41
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 -1) (*.f64 (sqrt.f64 -2) x)))
(*.f64 -1 (*.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(*.f64 -1 (*.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(*.f64 -1 (*.f64 (sqrt.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 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(*.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))

eval23.0ms (1%)

Compiler

Compiled 675 to 448 computations (33.6% saved)

prune15.0ms (0.7%)

Pruning

9 alts after pruning (4 fresh and 5 done)

PrunedKeptTotal
New85489
Fresh000
Picked011
Done145
Total86995
Error
0.0b
Counts
95 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
▶58.7b
(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓33.7b
(*.f64 (sqrt.f64 2) (neg.f64 x))
✓0.1b
(hypot.f64 x x)
✓60.7b
(*.f64 (*.f64 x x) 2)
✓29.4b
(*.f64 (sqrt.f64 2) x)
▶62.3b
(/.f64 1 (+.f64 x x))
▶30.1b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶56.4b
(+.f64 x x)
✓30.0b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 55 to 39 computations (29.1% saved)

localize2.0ms (0.1%)

Compiler

Compiled 5 to 2 computations (60% saved)

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓3.9b
(-.f64 (+.f64 1 (+.f64 x x)) 1)
Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms
x
@inf
(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms
x
@-inf
(-.f64 (+.f64 1 (+.f64 x x)) 1)

rewrite55.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
654×pow1_binary64
621×add-log-exp_binary64
619×log1p-expm1-u_binary64
619×expm1-log1p-u_binary64
611×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0610
11454
223484
Stop Event
1×node limit
Counts
1 → 93
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (+.f64 x x)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 2 x -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (-.f64 (+.f64 x x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 2 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 x -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (-.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x x) (fma.f64 2 x 1)) (*.f64 (+.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x x) x) (*.f64 (+.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 2 x 1) (+.f64 x x)) (*.f64 -1 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (+.f64 x x)) 1) (-.f64 (hypot.f64 1 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (*.f64 2 (pow.f64 x 3))) (*.f64 (fma.f64 x x 0) (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (*.f64 (+.f64 (+.f64 x x) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (*.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 2 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1)) (fma.f64 2 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 x x)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (+.f64 x x)) (hypot.f64 1 (+.f64 x x)) -1)))))

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
Stop Event
1×saturated
Counts
105 → 93
Calls
Call 1
Inputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
Outputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)

localize7.0ms (0.3%)

Compiler

Compiled 11 to 5 computations (54.5% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓0.3b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
0.5b
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 21 to 17 computations (19% saved)

series6.0ms (0.3%)

Counts
2 → 0
Calls

6 calls:

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

rewrite44.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
490×pow1_binary64
471×add-sqr-sqrt_binary64
462×*-un-lft-identity_binary64
454×add-log-exp_binary64
454×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
114414
2132214
Stop Event
1×node limit
Counts
2 → 50
Calls
Call 1
Inputs
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.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 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) 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 2) (*.f64 (cbrt.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 (sqrt.f64 2) x)) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) (sqrt.f64 (*.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 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4) (*.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 2) 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 2 1/4) (*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 (sqrt.f64 2) 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 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)) (pow.f64 (*.f64 (sqrt.f64 2) x) 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 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 (*.f64 (sqrt.f64 2) x)) (cbrt.f64 (*.f64 (sqrt.f64 2) x))) (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (pow.f64 2 1/4)) (sqrt.f64 x))))) (#(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 (sqrt.f64 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))) (#(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 -.f64 (+.f64 1 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2) (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))))

simplify6.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
50 → 50
Calls
Call 1
Inputs
Outputs

eval41.0ms (1.8%)

Compiler

Compiled 1762 to 1277 computations (27.5% saved)

prune24.0ms (1.1%)

Pruning

11 alts after pruning (3 fresh and 8 done)

PrunedKeptTotal
New1553158
Fresh000
Picked101
Done088
Total15611167
Error
0.0b
Counts
167 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
✓58.7b
(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓33.7b
(*.f64 (sqrt.f64 2) (neg.f64 x))
✓0.1b
(hypot.f64 x x)
✓60.7b
(*.f64 (*.f64 x x) 2)
✓29.4b
(*.f64 (sqrt.f64 2) x)
▶60.7b
(*.f64 4 (*.f64 x x))
✓56.4b
(+.f64 x x)
▶58.7b
(+.f64 (+.f64 1 x) (-.f64 x 1))
▶29.3b
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))
✓30.0b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓62.3b
(/.f64 1 (+.f64 x x))
Compiler

Compiled 71 to 51 computations (28.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 4 (*.f64 x x))
Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 4 (*.f64 x x))
0.0ms
x
@inf
(*.f64 4 (*.f64 x x))
0.0ms
x
@-inf
(*.f64 4 (*.f64 x x))

rewrite38.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
422×pow1_binary64
408×add-sqr-sqrt_binary64
401×*-un-lft-identity_binary64
392×add-log-exp_binary64
392×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11027
211287
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 4 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 4 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 x 2) 3) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 16 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 x 2) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (*.f64 x 2))))))))

simplify165.0ms (7.4%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
553×fabs-mul_binary64
523×pow-sqr_binary64
445×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533084
6124284
7212184
8228584
9246984
10267784
11297484
12336784
13384884
14441484
15510084
16593384
17632984
18662384
19689584
20696584
21699984
22794084
Stop Event
1×node limit
Counts
26 → 16
Calls
Call 1
Inputs
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
Outputs
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (*.f64 x x))
(*.f64 x (*.f64 4 x))

localize13.0ms (0.6%)

Local error

Found 2 expressions with local error:

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

Compiled 21 to 18 computations (14.3% saved)

series39.0ms (1.7%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
36.0ms
x
@0
(*.f64 (pow.f64 2 1/4) x)
0.0ms
x
@inf
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))
0.0ms
x
@inf
(*.f64 (pow.f64 2 1/4) x)
0.0ms
x
@-inf
(*.f64 (pow.f64 2 1/4) x)
0.0ms
x
@0
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))

rewrite48.0ms (2.2%)

Algorithm
1×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
2161113
Stop Event
1×node limit
Counts
2 → 22
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))
(*.f64 (pow.f64 2 1/4) 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 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 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 x (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))) (#(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 -.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 2 1/4) x)) 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 (*.f64 x x) (sqrt.f64 2)))))) (#(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 (pow.f64 2 1/4) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))))))

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0572
1672
Stop Event
1×saturated
Counts
34 → 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 (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)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓3.9b
(+.f64 (+.f64 1 x) (-.f64 x 1))
Compiler

Compiled 16 to 11 computations (31.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 (+.f64 1 x) (-.f64 x 1))
0.0ms
x
@inf
(+.f64 (+.f64 1 x) (-.f64 x 1))
0.0ms
x
@-inf
(+.f64 (+.f64 1 x) (-.f64 x 1))

rewrite55.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
911×pow1_binary64
858×log1p-expm1-u_binary64
858×expm1-log1p-u_binary64
857×add-log-exp_binary64
843×add-exp-log_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0610
114610
222834
Stop Event
1×node limit
Counts
1 → 46
Calls
Call 1
Inputs
(+.f64 (+.f64 1 x) (-.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 x (-.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 1 x) 2) (+.f64 x (-.f64 1 (+.f64 x -1)))) (/.f64 (pow.f64 (+.f64 x -1) 2) (+.f64 x (-.f64 1 (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (+.f64 x -1) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (/.f64 1 (+.f64 x (-.f64 1 (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))) (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (+.f64 x -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (-.f64 1 (+.f64 x -1))) (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (+.f64 x -1) 3)) (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (+.f64 x -1) 3)) (+.f64 (pow.f64 (+.f64 x -1) 2) (-.f64 (pow.f64 (+.f64 1 x) 2) (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (+.f64 x (-.f64 1 (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 (+.f64 x -1) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))) (neg.f64 (+.f64 x (-.f64 1 (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 1 (pow.f64 x 3)) (fma.f64 x x (+.f64 1 x))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (+.f64 (pow.f64 x 3) -1))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (fma.f64 x x (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 1 (*.f64 x x)) (fma.f64 x x (+.f64 1 x))) (*.f64 (-.f64 1 x) (+.f64 (pow.f64 x 3) -1))) (*.f64 (-.f64 1 x) (fma.f64 x x (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 1 x)) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (fma.f64 x x -1))) (*.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 1 (*.f64 x x)) (+.f64 1 x)) (*.f64 (-.f64 1 x) (fma.f64 x x -1))) (*.f64 (-.f64 1 x) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 x 3) -1) (+.f64 1 (-.f64 (*.f64 x x) x))) (*.f64 (fma.f64 x x (+.f64 1 x)) (+.f64 1 (pow.f64 x 3)))) (*.f64 (fma.f64 x x (+.f64 1 x)) (+.f64 1 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (fma.f64 x x -1) (+.f64 1 (-.f64 (*.f64 x x) x))) (*.f64 (+.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (*.f64 (+.f64 1 x) (+.f64 1 (-.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 x 3) -1) (-.f64 1 x)) (*.f64 (fma.f64 x x (+.f64 1 x)) (-.f64 1 (*.f64 x x)))) (*.f64 (fma.f64 x x (+.f64 1 x)) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (fma.f64 x x -1) (-.f64 1 x)) (*.f64 (+.f64 1 x) (-.f64 1 (*.f64 x x)))) (*.f64 (+.f64 1 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (+.f64 1 x)) 3) 1) (+.f64 (*.f64 (+.f64 x (+.f64 1 x)) (+.f64 x (+.f64 1 x))) (+.f64 1 (*.f64 (+.f64 x (+.f64 1 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x (+.f64 x -1)) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 x (+.f64 x -1)) (+.f64 x (+.f64 x -1))) (+.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 x (+.f64 1 x)) (+.f64 x (+.f64 1 x))) 1) (+.f64 (+.f64 x (+.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 x (+.f64 x -1)) (+.f64 x (+.f64 x -1)))) (-.f64 1 (+.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x -1) 2) (pow.f64 (+.f64 1 x) 2)) (-.f64 (+.f64 x -1) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 x) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x -1) (+.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2) (cbrt.f64 (+.f64 x -1)) (+.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) (cbrt.f64 (+.f64 1 x)) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x -1)) (+.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)) (+.f64 x -1))))))

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
Stop Event
1×saturated
Counts
58 → 47
Calls
Call 1
Inputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
Outputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)

eval27.0ms (1.2%)

Compiler

Compiled 1165 to 829 computations (28.8% saved)

prune15.0ms (0.7%)

Pruning

13 alts after pruning (3 fresh and 10 done)

PrunedKeptTotal
New83386
Fresh000
Picked101
Done01010
Total841397
Error
0.0b
Counts
97 → 13
Alt Table
Click to see full alt table
StatusErrorProgram
✓58.7b
(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓33.7b
(*.f64 (sqrt.f64 2) (neg.f64 x))
✓0.1b
(hypot.f64 x x)
✓60.7b
(*.f64 (*.f64 x x) 2)
✓29.4b
(*.f64 (sqrt.f64 2) x)
✓60.7b
(*.f64 4 (*.f64 x x))
✓29.3b
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))
56.4b
(-.f64 x (-.f64 1 (+.f64 1 x)))
✓56.4b
(+.f64 x x)
58.7b
(-.f64 (+.f64 x (+.f64 1 x)) 1)
60.6b
(/.f64 (-.f64 (*.f64 (+.f64 x (+.f64 1 x)) (+.f64 x (+.f64 1 x))) 1) (+.f64 (+.f64 x (+.f64 1 x)) 1))
✓30.0b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓62.3b
(/.f64 1 (+.f64 x x))
Compiler

Compiled 101 to 73 computations (27.7% saved)

regimes49.0ms (2.2%)

Counts
17 → 1
Calls
Call 1
Inputs
(+.f64 x x)
(/.f64 0 0)
(*.f64 4 (*.f64 x x))
(/.f64 1 (+.f64 x x))
(*.f64 (*.f64 x x) 2)
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 x (+.f64 1 x)) 1)
(+.f64 (+.f64 1 x) (-.f64 x 1))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(/.f64 (-.f64 (*.f64 (+.f64 x (+.f64 1 x)) (+.f64 x (+.f64 1 x))) 1) (+.f64 (+.f64 x (+.f64 1 x)) 1))
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
Outputs
(hypot.f64 x x)
Calls

7 calls:

10.0ms
x
6.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
6.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
6.0ms
(*.f64 x x)
6.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
Results
ErrorSegmentsBranch
0.1b1x
0.1b1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
0.1b1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
0.1b1(+.f64 (*.f64 x x) (*.f64 x x))
0.1b1(+.f64 (*.f64 x x) (*.f64 x x))
0.1b1(*.f64 x x)
0.1b1(*.f64 x x)
Compiler

Compiled 158 to 92 computations (41.8% saved)

regimes17.0ms (0.8%)

Counts
10 → 1
Calls
Call 1
Inputs
(+.f64 x x)
(/.f64 0 0)
(*.f64 4 (*.f64 x x))
(/.f64 1 (+.f64 x x))
(*.f64 (*.f64 x x) 2)
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 x (+.f64 1 x)) 1)
(+.f64 (+.f64 1 x) (-.f64 x 1))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(/.f64 (-.f64 (*.f64 (+.f64 x (+.f64 1 x)) (+.f64 x (+.f64 1 x))) 1) (+.f64 (+.f64 x (+.f64 1 x)) 1))
Outputs
(-.f64 x (-.f64 1 (+.f64 1 x)))
Calls

3 calls:

7.0ms
x
4.0ms
(*.f64 x x)
4.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
56.4b1x
56.4b1(*.f64 x x)
56.4b1(*.f64 x x)
Compiler

Compiled 81 to 51 computations (37% saved)

regimes12.0ms (0.5%)

Accuracy

Total -7.6b remaining (-13.5%)

Threshold costs -7.6b (-13.5%)

Counts
5 → 1
Calls
Call 1
Inputs
(+.f64 x x)
(/.f64 0 0)
(*.f64 4 (*.f64 x x))
(/.f64 1 (+.f64 x x))
(*.f64 (*.f64 x x) 2)
Outputs
(+.f64 x x)
Calls

3 calls:

4.0ms
x
3.0ms
(*.f64 x x)
3.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
56.4b1x
56.4b1(*.f64 x x)
56.4b1(*.f64 x x)
Compiler

Compiled 32 to 17 computations (46.9% saved)

simplify5.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
15×cancel-sign-sub-inv_binary64
10×distribute-neg-in_binary64
10×sub-neg_binary64
9×+-commutative_binary64
9×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
11518
22818
34518
46418
58818
610218
710918
811918
912318
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
(-.f64 x (-.f64 1 (+.f64 1 x)))
(+.f64 x x)
Outputs
(hypot.f64 x x)
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 x (-.f64 1 (+.f64 x 1)))
(+.f64 x (+.f64 (+.f64 x 1) -1))
(+.f64 x x)
Compiler

Compiled 16 to 10 computations (37.5% saved)

soundness6.0ms (0.3%)

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
Compiler

Compiled 13 to 6 computations (53.8% saved)

end21.0ms (0.9%)

Compiler

Compiled 14 to 8 computations (42.9% saved)

Profiling

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