Details

Time bar (total: 3.3s)

analyze128.0ms (3.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
40.6%59.3%0.1%7
45.3%53.1%1.7%8
63.2%33.6%3.2%9
66%28.9%5.2%10
75.1%17.8%7.1%11
76.6%15%8.4%12
Compiler

Compiled 10 to 6 computations (40% saved)

sample1.5s (45.6%)

Results
1.5s8256×body256valid
32.0ms385×body256invalid

preprocess17.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
4×associate-/r*_binary64
2×*-commutative_binary64
2×count-2_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
11320
21820
32220
022
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (+.f64 x x))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
2×associate-/r*_binary64
1×+-commutative_binary64
1×*-commutative_binary64
1×count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
1910
21210
31410
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

eval0.0ms (0%)

Compiler

Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 17 to 5 computations (70.6% saved)

series5.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
y
@0
(/.f64 (+.f64 x y) (+.f64 y y))
1.0ms
x
@inf
(/.f64 (+.f64 x y) (+.f64 y y))
1.0ms
x
@0
(/.f64 (+.f64 x y) (+.f64 y y))
1.0ms
y
@inf
(/.f64 (+.f64 x y) (+.f64 y y))
1.0ms
y
@-inf
(/.f64 (+.f64 x y) (+.f64 y y))

rewrite54.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
803×pow1_binary64
753×add-log-exp_binary64
752×log1p-expm1-u_binary64
752×expm1-log1p-u_binary64
737×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
114210
2237810
Stop Event
1×node limit
Counts
1 → 33
Calls
Call 1
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 x y) (+.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y y) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y y) (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x y)) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (+.f64 x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (+.f64 y y)) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) 0) 0)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))))

simplify12.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
4×fma-def_binary64
2×+-commutative_binary64
2×associate-/l*_binary64
1×associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07204
111168
220168
328168
432168
533168
Stop Event
1×saturated
Counts
57 → 38
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Outputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)

eval8.0ms (0.2%)

Compiler

Compiled 401 to 119 computations (70.3% saved)

prune7.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New34438
Fresh000
Picked101
Done000
Total35439
Error
0b
Counts
39 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶38.2b
(/.f64 x (/.f64 y 1/2))
▶0.0b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
25.1b
1/2
▶0.1b
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
Compiler

Compiled 30 to 23 computations (23.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓0.0b
(*.f64 1/2 (/.f64 x y))
Compiler

Compiled 20 to 10 computations (50% saved)

series22.0ms (0.7%)

Counts
2 → 6
Calls

12 calls:

TimeVariablePointExpression
16.0ms
y
@0
(*.f64 1/2 (/.f64 x y))
1.0ms
x
@0
(*.f64 1/2 (/.f64 x y))
1.0ms
y
@inf
(*.f64 1/2 (/.f64 x y))
1.0ms
x
@inf
(*.f64 1/2 (/.f64 x y))
0.0ms
x
@-inf
(*.f64 1/2 (/.f64 x y))

rewrite62.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
890×pow1_binary64
830×add-log-exp_binary64
830×log1p-expm1-u_binary64
830×expm1-log1p-u_binary64
815×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0717
115815
2215715
Stop Event
1×node limit
Counts
2 → 53
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 y (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 1/2 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (/.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/2 (/.f64 x y) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))) (/.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 (/.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8)) (/.f64 1 (+.f64 1/4 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (*.f64 1/4 (/.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4)) (/.f64 1 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 x y) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (*.f64 1/4 (/.f64 x y)))) (+.f64 1/8 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y))) (-.f64 1/4 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8)) (+.f64 1/4 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (*.f64 1/4 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8)) (+.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (-.f64 1/4 (*.f64 1/4 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4)) (+.f64 1/2 (*.f64 -1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (*.f64 (pow.f64 (/.f64 x y) 3) 1/8))) (neg.f64 (+.f64 1/4 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) (*.f64 1/4 (/.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))) (neg.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) 1/4) (-.f64 (*.f64 1/2 (/.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 x y) 1/2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 (/.f64 x y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4)) (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 1/2)))))

simplify118.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
2×associate-/l*_binary64
1×associate-*r/_binary64
1×associate-*l/_binary64
1×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0624
1924
21324
31724
41824
Stop Event
1×saturated
Counts
59 → 55
Calls
Call 1
Inputs
1/2
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
1/2
1/2
Outputs
1/2
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
1/2
1/2

localize5.0ms (0.2%)

Compiler

Compiled 13 to 8 computations (38.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 y (+.f64 x y))
✓0.1b
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
Compiler

Compiled 30 to 12 computations (60% saved)

series12.0ms (0.4%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
4.0ms
y
@0
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
2.0ms
x
@0
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
1.0ms
y
@inf
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
1.0ms
x
@inf
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
1.0ms
y
@-inf
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)

rewrite160.0ms (4.8%)

Algorithm
1×batch-egg-rewrite
Rules
484×log-prod_binary64
473×prod-diff_binary64
278×pow-prod-down_binary64
260×pow2_binary64
179×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0920
120317
2273717
Stop Event
1×node limit
Counts
2 → 82
Calls
Call 1
Inputs
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
(/.f64 y (+.f64 x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/2 (/.f64 (+.f64 y x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 (+.f64 y x) y))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 (+.f64 y x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 (+.f64 y x) y)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 (+.f64 y x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (/.f64 (+.f64 y x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) 2) (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (+.f64 y x) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 y x) y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) (sqrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 2 y)) (+.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (+.f64 y x) y))) -2) (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (/.f64 (+.f64 y x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 2 (/.f64 (+.f64 y x) y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 y (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 y x) y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) (sqrt.f64 (/.f64 2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (+.f64 y x) y))) -2) (cbrt.f64 (/.f64 2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 (/.f64 y (+.f64 y x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (/.f64 (+.f64 y x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (+.f64 y x) y)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (/.f64 2 (/.f64 (+.f64 y x) y)))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (+.f64 y x) y))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 1/2 (/.f64 (+.f64 y x) y))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (+.f64 y x) y))) -1/2) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 y (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 y (+.f64 y x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 y (+.f64 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 y (+.f64 y x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 y (+.f64 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 y (+.f64 y x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (/.f64 1 (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 y (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 y (+.f64 y x))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) y) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) y) -2)) (cbrt.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (/.f64 1 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 y (+.f64 y x))) (sqrt.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (/.f64 1 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 y) (/.f64 1 (neg.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 y x)) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) 1) (/.f64 (cbrt.f64 y) (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 y x)) -2) (/.f64 y (cbrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (pow.f64 (cbrt.f64 (+.f64 y x)) 2)) (cbrt.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) (pow.f64 (cbrt.f64 (+.f64 y x)) 2)) (/.f64 (sqrt.f64 y) (cbrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 y x) -1/2) (/.f64 y (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (sqrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 y) (sqrt.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 y (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 y x) y) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 y (+.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 y (+.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 y (+.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 y x) y) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 y 3) (pow.f64 (+.f64 y x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 y x) y) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 y (neg.f64 (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 y x) y) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 y (+.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 y (+.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 y 3) (pow.f64 (+.f64 y x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 y (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 y (+.f64 y x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 y (+.f64 y x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 y (+.f64 y x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 y (+.f64 y x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 y x) y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 y (+.f64 y x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 y (+.f64 y x))) -1) -1))))))

simplify190.0ms (5.7%)

Algorithm
1×egg-herbie
Rules
775×fma-neg_binary64
495×fma-def_binary64
446×cancel-sign-sub-inv_binary64
318×associate-/l/_binary64
285×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
096684
1310606
21246555
34536534
Stop Event
1×node limit
Counts
130 → 107
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) x) (+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 3)))) (pow.f64 y 3))) (*.f64 1/2 (/.f64 x y)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) x) (pow.f64 y 3))) (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)) x)) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)) x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (pow.f64 y 2)) (+.f64 (*.f64 1/2 (pow.f64 y 2)) (*.f64 y (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y))))) (pow.f64 x 2))) (*.f64 1/2 (/.f64 x y)))))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 y x)) (*.f64 1/2 (/.f64 x y)))))
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (pow.f64 y 2)) (+.f64 (*.f64 1/2 (pow.f64 y 2)) (*.f64 -1 (*.f64 y (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)))))) (pow.f64 x 2))) (*.f64 1/2 (/.f64 x y))))))
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
Outputs
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) x) (+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 3)))) (pow.f64 y 3))) (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 2))) x) (pow.f64 y 3))) (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)) x)) (*.f64 1/2 (/.f64 x y))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)) x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (pow.f64 y 2)) (+.f64 (*.f64 1/2 (pow.f64 y 2)) (*.f64 y (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y))))) (pow.f64 x 2))) (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 y x)) (*.f64 1/2 (/.f64 x y)))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 (*.f64 -1/2 (/.f64 y x)) (+.f64 1/2 (+.f64 (*.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (pow.f64 y 2)) (+.f64 (*.f64 1/2 (pow.f64 y 2)) (*.f64 -1 (*.f64 y (+.f64 (*.f64 -1/2 y) (*.f64 1/2 y)))))) (pow.f64 x 2))) (*.f64 1/2 (/.f64 x y))))))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x))))
(-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x)))
(*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x)))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(+.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (*.f64 (/.f64 y x) (/.f64 y x)))
(+.f64 (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)) (pow.f64 (/.f64 y x) 3))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (/.f64 y x)) (fma.f64 -1 (/.f64 (*.f64 y y) (*.f64 x x)) (neg.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (-.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 4) (pow.f64 x 4))))
(+.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (fma.f64 (/.f64 y x) (/.f64 y x) (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(*.f64 (+.f64 (*.f64 (/.f64 y x) (/.f64 y x)) 1) (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 1 (neg.f64 (/.f64 x y)))
(-.f64 1 (/.f64 x y))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (+.f64 1 (neg.f64 (/.f64 x y))) (/.f64 (*.f64 x x) (*.f64 y y)))
(+.f64 (-.f64 1 (/.f64 x y)) (*.f64 (/.f64 x y) (/.f64 x y)))
(+.f64 1 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
(+.f64 (+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) 1) (*.f64 -1 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 x y))))
(+.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (-.f64 (-.f64 1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (/.f64 x y)))
(+.f64 1 (-.f64 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))) (pow.f64 (/.f64 x y) 3)))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 1 (neg.f64 (/.f64 x y)))
(-.f64 1 (/.f64 x y))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (+.f64 1 (neg.f64 (/.f64 x y))) (/.f64 (*.f64 x x) (*.f64 y y)))
(+.f64 (-.f64 1 (/.f64 x y)) (*.f64 (/.f64 x y) (/.f64 x y)))
(+.f64 1 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
(+.f64 (+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) 1) (*.f64 -1 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 x y))))
(+.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (-.f64 (-.f64 1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (/.f64 x y)))
(+.f64 1 (-.f64 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))) (pow.f64 (/.f64 x y) 3)))
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 1 (neg.f64 (/.f64 x y)))
(-.f64 1 (/.f64 x y))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (*.f64 -1 (/.f64 x y))))
(+.f64 (+.f64 1 (neg.f64 (/.f64 x y))) (/.f64 (*.f64 x x) (*.f64 y y)))
(+.f64 (-.f64 1 (/.f64 x y)) (*.f64 (/.f64 x y) (/.f64 x y)))
(+.f64 1 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))))
(+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 -1 (/.f64 x y)))))
(+.f64 (+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) 1) (*.f64 -1 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 x y))))
(+.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (-.f64 (-.f64 1 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (/.f64 x y)))
(+.f64 1 (-.f64 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 x y))) (pow.f64 (/.f64 x y) 3)))
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x))))
(-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x)))
(*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x)))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(+.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (*.f64 (/.f64 y x) (/.f64 y x)))
(+.f64 (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)) (pow.f64 (/.f64 y x) 3))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (/.f64 y x)) (fma.f64 -1 (/.f64 (*.f64 y y) (*.f64 x x)) (neg.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (-.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 4) (pow.f64 x 4))))
(+.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (fma.f64 (/.f64 y x) (/.f64 y x) (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(*.f64 (+.f64 (*.f64 (/.f64 y x) (/.f64 y x)) 1) (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)))
(/.f64 y x)
(+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x))))
(-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x)))
(*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))))
(+.f64 (+.f64 (/.f64 y x) (neg.f64 (/.f64 (*.f64 y y) (*.f64 x x)))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(+.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (*.f64 (/.f64 y x) (/.f64 y x)))
(+.f64 (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)) (pow.f64 (/.f64 y x) 3))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (+.f64 (/.f64 y x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (/.f64 y x)) (fma.f64 -1 (/.f64 (*.f64 y y) (*.f64 x x)) (neg.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (-.f64 (-.f64 (/.f64 y x) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 (pow.f64 y 4) (pow.f64 x 4))))
(+.f64 (/.f64 y x) (-.f64 (pow.f64 (/.f64 y x) 3) (fma.f64 (/.f64 y x) (/.f64 y x) (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(*.f64 (+.f64 (*.f64 (/.f64 y x) (/.f64 y x)) 1) (*.f64 (+.f64 (/.f64 (neg.f64 y) x) 1) (/.f64 y x)))

eval100.0ms (3%)

Compiler

Compiled 2325 to 1405 computations (39.6% saved)

prune159.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1602162
Fresh101
Picked101
Done022
Total1624166
Error
0b
Counts
166 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓38.2b
(/.f64 x (/.f64 y 1/2))
✓0.0b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
25.1b
1/2
▶0.1b
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
Compiler

Compiled 28 to 22 computations (21.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
✓0.9b
(/.f64 1/2 (/.f64 y x))
Compiler

Compiled 20 to 10 computations (50% saved)

series3.0ms (0.1%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
0.0ms
y
@0
(/.f64 1/2 (/.f64 y x))
0.0ms
y
@inf
(/.f64 1/2 (/.f64 y x))
0.0ms
x
@inf
(/.f64 1/2 (/.f64 y x))
0.0ms
y
@-inf
(/.f64 1/2 (/.f64 y x))
0.0ms
y
@0
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))

rewrite98.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
937×pow1_binary64
876×add-log-exp_binary64
876×log1p-expm1-u_binary64
876×expm1-log1p-u_binary64
860×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0717
116515
2232515
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(/.f64 1/2 (/.f64 y x))
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (/.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (/.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) (cbrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2))) (cbrt.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) (sqrt.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (/.f64 (neg.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (neg.f64 y)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (/.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/8 (pow.f64 (/.f64 x y) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 y x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/8 (pow.f64 (/.f64 x y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/2 (/.f64 x y) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))) (/.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 (/.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (*.f64 1/8 (pow.f64 (/.f64 x y) 3))) (/.f64 1 (+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 1/4 (/.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 1/4 (pow.f64 (/.f64 y x) 2))) (/.f64 1 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 1/4 (/.f64 x y)))) (+.f64 1/8 (*.f64 1/8 (pow.f64 (/.f64 x y) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y))) (-.f64 1/4 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 1/8 (pow.f64 (/.f64 x y) 3))) (+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 1/4 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 1/8 (pow.f64 (/.f64 x y) 3))) (+.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (-.f64 1/4 (*.f64 1/4 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 1/4 (pow.f64 (/.f64 y x) 2))) (+.f64 1/2 (*.f64 -1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (*.f64 1/8 (pow.f64 (/.f64 x y) 3)))) (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 1/4 (/.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))) (neg.f64 (+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)) 1/4) (-.f64 (*.f64 1/2 (/.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x y) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x y) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 (/.f64 x y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2))) (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 y) x 1/2)))))

simplify42.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
4×fma-def_binary64
2×+-commutative_binary64
2×associate-/l*_binary64
1×associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07372
111336
220336
328336
432336
533336
Stop Event
1×saturated
Counts
106 → 61
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Outputs
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)

eval16.0ms (0.5%)

Compiler

Compiled 738 to 489 computations (33.7% saved)

prune9.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New61061
Fresh011
Picked011
Done022
Total61465
Error
0b
Counts
65 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓38.2b
(/.f64 x (/.f64 y 1/2))
✓0.0b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
25.1b
1/2
✓0.1b
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
Compiler

Compiled 28 to 22 computations (21.4% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune51.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓38.2b
(/.f64 x (/.f64 y 1/2))
✓0.0b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
25.1b
1/2
✓0.1b
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
Compiler

Compiled 28 to 22 computations (21.4% saved)

regimes19.0ms (0.6%)

Counts
7 → 1
Calls
Call 1
Inputs
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
(+.f64 1/2 (/.f64 1/2 (/.f64 y x)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 x (/.f64 y 1/2))
1/2
1/2
Outputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Calls

4 calls:

5.0ms
y
5.0ms
x
3.0ms
(/.f64 (+.f64 x y) (+.f64 y y))
3.0ms
(/.f64 (+.f64 x y) (+.f64 y y))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(/.f64 (+.f64 x y) (+.f64 y y))
0.0b1(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 63 to 39 computations (38.1% saved)

regimes145.0ms (4.4%)

Accuracy

Total -47.4b remaining (-333%)

Threshold costs -47.4b (-333%)

Counts
3 → 5
Calls
Call 1
Inputs
(/.f64 x (/.f64 y 1/2))
1/2
1/2
Outputs
1/2
(/.f64 x (/.f64 y 1/2))
1/2
(/.f64 x (/.f64 y 1/2))
1/2
Calls

2 calls:

108.0ms
x
35.0ms
y
Results
ErrorSegmentsBranch
14.9b5x
14.2b5y
Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch256.0ms (7.7%)

Algorithm
4×binary-search
Steps
TimeLeftRight
16.0ms
7.802028742053584e-50
3.354810018252415e-47
178.0ms
-1.2875722218317122e-84
-1.5650020662113247e-90
46.0ms
-1.4185718682919113e-46
-1.5256332743064438e-51
16.0ms
-14429.236554431247
-6622.964894762561
Compiler

Compiled 122 to 99 computations (18.9% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02252
12452
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 y -7932556685763831/549755813888) 1/2 (if (<=.f64 y -7294582731756243/51422017416287688817342786954917203280710495801049370729644032) (/.f64 x (/.f64 y 1/2)) (if (<=.f64 y -14678391142336458/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496) 1/2 (if (<=.f64 y 2103422787813410304/26959946667150639794667015087019630673637144422540572481103610249216) (/.f64 x (/.f64 y 1/2)) 1/2))))
1/2
Outputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 y -7932556685763831/549755813888) 1/2 (if (<=.f64 y -7294582731756243/51422017416287688817342786954917203280710495801049370729644032) (/.f64 x (/.f64 y 1/2)) (if (<=.f64 y -14678391142336458/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496) 1/2 (if (<=.f64 y 2103422787813410304/26959946667150639794667015087019630673637144422540572481103610249216) (/.f64 x (/.f64 y 1/2)) 1/2))))
(if (<=.f64 y -7932556685763831/549755813888) 1/2 (if (<=.f64 y -7294582731756243/51422017416287688817342786954917203280710495801049370729644032) (/.f64 x (/.f64 y 1/2)) (if (<=.f64 y -7339195571168229/4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220251373109248) 1/2 (if (<=.f64 y 4108247632448067/52656145834278593348959013841835216159447547700274555627155488768) (/.f64 x (/.f64 y 1/2)) 1/2))))
1/2
Compiler

Compiled 43 to 33 computations (23.3% saved)

soundness0.0ms (0%)

end60.0ms (1.8%)

Compiler

Compiled 39 to 29 computations (25.6% saved)

Profiling

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