Details

Time bar (total: 1.0s)

analyze104.0ms (10%)

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
25%74.9%0.1%5
37.5%62.4%0.1%6
56.2%43.7%0.1%7
62.4%34.3%3.2%8
71.8%23.4%4.8%9
74.9%18%7.1%10
79.6%12.1%8.3%11
81.2%9.2%9.7%12
83.5%6.1%10.3%13
84.3%4.6%11.1%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample724.0ms (69.4%)

Results
698.0ms8256×body128valid
10.0ms128×body128invalid
Compiler

Compiled 16 to 12 computations (25% saved)

preprocess14.0ms (1.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
21614
31814
022
122
Stop Event
1×unsound
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Call 2
Inputs
(/.f64 (*.f64 x y) 2)
(/.f64 (*.f64 y x) 2)
Outputs
(/.f64 (*.f64 x y) 2)
(/.f64 x (/.f64 2 y))
(*.f64 (/.f64 x 2) y)
(*.f64 x (/.f64 y 2))
(/.f64 (*.f64 y x) 2)
(/.f64 x (/.f64 2 y))
(*.f64 (/.f64 x 2) y)
(*.f64 x (/.f64 y 2))
Symmetry

(sort x y)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify12.0ms (1.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2137
3167
4177
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) 2)
Outputs
(/.f64 (*.f64 x y) 2)
(/.f64 x (/.f64 2 y))
(/.f64 y (/.f64 2 x))
(*.f64 x (/.f64 y 2))

prune3.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.0b
(*.f64 x (/.f64 y 2))
▶0.0b
(/.f64 (*.f64 x y) 2)
Compiler

Compiled 40 to 28 computations (30% saved)

localize5.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.4%)

Counts
1 → 24
Calls

6 calls:

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

rewrite37.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
620×pow1_binary64
578×add-log-exp_binary64
578×log1p-expm1-u_binary64
578×expm1-log1p-u_binary64
64×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11297
215727
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (/.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 y 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (*.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2) (cbrt.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) (sqrt.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (*.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (neg.f64 y)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (*.f64 x y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 x y) -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2))))))))

simplify10.0ms (1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
06168
110168
217168
319168
Stop Event
1×saturated
Counts
52 → 30
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
Outputs
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))

prune14.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New30030
Fresh011
Picked011
Done000
Total30232
Error
0b
Counts
32 → 2
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 x (/.f64 y 2))
✓0.0b
(/.f64 (*.f64 x y) 2)
Compiler

Compiled 258 to 173 computations (32.9% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

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

rewrite35.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
610×pow1_binary64
568×add-log-exp_binary64
568×log1p-expm1-u_binary64
568×expm1-log1p-u_binary64
64×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11297
215547
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 x (/.f64 y 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 2 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x y)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 y) x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (neg.f64 y)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 y 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 y 1/2) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2))))))))

simplify9.0ms (0.9%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
06168
110168
217168
319168
Stop Event
1×saturated
Counts
44 → 22
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
Outputs
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 1/2 y))

prune9.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New22022
Fresh000
Picked011
Done011
Total22224
Error
0b
Counts
24 → 2
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 x (/.f64 y 2))
✓0.0b
(/.f64 (*.f64 x y) 2)
Compiler

Compiled 174 to 123 computations (29.3% saved)

regimes21.0ms (2%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts
2 → 1
Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify2.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
067
177
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 x (/.f64 y 2))
Outputs
(*.f64 x (/.f64 y 2))

end35.0ms (3.4%)

Stop Event
1×done
Remove

(sort x y)

Compiler

Compiled 42 to 30 computations (28.6% saved)

Profiling

Loading profile data...