Details

Time bar (total: 1.2s)

analyze109.0ms (9.4%)

Algorithm
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
25%56.2%18.8%6
37.5%40.6%22%7
46.8%31.2%22%8
54.6%21.9%23.5%9
60.1%16.4%23.5%10
64.4%11.3%24.3%11
67.3%8.4%24.3%12
69.6%5.8%24.7%13
71.1%4.2%24.7%14
Compiler

Compiled 10 to 6 computations (40% saved)

sample802.0ms (69.5%)

Results
785.0ms8256×body128valid
5.0ms64×body128invalid
Compiler

Compiled 20 to 12 computations (40% saved)

preprocess19.0ms (1.6%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
associate-+r+_binary64
associate-+l+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
11916
22616
33016
43216
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 (+.f64 (*.f64 y y) x) x)
Outputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (fma.f64 x x y))
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 y y) x) x)
(+.f64 x (fma.f64 y y x))
Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify7.0ms (0.6%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
associate-+r+_binary64
associate-+l+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1118
2158
3178
4188
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)
Outputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (fma.f64 x x y))

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.0b
(+.f64 y (fma.f64 x x y))
Compiler

Compiled 31 to 15 computations (51.6% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(+.f64 y (fma.f64 x x y))

series3.0ms (0.3%)

Counts
1 → 24
Calls

6 calls:

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

rewrite35.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
620×pow1_binary64
577×add-log-exp_binary64
577×log1p-expm1-u_binary64
577×expm1-log1p-u_binary64
59×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
11098
215318
Stop Event
node limit
Counts
1 → 34
Calls
Call 1
Inputs
(+.f64 y (fma.f64 x x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 y (fma.f64 x x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 y y) (-.f64 y (fma.f64 x x y))) (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2)) (cbrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (/.f64 1 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 y (fma.f64 x x y)) (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (*.f64 y y) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2))) (neg.f64 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))))))

simplify58.0ms (5%)

Algorithm
egg-herbie
Rules
783×sqr-pow_binary64
434×unswap-sqr_binary64
354×cube-prod_binary64
341×fabs-mul_binary64
312×pow-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07168
115168
225168
336168
465168
5170168
6595168
71463168
81647168
91831168
102039168
112324168
122717168
133195168
143754168
154442168
Stop Event
node limit
Counts
58 → 39
Calls
Call 1
Inputs
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))

prune45.0ms (3.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New38139
Fresh000
Picked101
Done000
Total39140
Error
0b
Counts
40 → 1
Alt Table
StatusErrorProgram
0b
(fma.f64 x x (*.f64 2 y))
Compiler

Compiled 518 to 164 computations (68.3% saved)

localize4.0ms (0.3%)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Error
0b
Counts
1 → 1
Alt Table
StatusErrorProgram
0b
(fma.f64 x x (*.f64 2 y))
Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes34.0ms (2.9%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts
7 → 1
Compiler

Compiled 62 to 34 computations (45.2% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 2 y))
Outputs
(fma.f64 x x (*.f64 2 y))

end32.0ms (2.8%)

Stop Event
done
Compiler

Compiled 24 to 15 computations (37.5% saved)

Profiling

Loading profile data...