Details

Time bar (total: 1.1s)

analyze121.0ms (10.7%)

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
37.5%62.4%0.1%6
56.2%43.7%0.1%7
65.6%34.3%0.1%8
76.5%23.4%0.1%9
82%18%0.1%10
87.8%12.1%0.1%11
90.7%9.2%0.1%12
93.8%6.1%0.1%13
95.3%4.6%0.1%14
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample829.0ms (73.2%)

Results
728.0ms7935×body128valid
33.0ms86×body2048valid
32.0ms111×body1024valid
16.0ms76×body512valid
7.0ms48×body256valid
Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess27.0ms (2.3%)

Algorithm
egg-herbie
Rules
128×fma-neg_binary64
44×fma-def_binary64
40×cancel-sign-sub-inv_binary64
35×sub-neg_binary64
19×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01224
12024
22824
34024
47024
513424
618124
728524
835020
941320
1048520
1153020
1254320
1354820
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
(+.f64 y (/.f64 (fabs.f64 (-.f64 x y)) 2))
Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
(+.f64 y (/.f64 (fabs.f64 (-.f64 x y)) 2))
(+.f64 y (/.f64 (fabs.f64 (-.f64 y x)) 2))
(+.f64 y (*.f64 1/2 (fabs.f64 (-.f64 y x))))
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) y)
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 y)
Compiler

Compiled 10 to 7 computations (30% saved)

simplify16.0ms (1.4%)

Algorithm
egg-herbie
Rules
97×fma-neg_binary64
34×fma-def_binary64
32×cancel-sign-sub-inv_binary64
27×sub-neg_binary64
17×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
0812
11312
22012
32912
45012
510412
616012
720812
827210
931710
1037610
1142110
1244410
1345210
1445710
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
(+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) 2))
(+.f64 x (*.f64 1/2 (fabs.f64 (-.f64 y x))))
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

prune2.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Compiler

Compiled 35 to 21 computations (40% saved)

localize4.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

series3.0ms (0.3%)

Counts
1 → 24
Calls

6 calls:

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

rewrite36.0ms (3.2%)

Algorithm
batch-egg-rewrite
Rules
777×pow1_binary64
725×log1p-expm1-u_binary64
725×expm1-log1p-u_binary64
82×add-sqr-sqrt_binary64
79×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
11558
221168
Stop Event
node limit
Counts
1 → 23
Calls
Call 1
Inputs
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (-.f64 y x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 y x) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (-.f64 y x) 1/2) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (-.f64 y x) 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (-.f64 y x) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (-.f64 y x) 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) 2) (cbrt.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (-.f64 y x) 1/2) 3) (pow.f64 x 3)) (+.f64 (*.f64 (*.f64 (-.f64 y x) 1/2) (*.f64 (-.f64 y x) 1/2)) (-.f64 (*.f64 x x) (*.f64 (*.f64 (-.f64 y x) 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (-.f64 y x) 1/2) (*.f64 (-.f64 y x) 1/2)) (*.f64 x x)) (-.f64 (*.f64 (-.f64 y x) 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (-.f64 y x) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (-.f64 y x) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (-.f64 y x) 1/2 x)) 1))))))

simplify25.0ms (2.2%)

Algorithm
egg-herbie
Rules
97×fma-neg_binary64
46×fma-def_binary64
34×cancel-sign-sub-inv_binary64
26×sub-neg_binary64
19×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08221
115221
223221
332221
453221
5105221
6161221
7211221
8289221
9351221
10402221
11426221
12432221
13437221
Stop Event
saturated
Counts
47 → 28
Calls
Call 1
Inputs
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(*.f64 1/2 (fabs.f64 (-.f64 y x)))
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
x
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
x
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
Outputs
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(*.f64 1/2 (fabs.f64 (-.f64 y x)))
(*.f64 1/2 (fabs.f64 (-.f64 x y)))
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
x
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
x
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)
(+.f64 (*.f64 1/2 (fabs.f64 (-.f64 y x))) x)
(fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)
(fma.f64 1/2 (fabs.f64 (-.f64 x y)) x)

prune10.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New27128
Fresh000
Picked011
Done000
Total27229
Error
0.1b
Counts
29 → 2
Alt Table
StatusErrorProgram
0.1b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
31.1b
(*.f64 1/2 (fabs.f64 (-.f64 y x)))
Compiler

Compiled 317 to 170 computations (46.4% saved)

localize4.0ms (0.3%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Error
0.1b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.1b
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
31.1b
(*.f64 1/2 (fabs.f64 (-.f64 y x)))
Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes16.0ms (1.4%)

Accuracy

Total 0.0b remaining (1%)

Threshold costs 0.0b (1%)

Counts
3 → 1
Compiler

Compiled 39 to 22 computations (43.6% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11110
21810
32310
42610
52710
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
Outputs
(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

end37.0ms (3.3%)

Stop Event
done
Compiler

Compiled 35 to 24 computations (31.4% saved)

Profiling

Loading profile data...