Details

Time bar (total: 1.8s)

analyze424.0ms (24.1%)

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
0%99.9%0.1%5
0%99.9%0.1%6
12.5%87.4%0.1%7
18.7%81.1%0.1%8
31.2%68.6%0.1%9
40.6%52.7%6.8%10
48.4%42.1%9.5%11
54.2%35.5%10.3%12
59.1%26.6%14.3%13
63.9%20.9%15.3%14
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample890.0ms (50.5%)

Results
812.0ms8256×body128valid
63.0ms647×body128invalid
Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess54.0ms (3.1%)

Algorithm
egg-herbie
Rules
869×fma-neg_binary64
384×fma-def_binary64
156×unsub-neg_binary64
145×distribute-rgt-in_binary64
108×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
13132
27332
317632
431732
565632
6127232
7202132
8274732
9291032
10293832
11293832
033
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
2
Outputs
0
1
2
Call 2
Inputs
(+.f64 x (*.f64 (-.f64 y x) z))
(+.f64 y (*.f64 (-.f64 x y) z))
(+.f64 z (*.f64 (-.f64 y z) x))
(+.f64 x (*.f64 (-.f64 z x) y))
Outputs
(+.f64 x (*.f64 (-.f64 y x) z))
(fma.f64 (-.f64 y x) z x)
(+.f64 y (*.f64 (-.f64 x y) z))
(+.f64 y (*.f64 z (-.f64 x y)))
(fma.f64 z (-.f64 x y) y)
(+.f64 z (*.f64 (-.f64 y z) x))
(+.f64 z (*.f64 x (-.f64 y z)))
(fma.f64 x (-.f64 y z) z)
(+.f64 x (*.f64 (-.f64 z x) y))
(+.f64 x (*.f64 y (-.f64 z x)))
(fma.f64 y (-.f64 z x) x)
Compiler

Compiled 10 to 6 computations (40% saved)

simplify19.0ms (1.1%)

Algorithm
egg-herbie
Rules
276×fma-def_binary64
251×fma-neg_binary64
71×cancel-sign-sub-inv_binary64
55×distribute-rgt-in_binary64
42×sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
1118
2248
3528
41008
51718
62818
74818
88758
911168
1012168
1112238
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 x (*.f64 (-.f64 y x) z))
Outputs
(+.f64 x (*.f64 (-.f64 y x) z))
(fma.f64 (-.f64 y x) z x)

prune2.0ms (0.1%)

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
(fma.f64 (-.f64 y x) z x)
Compiler

Compiled 34 to 17 computations (50% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (-.f64 y x) z x)

series5.0ms (0.3%)

Counts
1 → 36
Calls

9 calls:

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

rewrite37.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
736×pow1_binary64
682×add-log-exp_binary64
682×log1p-expm1-u_binary64
682×expm1-log1p-u_binary64
71×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11308
217878
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(fma.f64 (-.f64 y x) z x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (-.f64 y x) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 y x) z) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (-.f64 y x) z) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (-.f64 y x) z x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (-.f64 y x) z x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (-.f64 y x) z x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (-.f64 y x) z x)) (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) z x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) z x) 2)) (cbrt.f64 (fma.f64 (-.f64 y x) z x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (-.f64 y x) z x)) (sqrt.f64 (fma.f64 (-.f64 y x) z x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (-.f64 y x) z) 3) (pow.f64 x 3)) (+.f64 (*.f64 (*.f64 (-.f64 y x) z) (*.f64 (-.f64 y x) z)) (-.f64 (*.f64 x x) (*.f64 (*.f64 (-.f64 y x) z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (-.f64 y x) z) (*.f64 (-.f64 y x) z)) (*.f64 x x)) (-.f64 (*.f64 (-.f64 y x) z) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (-.f64 y x) z x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 y x) z x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) z x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) z x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (-.f64 y x) z x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (-.f64 y x) z x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (-.f64 y x) z x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) z x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (-.f64 y x) z x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (-.f64 y x) z x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (-.f64 y x) z x)))))))

simplify24.0ms (1.4%)

Algorithm
egg-herbie
Rules
263×fma-neg_binary64
255×fma-def_binary64
61×distribute-rgt-in_binary64
39×associate--r+_binary64
36×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
021345
154318
2121318
3246264
4533264
5959264
61141264
71165264
Stop Event
saturated
Counts
58 → 33
Calls
Call 1
Inputs
(-.f64 x (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 y z)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 y z)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 y z)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 -1 (*.f64 x (-.f64 z 1)))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
x
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 z (-.f64 y x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(*.f64 -1 (*.f64 (-.f64 x y) z))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
Outputs
(-.f64 x (*.f64 z x))
(-.f64 x (*.f64 x z))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 y z)
(*.f64 z y)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 y z)
(*.f64 z y)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 y z)
(*.f64 z y)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 x z))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 -1 (*.f64 x (-.f64 z 1)))
(-.f64 x (*.f64 x z))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
x
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 z (-.f64 y x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(*.f64 -1 (*.f64 (-.f64 x y) z))
(*.f64 z (-.f64 y x))
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
(-.f64 (fma.f64 y z x) (*.f64 x z))
(+.f64 x (*.f64 z (-.f64 y x)))
(fma.f64 z (-.f64 y x) x)

prune16.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New32133
Fresh000
Picked011
Done000
Total32234
Error
0b
Counts
34 → 2
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
0.0b
(fma.f64 (-.f64 y x) z x)
Compiler

Compiled 344 to 111 computations (67.7% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))

series6.0ms (0.3%)

Counts
1 → 9
Calls

9 calls:

TimeVariablePointExpression
2.0ms
y
@-inf
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
1.0ms
z
@inf
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
1.0ms
y
@0
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
0.0ms
z
@0
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
0.0ms
y
@inf
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))

rewrite53.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
582×fma-def_binary64
504×log-prod_binary64
269×fma-neg_binary64
176×expm1-udef_binary64
176×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
118511
2284011
Stop Event
node limit
Counts
1 → 153
Calls
Call 1
Inputs
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
Outputs
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1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (fma.f64 y z x) (*.f64 z x))))))))

simplify17.0ms (1%)

Algorithm
egg-herbie
Rules
212×fma-def_binary64
132×fma-neg_binary64
43×distribute-rgt-in_binary64
32×associate-*r*_binary64
31×unsub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01948
14748
210548
321648
445348
572648
684948
785848
Stop Event
saturated
Counts
162 → 162
Calls
Call 1
Inputs
(-.f64 x (*.f64 z x))
(*.f64 y z)
(*.f64 y z)
x
(*.f64 z (-.f64 y x))
(*.f64 -1 (*.f64 (-.f64 x y) z))
(*.f64 y z)
(*.f64 (-.f64 1 z) x)
(*.f64 -1 (*.f64 x (-.f64 z 1)))
Outputs
(-.f64 x (*.f64 z x))
(-.f64 x (*.f64 x z))
(*.f64 y z)
(*.f64 z y)
(*.f64 y z)
(*.f64 z y)
x
(*.f64 z (-.f64 y x))
(*.f64 -1 (*.f64 (-.f64 x y) z))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 x z))
(*.f64 -1 (*.f64 x (-.f64 z 1)))
(-.f64 x (*.f64 x z))

prune72.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1620162
Fresh000
Picked011
Done011
Total1622164
Error
0b
Counts
164 → 2
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 y z) x) (*.f64 z x))
0.0b
(fma.f64 (-.f64 y x) z x)
Compiler

Compiled 2754 to 674 computations (75.5% saved)

regimes85.0ms (4.8%)

Accuracy

Total 0.0b remaining (71.2%)

Threshold costs 0.0b (71.2%)

Counts
17 → 1
Compiler

Compiled 130 to 46 computations (64.6% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
22511
33111
43511
53611
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 z y (-.f64 x (*.f64 z x)))
Outputs
(fma.f64 z y (-.f64 x (*.f64 z x)))

end47.0ms (2.6%)

Stop Event
done
Compiler

Compiled 43 to 24 computations (44.2% saved)

Profiling

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