Details

Time bar (total: 1.3s)

analyze136.0ms (10.1%)

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
25%74.9%0.1%5
37.5%62.4%0.1%6
50%46.8%3.2%7
59.3%37.5%3.2%8
67.1%25.8%7.1%9
72.6%20.3%7.1%10
76.9%13.5%9.7%11
79.8%10.5%9.7%12
82%6.9%11.1%13
83.6%5.4%11.1%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample806.0ms (59.8%)

Results
776.0ms8256×body128valid
15.0ms150×body128invalid
Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess70.0ms (5.2%)

Algorithm
egg-herbie
Rules
1297×fma-neg_binary64
333×cancel-sign-sub-inv_binary64
300×fma-def_binary64
262×sub-neg_binary64
200×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
14428
210624
324724
455722
5122122
6225522
7343022
8382622
9384422
10384422
11450222
12450222
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y (-.f64 x 1)) (*.f64 x 1/2)) 918938533204673/1000000000000000)
Outputs
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 x (+.f64 y -1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (-.f64 y 1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
(+.f64 (-.f64 (*.f64 y (-.f64 x 1)) (*.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 y (+.f64 x -1)) (*.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1) (*.f64 x -1/2)))
(fma.f64 y (+.f64 x -1) (fma.f64 x -1/2 918938533204673/1000000000000000))
(fma.f64 x -1/2 (fma.f64 y (+.f64 x -1) 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1/2) (-.f64 918938533204673/1000000000000000 y))
(-.f64 918938533204673/1000000000000000 (fma.f64 x (-.f64 1/2 y) y))
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify34.0ms (2.5%)

Algorithm
egg-herbie
Rules
712×fma-neg_binary64
578×fma-def_binary64
222×cancel-sign-sub-inv_binary64
114×sub-neg_binary64
81×distribute-rgt-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01116
12714
26212
312912
426811
558011
6107511
7179411
8258111
9275211
10277911
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
Outputs
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (neg.f64 (*.f64 y 1/2))) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

prune3.0ms (0.2%)

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 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
0.0b
(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)
Compiler

Compiled 67 to 49 computations (26.9% saved)

localize7.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.3%)

Counts
1 → 24
Calls

6 calls:

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

rewrite56.0ms (4.2%)

Algorithm
batch-egg-rewrite
Rules
459×log-prod_binary64
426×fma-def_binary64
238×fma-neg_binary64
174×expm1-udef_binary64
174×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0913
120811
2275211
Stop Event
node limit
Counts
1 → 171
Calls
Call 1
Inputs
(-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2))
Outputs
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(cbrt.f64 (*.f64 y -1/2)) (*.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 y -1/2 (*.f64 y 1/2))) (sqrt.f64 (fma.f64 y -1/2 (*.f64 y 1/2))) (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y -1/2)) (sqrt.f64 (*.f64 y -1/2)) (*.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (*.f64 y 1/2))) (sqrt.f64 (*.f64 y 1/2)) (*.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (*.f64 y 1/2))) (-.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) (sqrt.f64 (*.f64 y 1/2))) (fma.f64 y -1/2 (*.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (*.f64 y 1/2))) (-.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) (sqrt.f64 (*.f64 y 1/2))) (fma.f64 (*.f64 y -1/2) 1 (*.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (*.f64 y 1/2))) (-.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) (sqrt.f64 (*.f64 y 1/2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 y 1/2))) (cbrt.f64 (*.f64 (*.f64 y y) 1/4)) (*.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (*.f64 y 1/2))) (-.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) (sqrt.f64 (*.f64 y 1/2))) (*.f64 (fma.f64 y -1/2 (*.f64 y 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (*.f64 y 1/2))) (-.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) (sqrt.f64 (*.f64 y 1/2))) (+.f64 (fma.f64 y -1/2 (*.f64 y 1/2)) (fma.f64 y -1/2 (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 (*.f64 y y) 1/4))) (cbrt.f64 (*.f64 y 1/2)) (*.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 y -1)) 2)) (cbrt.f64 (+.f64 y -1)) (*.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 y -1)) 2)) (cbrt.f64 (+.f64 y -1)) (*.f64 (*.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 y -1)) 2)) (cbrt.f64 (+.f64 y -1)) (fma.f64 y -1/2 (fma.f64 y -1/2 (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 y -1)) 2)) (cbrt.f64 (+.f64 y -1)) (neg.f64 (-.f64 (*.f64 y 1/2) (fma.f64 y -1/2 (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 y -1))) (sqrt.f64 (+.f64 y -1)) (*.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 y -1))) (sqrt.f64 (+.f64 y -1)) (*.f64 (*.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 y -1))) (sqrt.f64 (+.f64 y -1)) (fma.f64 y -1/2 (fma.f64 y -1/2 (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 y -1))) (sqrt.f64 (+.f64 y -1)) (neg.f64 (-.f64 (*.f64 y 1/2) (fma.f64 y -1/2 (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 (*.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (fma.f64 y -1/2 (fma.f64 y -1/2 (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (neg.f64 (-.f64 (*.f64 y 1/2) (fma.f64 y -1/2 (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (*.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 y -1/2 (fma.f64 y -1/2 (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y -1) (sqrt.f64 x)) (sqrt.f64 x) (neg.f64 (-.f64 (*.f64 y 1/2) (fma.f64 y -1/2 (*.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2))))))))

simplify30.0ms (2.2%)

Algorithm
egg-herbie
Rules
208×fma-neg_binary64
184×fma-def_binary64
42×sub-neg_binary64
37×cancel-sign-sub-inv_binary64
34×distribute-rgt-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023233
156215
2120215
3239215
4477215
5780215
6935215
7953215
8957215
Stop Event
saturated
Counts
195 → 182
Calls
Call 1
Inputs
(*.f64 -1/2 y)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(*.f64 (-.f64 y 1) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(*.f64 -1 (*.f64 (-.f64 1 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(*.f64 -1 x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(*.f64 (-.f64 x 1/2) y)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(*.f64 -1 (*.f64 y (-.f64 1/2 x)))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
Outputs
(*.f64 -1/2 y)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(-.f64 (*.f64 y x) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(*.f64 -1 (*.f64 (-.f64 1 y) x))
(*.f64 x (+.f64 y -1))
(-.f64 (*.f64 y x) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(*.f64 (-.f64 x 1/2) y)
(*.f64 y (+.f64 x -1/2))
(*.f64 y (+.f64 -1/2 x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(*.f64 -1 (*.f64 y (-.f64 1/2 x)))
(*.f64 y (+.f64 x -1/2))
(*.f64 y (+.f64 -1/2 x))
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)
(-.f64 (*.f64 y x) (+.f64 (*.f64 1/2 y) x))
(-.f64 (*.f64 y x) (fma.f64 1/2 y x))
(-.f64 (*.f64 y (+.f64 -1/2 x)) x)

prune128.0ms (9.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1811182
Fresh101
Picked101
Done000
Total1831184
Error
0b
Counts
184 → 1
Alt Table
StatusErrorProgram
0b
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
Compiler

Compiled 3977 to 2879 computations (27.6% saved)

localize6.0ms (0.4%)

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
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
Compiler

Compiled 12 to 9 computations (25% saved)

regimes32.0ms (2.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
11 → 1
Compiler

Compiled 112 to 81 computations (27.7% saved)

simplify3.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11314
Stop Event
saturated
Calls
Call 1
Inputs
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
Outputs
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

end34.0ms (2.5%)

Stop Event
done
Compiler

Compiled 36 to 27 computations (25% saved)

Profiling

Loading profile data...