Details

Time bar (total: 2.5s)

analyze212.0ms (8.5%)

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
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
28.1%71.8%0.1%9
42.1%57.7%0.1%10
46.8%50.3%2.9%11
53.8%41.9%4.2%12
Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.0s (40.3%)

Results
899.0ms8256×body256valid
92.0ms823×body256invalid

preprocess76.0ms (3%)

Algorithm
2×egg-herbie
Rules
774×fma-def_binary64
513×fma-neg_binary64
147×associate-/l*_binary64
135×cancel-sign-sub-inv_binary64
96×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02152
13752
26352
310052
418244
531344
667044
7128244
8215244
9282544
10291844
11292444
12292444
033
133
Stop Event
1×unsound
1×saturated
Calls
Call 1
Inputs
0
1
2
Outputs
0
1
0
2
Call 2
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 y (/.f64 2 x)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (*.f64 1/2 y) (*.f64 z -1/8))
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 y (/.f64 2 x)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (*.f64 1/2 y) (*.f64 z -1/8))
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 z (/.f64 2 y)) (/.f64 x 8))
(-.f64 (*.f64 (/.f64 y 2) z) (/.f64 x 8))
(-.f64 (*.f64 z (/.f64 y 2)) (/.f64 x 8))
(fma.f64 y (/.f64 z 2) (/.f64 x -8))
(fma.f64 y (/.f64 z 2) (*.f64 x -1/8))
(fma.f64 x -1/8 (*.f64 y (/.f64 z 2)))
(fma.f64 x -1/8 (*.f64 y (*.f64 1/2 z)))
(fma.f64 x -1/8 (*.f64 y (*.f64 z 1/2)))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
(-.f64 (/.f64 x (/.f64 2 z)) (/.f64 y 8))
(-.f64 (*.f64 (/.f64 x 2) z) (/.f64 y 8))
(fma.f64 (/.f64 x 2) z (/.f64 (neg.f64 y) 8))
(-.f64 (*.f64 x (/.f64 z 2)) (/.f64 y 8))
(fma.f64 z (/.f64 x 2) (*.f64 -1/8 y))
(fma.f64 x (/.f64 z 2) (*.f64 y -1/8))
(fma.f64 x (*.f64 1/2 z) (*.f64 y -1/8))
(fma.f64 x (*.f64 z 1/2) (*.f64 y -1/8))
Symmetry

(sort x y)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify34.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
209×fma-def_binary64
157×fma-neg_binary64
57×cancel-sign-sub-inv_binary64
42×distribute-rgt-neg-in_binary64
38×associate-/l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01013
11513
22613
33913
46911
512211
623711
742711
867811
996811
10108311
11111311
12111611
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(fma.f64 y (/.f64 x 2) (/.f64 (neg.f64 z) 8))
(fma.f64 y (/.f64 x 2) (*.f64 -1/8 z))
(fma.f64 y (/.f64 x 2) (*.f64 z -1/8))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (*.f64 1/2 y) (*.f64 z -1/8))
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))

eval1.0ms (0%)

Compiler

Compiled 20 to 14 computations (30% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
▶0b
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
Compiler

Compiled 23 to 17 computations (26.1% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (*.f64 x y) 2)
✓0.0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Compiler

Compiled 28 to 15 computations (46.4% saved)

series8.0ms (0.3%)

Counts
2 → 60
Calls

15 calls:

TimeVariablePointExpression
1.0ms
y
@0
(/.f64 (*.f64 x y) 2)
1.0ms
x
@0
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
1.0ms
y
@0
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
1.0ms
x
@inf
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
1.0ms
z
@0
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

rewrite170.0ms (6.8%)

Algorithm
1×batch-egg-rewrite
Rules
834×prod-diff_binary64
533×log-prod_binary64
293×pow2_binary64
279×fma-def_binary64
206×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01020
123118
2322018
Stop Event
1×node limit
Counts
2 → 218
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(/.f64 (*.f64 x y) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 y 1/2)) (*.f64 z -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 y 1/2)) (*.f64 (*.f64 z -1/8) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (fma.f64 -1/8 z (*.f64 z 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (fma.f64 (*.f64 z -1/8) 1 (*.f64 z 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 z) 1/2)) (cbrt.f64 (*.f64 (*.f64 z z) 1/64)) (*.f64 z 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (+.f64 (*.f64 z -1/8) (*.f64 z 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (fma.f64 -1 (*.f64 z 1/8) (*.f64 z 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8)) (fma.f64 (neg.f64 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simplify23.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
8×fma-def_binary64
6×*-commutative_binary64
3×associate-*r*_binary64
3×associate-*l*_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011516
118516
228516
334516
Stop Event
1×saturated
Counts
278 → 223
Calls
Call 1
Inputs
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.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 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 -1/8 z (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(*.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))

localize9.0ms (0.4%)

Compiler

Compiled 22 to 14 computations (36.4% saved)

eval108.0ms (4.3%)

Compiler

Compiled 4423 to 2764 computations (37.5% saved)

prune47.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2203223
Fresh000
Picked011
Done011
Total2205225
Error
0b
Counts
225 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶35.7b
(*.f64 1/2 (*.f64 y x))
▶27.2b
(*.f64 -1/8 z)
✓0.0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
✓0b
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
▶0.1b
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
Compiler

Compiled 51 to 39 computations (23.5% saved)

localize4.0ms (0.2%)

Compiler

Compiled 8 to 6 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 14 to 7 computations (50% saved)

series2.0ms (0.1%)

Counts
1 → 0
Calls

6 calls:

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

rewrite44.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
555×pow1_binary64
511×add-log-exp_binary64
511×log1p-expm1-u_binary64
511×expm1-log1p-u_binary64
501×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11217
213937
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 y x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (*.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (*.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (*.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (*.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 y x) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (*.f64 y x))))))))

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
11 → 11
Calls
Call 1
Inputs
Outputs

localize15.0ms (0.6%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
✓0.2b
(/.f64 1 (/.f64 2 y))
Compiler

Compiled 38 to 27 computations (28.9% saved)

series5.0ms (0.2%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
z
@inf
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
1.0ms
y
@0
(/.f64 1 (/.f64 2 y))
1.0ms
y
@-inf
(/.f64 1 (/.f64 2 y))
0.0ms
y
@inf
(/.f64 1 (/.f64 2 y))
0.0ms
x
@inf
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))

rewrite105.0ms (4.2%)

Algorithm
1×batch-egg-rewrite
Rules
593×log-prod_binary64
364×pow-prod-down_binary64
316×pow2_binary64
304×fma-def_binary64
221×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01217
126815
2352515
Stop Event
1×node limit
Counts
2 → 194
Calls
Call 1
Inputs
(/.f64 1 (/.f64 2 y))
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
Outputs
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simplify42.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
5×*-commutative_binary64
3×associate-*r*_binary64
3×associate-*l*_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012396
119396
228396
333396
Stop Event
1×saturated
Counts
242 → 200
Calls
Call 1
Inputs
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 1/2 (*.f64 y x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
Outputs
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 1/2 y)
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 -1/8 z) (*.f64 1/2 (*.f64 y x)))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(*.f64 -1/8 z)
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))
(+.f64 (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z))
(fma.f64 1/2 (*.f64 y x) (*.f64 -1/8 z))
(fma.f64 (*.f64 1/2 y) x (*.f64 -1/8 z))
(fma.f64 y (*.f64 1/2 x) (*.f64 -1/8 z))

eval71.0ms (2.9%)

Compiler

Compiled 3500 to 2381 computations (32% saved)

prune30.0ms (1.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New2110211
Fresh000
Picked011
Done044
Total2115216
Error
0b
Counts
216 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓35.7b
(*.f64 1/2 (*.f64 y x))
✓27.2b
(*.f64 -1/8 z)
✓0.0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
✓0b
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
✓0.1b
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
Compiler

Compiled 51 to 39 computations (23.5% saved)

regimes88.0ms (3.5%)

Counts
5 → 1
Calls
Call 1
Inputs
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(*.f64 1/2 (*.f64 y x))
(*.f64 -1/8 z)
Outputs
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
Calls

10 calls:

48.0ms
(/.f64 (*.f64 x y) 2)
5.0ms
(/.f64 z 8)
4.0ms
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
4.0ms
(/.f64 z 8)
4.0ms
y
Results
ErrorSegmentsBranch
0b1x
0b1y
0b1z
0b1(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
0b1(/.f64 (*.f64 x y) 2)
0b1(/.f64 (*.f64 x y) 2)
0b1(*.f64 x y)
0b1(*.f64 x y)
0b1(/.f64 z 8)
0b1(/.f64 z 8)
Compiler

Compiled 103 to 75 computations (27.2% saved)

regimes73.0ms (2.9%)

Counts
4 → 1
Calls
Call 1
Inputs
(-.f64 (*.f64 x (/.f64 1 (/.f64 2 y))) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(*.f64 1/2 (*.f64 y x))
(*.f64 -1/8 z)
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Calls

7 calls:

21.0ms
z
16.0ms
x
9.0ms
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
9.0ms
y
7.0ms
(/.f64 (*.f64 x y) 2)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1z
0.0b1(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
0.0b1(/.f64 (*.f64 x y) 2)
0.0b1(*.f64 x y)
0.0b1(/.f64 z 8)
Compiler

Compiled 75 to 55 computations (26.7% saved)

regimes97.0ms (3.9%)

Accuracy

Total -49.7b remaining (-400.6%)

Threshold costs -49.7b (-400.6%)

Counts
2 → 3
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 y x))
(*.f64 -1/8 z)
Outputs
(*.f64 -1/8 z)
(*.f64 1/2 (*.f64 y x))
(*.f64 -1/8 z)
Calls

3 calls:

59.0ms
x
19.0ms
z
17.0ms
y
Results
ErrorSegmentsBranch
16.7b7x
19.0b3y
12.4b3z
Compiler

Compiled 23 to 17 computations (26.1% saved)

bsearch64.0ms (2.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
41.0ms
6.77469496879694e-53
3.7938344616436135e-46
23.0ms
-0.007100871387814097
-0.000524188534770326
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify5.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02551
13151
23851
34251
44551
54651
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(if (<=.f64 z -130987957191333408/18446744073709551616) (*.f64 -1/8 z) (if (<=.f64 z 7305816601799171/107839786668602559178668060348078522694548577690162289924414440996864) (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z)))
Outputs
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(if (<=.f64 z -130987957191333408/18446744073709551616) (*.f64 -1/8 z) (if (<=.f64 z 7305816601799171/107839786668602559178668060348078522694548577690162289924414440996864) (*.f64 1/2 (*.f64 y x)) (*.f64 -1/8 z)))
(if (<=.f64 z -4093373662229169/576460752303423488) (*.f64 z -1/8) (if (<=.f64 z 7305816601799171/107839786668602559178668060348078522694548577690162289924414440996864) (*.f64 1/2 (*.f64 x y)) (*.f64 z -1/8)))
Compiler

Compiled 45 to 33 computations (26.7% saved)

soundness77.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
209×fma-def_binary64
157×fma-neg_binary64
57×cancel-sign-sub-inv_binary64
42×distribute-rgt-neg-in_binary64
38×associate-/l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01013
11513
22613
33913
46911
512211
623711
742711
867811
996811
10108311
11111311
12111611
Stop Event
1×saturated
Compiler

Compiled 230 to 176 computations (23.5% saved)

end53.0ms (2.1%)

Remove

(sort x y)

Compiler

Compiled 61 to 42 computations (31.1% saved)

Profiling

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