Details

Time bar (total: 2.5s)

analyze413.0ms (16.5%)

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
34.3%56.9%8.7%10
40.6%49.9%9.5%11
48%41.9%10.1%12
Compiler

Compiled 9 to 6 computations (33.3% saved)

sample921.0ms (36.7%)

Results
796.0ms8256×body256valid
111.0ms1109×body256invalid

preprocess15.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
12×fma-def_binary64
7×*-commutative_binary64
6×distribute-lft-in_binary64
6×distribute-rgt-in_binary64
4×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01228
11828
23628
35628
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 x y) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 z y) x)
(*.f64 (+.f64 x z) y)
Outputs
(*.f64 (+.f64 x y) z)
(*.f64 z (+.f64 x y))
(*.f64 (+.f64 y x) z)
(*.f64 z (+.f64 x y))
(*.f64 (+.f64 z y) x)
(*.f64 x (+.f64 y z))
(*.f64 (+.f64 x z) y)
(*.f64 y (+.f64 x z))
Symmetry

(sort x y)

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×fma-def_binary64
3×*-commutative_binary64
2×distribute-lft-in_binary64
2×distribute-rgt-in_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
2167
3227
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (+.f64 x y) z)
Outputs
(*.f64 (+.f64 x y) z)

eval0.0ms (0%)

Compiler

Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(*.f64 (+.f64 x y) z)
Compiler

Compiled 8 to 5 computations (37.5% saved)

localize21.0ms (0.8%)

Local error

Found 1 expressions with local error:

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

Compiled 14 to 5 computations (64.3% saved)

series5.0ms (0.2%)

Counts
1 → 36
Calls

9 calls:

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

rewrite47.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
715×pow1_binary64
663×add-log-exp_binary64
663×log1p-expm1-u_binary64
663×expm1-log1p-u_binary64
648×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11287
217767
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(*.f64 (+.f64 x y) z)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x z) (*.f64 y z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y z) (*.f64 x z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z x) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z y) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 x y) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 y y)) z) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 z (-.f64 (*.f64 x x) (*.f64 y y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) z) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 x y) z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (+.f64 x y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 x y) z)))))))

simplify129.0ms (5.1%)

Algorithm
1×egg-herbie
Rules
4×fma-def_binary64
3×*-commutative_binary64
2×+-commutative_binary64
1×distribute-rgt-out_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
09264
115234
218234
Stop Event
1×saturated
Counts
57 → 26
Calls
Call 1
Inputs
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
Outputs
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))
(*.f64 (+.f64 y x) z)
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 y x))

eval4.0ms (0.2%)

Compiler

Compiled 221 to 85 computations (61.5% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New22426
Fresh000
Picked011
Done000
Total22527
Error
0.0b
Counts
27 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶29.6b
(*.f64 z x)
▶32.5b
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
▶30.5b
(*.f64 y z)
✓0.0b
(*.f64 (+.f64 x y) z)
▶0.0b
(+.f64 (*.f64 z y) (*.f64 z x))
Compiler

Compiled 41 to 27 computations (34.1% saved)

localize3.0ms (0.1%)

Compiler

Compiled 8 to 4 computations (50% saved)

localize3.0ms (0.1%)

Compiler

Compiled 8 to 4 computations (50% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 6 computations (68.4% saved)

series5.0ms (0.2%)

Counts
1 → 36
Calls

9 calls:

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

rewrite51.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
836×pow1_binary64
774×add-log-exp_binary64
774×log1p-expm1-u_binary64
774×expm1-log1p-u_binary64
757×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
11517
221067
Stop Event
1×node limit
Counts
1 → 41
Calls
Call 1
Inputs
(+.f64 (*.f64 z y) (*.f64 z x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (+.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 z y) 2) (*.f64 z (-.f64 y x))) (/.f64 (pow.f64 (*.f64 z x) 2) (*.f64 z (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (+.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 z (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (+.f64 y x))) (pow.f64 (cbrt.f64 (*.f64 z (+.f64 y x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 z (+.f64 y x))) 2) (cbrt.f64 (*.f64 z (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z (+.f64 y x))) (sqrt.f64 (*.f64 z (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 z y) 3) (pow.f64 (*.f64 z x) 3)) (/.f64 1 (+.f64 (pow.f64 (*.f64 z y) 2) (*.f64 (*.f64 z x) (-.f64 (*.f64 z x) (*.f64 z y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 z y) 2) (pow.f64 (*.f64 z x) 2)) (/.f64 1 (*.f64 z (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y x) z)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 z y) 2) (*.f64 (*.f64 z x) (-.f64 (*.f64 z x) (*.f64 z y)))) (+.f64 (pow.f64 (*.f64 z y) 3) (pow.f64 (*.f64 z x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 z (-.f64 y x)) (-.f64 (pow.f64 (*.f64 z y) 2) (pow.f64 (*.f64 z x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 z y) 3) (pow.f64 (*.f64 z x) 3)) (+.f64 (pow.f64 (*.f64 z y) 2) (*.f64 (*.f64 z x) (-.f64 (*.f64 z x) (*.f64 z y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 z y) 3) (pow.f64 (*.f64 z x) 3)) (+.f64 (pow.f64 (*.f64 z x) 2) (-.f64 (pow.f64 (*.f64 z y) 2) (*.f64 z (*.f64 y (*.f64 z x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 z y) 2) (pow.f64 (*.f64 z x) 2)) (*.f64 z (-.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 z y) 3) (pow.f64 (*.f64 z x) 3))) (neg.f64 (+.f64 (pow.f64 (*.f64 z y) 2) (*.f64 (*.f64 z x) (-.f64 (*.f64 z x) (*.f64 z y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 z y) 2) (pow.f64 (*.f64 z x) 2))) (neg.f64 (*.f64 z (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 z x) 2) (pow.f64 (*.f64 z y) 2)) (-.f64 (*.f64 z x) (*.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (+.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (+.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (+.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (+.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 z (+.f64 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (+.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (+.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (+.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z y (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z x (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y z (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x z (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 z y) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 z x) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 z x)) 2) (cbrt.f64 (*.f64 z x)) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 z y)) 2) (cbrt.f64 (*.f64 z y)) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 z x)) (sqrt.f64 (*.f64 z x)) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 z y)) (sqrt.f64 (*.f64 z y)) (*.f64 z x))))))

simplify37.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
90×fma-neg_binary64
85×fma-def_binary64
42×cancel-sign-sub-inv_binary64
38×distribute-rgt-in_binary64
34×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015234
134234
280234
3210234
4434234
5567234
6677234
7682234
Stop Event
1×saturated
Counts
77 → 46
Calls
Call 1
Inputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
Outputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 x y) z)
✓0.3b
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
✓2.7b
(sqrt.f64 (*.f64 (+.f64 x y) z))
Compiler

Compiled 29 to 9 computations (69% saved)

series19.0ms (0.8%)

Counts
2 → 16
Calls

18 calls:

TimeVariablePointExpression
2.0ms
x
@0
(sqrt.f64 (*.f64 (+.f64 x y) z))
2.0ms
x
@0
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
1.0ms
y
@inf
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
1.0ms
z
@-inf
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
1.0ms
x
@inf
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)

rewrite80.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
864×pow1_binary64
804×add-log-exp_binary64
803×log1p-expm1-u_binary64
803×expm1-log1p-u_binary64
785×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
119416
2221916
Stop Event
1×node limit
Counts
2 → 60
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (+.f64 x y) z))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 (+.f64 x y) z))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (+.f64 x y) z) 1/4) (pow.f64 (*.f64 (+.f64 x y) z) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) z) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) z) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x z) (*.f64 y z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y z) (*.f64 x z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z x) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z y) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 x y) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) z)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) z) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 x y) z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))) (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) z)) 2) (cbrt.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (*.f64 (cbrt.f64 (+.f64 x y)) z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (+.f64 x y) z) 1/4) (*.f64 (pow.f64 (*.f64 (+.f64 x y) z) 1/4) (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (sqrt.f64 (+.f64 x y)) z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (sqrt.f64 z) (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) (pow.f64 (*.f64 (+.f64 x y) z) 1/4)) (pow.f64 (*.f64 (+.f64 x y) z) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) (sqrt.f64 z)) (sqrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (cbrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z))) (cbrt.f64 (sqrt.f64 (*.f64 (+.f64 x y) z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) (sqrt.f64 (+.f64 x y))) (sqrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 y y)) z) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (-.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 z (-.f64 (*.f64 x x) (*.f64 y y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 x y) z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) z) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (+.f64 x y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 x y) z)))))))

simplify48.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
598×associate-+r+_binary64
568×associate-*l/_binary64
516×fma-def_binary64
507×associate-*r/_binary64
463×*-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
086288
1246278
2779278
33206278
Stop Event
1×node limit
Counts
76 → 82
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 y z))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (sqrt.f64 (*.f64 y z)))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (+.f64 (sqrt.f64 (*.f64 y z)) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (pow.f64 x 2)))))
(+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (+.f64 (sqrt.f64 (*.f64 y z)) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (pow.f64 x 2))))))
(sqrt.f64 (*.f64 z x))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (sqrt.f64 (*.f64 z x)))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 z (pow.f64 x 3))))) (sqrt.f64 (*.f64 z x))))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 z (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 z (pow.f64 x 5))))) (sqrt.f64 (*.f64 z x)))))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 z x) (*.f64 (+.f64 (*.f64 1/4 (/.f64 z y)) (*.f64 -1/4 (/.f64 z y))) (pow.f64 x 2))))
(+.f64 (*.f64 y z) (+.f64 (*.f64 z x) (+.f64 (*.f64 (+.f64 (*.f64 1/4 (/.f64 z y)) (*.f64 -1/4 (/.f64 z y))) (pow.f64 x 2)) (*.f64 (+.f64 (*.f64 1/8 (/.f64 z (pow.f64 y 2))) (*.f64 -1/8 (/.f64 z (pow.f64 y 2)))) (pow.f64 x 3)))))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/4 (/.f64 z x)) (*.f64 -1/4 (/.f64 z x)))) (*.f64 z x)))
(+.f64 (*.f64 y z) (+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/4 (/.f64 z x)) (*.f64 -1/4 (/.f64 z x)))) (+.f64 (*.f64 z x) (*.f64 (pow.f64 y 3) (+.f64 (*.f64 -1/8 (/.f64 z (pow.f64 x 2))) (*.f64 1/8 (/.f64 z (pow.f64 x 2))))))))
Outputs
(sqrt.f64 (*.f64 y z))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (sqrt.f64 (*.f64 y z)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (sqrt.f64 (*.f64 y z)))
(fma.f64 (*.f64 1/2 (sqrt.f64 (/.f64 z y))) x (sqrt.f64 (*.f64 y z)))
(fma.f64 (sqrt.f64 (/.f64 z y)) (*.f64 1/2 x) (sqrt.f64 (*.f64 y z)))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (+.f64 (sqrt.f64 (*.f64 y z)) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (pow.f64 x 2)))))
(+.f64 (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (sqrt.f64 (*.f64 y z))) (*.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 z (pow.f64 y 3)))) (*.f64 x x)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 z (pow.f64 y 3))))) (sqrt.f64 (*.f64 y z))))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (*.f64 -1/8 (*.f64 x x)) (sqrt.f64 (*.f64 y z))))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (sqrt.f64 (*.f64 y z))))
(+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x)) (+.f64 (sqrt.f64 (*.f64 y z)) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (pow.f64 x 2))))))
(fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (pow.f64 x 3)) (+.f64 (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (sqrt.f64 (*.f64 y z))) (*.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 z (pow.f64 y 3)))) (*.f64 x x))))
(fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (pow.f64 x 3)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 z (pow.f64 y 3))))) (sqrt.f64 (*.f64 y z)))))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (*.f64 1/16 (pow.f64 x 3)) (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (*.f64 -1/8 (*.f64 x x)) (sqrt.f64 (*.f64 y z)))))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 z y)) x) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 z (pow.f64 y 5))) (pow.f64 x 3)) (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (sqrt.f64 (*.f64 y z)))))
(sqrt.f64 (*.f64 z x))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (sqrt.f64 (*.f64 z x)))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x))) (sqrt.f64 (*.f64 z x)))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 z x))) (sqrt.f64 (*.f64 z x)))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 z (pow.f64 x 3))))) (sqrt.f64 (*.f64 z x))))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 z (pow.f64 x 3)))) (sqrt.f64 (*.f64 z x))))
(fma.f64 (sqrt.f64 (/.f64 z (pow.f64 x 3))) (*.f64 -1/8 (*.f64 y y)) (fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 z x))) (sqrt.f64 (*.f64 z x))))
(fma.f64 (*.f64 y y) (*.f64 -1/8 (sqrt.f64 (/.f64 z (pow.f64 x 3)))) (fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 z x))) (sqrt.f64 (*.f64 z x))))
(+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 z (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 z (pow.f64 x 5))))) (sqrt.f64 (*.f64 z x)))))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (*.f64 (*.f64 y y) (sqrt.f64 (/.f64 z (pow.f64 x 3)))) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 z (pow.f64 x 5)))) (sqrt.f64 (*.f64 z x)))))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (*.f64 y (*.f64 y (sqrt.f64 (/.f64 z (pow.f64 x 3))))) (fma.f64 (pow.f64 y 3) (*.f64 1/16 (sqrt.f64 (/.f64 z (pow.f64 x 5)))) (sqrt.f64 (*.f64 z x)))))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 z x) (*.f64 (+.f64 (*.f64 1/4 (/.f64 z y)) (*.f64 -1/4 (/.f64 z y))) (pow.f64 x 2))))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 z x) (+.f64 (*.f64 (+.f64 (*.f64 1/4 (/.f64 z y)) (*.f64 -1/4 (/.f64 z y))) (pow.f64 x 2)) (*.f64 (+.f64 (*.f64 1/8 (/.f64 z (pow.f64 y 2))) (*.f64 -1/8 (/.f64 z (pow.f64 y 2)))) (pow.f64 x 3)))))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/4 (/.f64 z x)) (*.f64 -1/4 (/.f64 z x)))) (*.f64 z x)))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))
(+.f64 (*.f64 y z) (+.f64 (*.f64 (pow.f64 y 2) (+.f64 (*.f64 1/4 (/.f64 z x)) (*.f64 -1/4 (/.f64 z x)))) (+.f64 (*.f64 z x) (*.f64 (pow.f64 y 3) (+.f64 (*.f64 -1/8 (/.f64 z (pow.f64 x 2))) (*.f64 1/8 (/.f64 z (pow.f64 x 2))))))))
(fma.f64 y z (*.f64 z x))
(*.f64 z (+.f64 x y))
(*.f64 z (+.f64 y x))

eval92.0ms (3.7%)

Compiler

Compiled 2039 to 787 computations (61.4% saved)

prune176.0ms (7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1531154
Fresh000
Picked101
Done044
Total1545159
Error
0b
Counts
159 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(fma.f64 z x (*.f64 z y))
✓29.6b
(*.f64 z x)
✓30.5b
(*.f64 y z)
✓0.0b
(*.f64 (+.f64 x y) z)
✓0.0b
(+.f64 (*.f64 z y) (*.f64 z x))
Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 z x (*.f64 z y))
Compiler

Compiled 15 to 5 computations (66.7% saved)

series3.0ms (0.1%)

Counts
1 → 36
Calls

9 calls:

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

rewrite43.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
575×pow1_binary64
525×add-log-exp_binary64
525×log1p-expm1-u_binary64
525×expm1-log1p-u_binary64
512×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068
11187
214147
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(fma.f64 z x (*.f64 z y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z y) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z x) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 z x) 1) (*.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (+.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 z (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (+.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 z (+.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 z (+.f64 x y))) 2) (cbrt.f64 (*.f64 z (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z (+.f64 x y))) (sqrt.f64 (*.f64 z (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 z x) 3) (pow.f64 (*.f64 z y) 3)) (+.f64 (*.f64 (*.f64 z x) (*.f64 z x)) (-.f64 (pow.f64 (*.f64 z y) 2) (*.f64 (*.f64 z x) (*.f64 z y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 z x) (*.f64 z x)) (pow.f64 (*.f64 z y) 2)) (-.f64 (*.f64 z x) (*.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (+.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (+.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (+.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 z (+.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 z (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (+.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (+.f64 x y))))))))

simplify27.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
90×fma-neg_binary64
85×fma-def_binary64
42×cancel-sign-sub-inv_binary64
38×distribute-rgt-in_binary64
34×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015234
134234
280234
3210234
4434234
5567234
6677234
7682234
Stop Event
1×saturated
Counts
58 → 28
Calls
Call 1
Inputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 z x)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
(+.f64 (*.f64 y z) (*.f64 z x))
Outputs
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 -1 (*.f64 (+.f64 (*.f64 -1 x) (*.f64 -1 y)) z))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 z x)
(*.f64 x z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(*.f64 y z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)
(+.f64 (*.f64 y z) (*.f64 z x))
(*.f64 (+.f64 y x) z)

eval5.0ms (0.2%)

Compiler

Compiled 259 to 83 computations (68% saved)

prune6.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New28028
Fresh000
Picked011
Done044
Total28533
Error
0b
Counts
33 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.0b
(fma.f64 z x (*.f64 z y))
✓29.6b
(*.f64 z x)
✓30.5b
(*.f64 y z)
✓0.0b
(*.f64 (+.f64 x y) z)
✓0.0b
(+.f64 (*.f64 z y) (*.f64 z x))
Compiler

Compiled 39 to 24 computations (38.5% saved)

regimes44.0ms (1.7%)

Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 z x)
(*.f64 y z)
(*.f64 (+.f64 x y) z)
(+.f64 (*.f64 z y) (*.f64 z x))
(fma.f64 z x (*.f64 z y))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) z)) 2)
Outputs
(fma.f64 z x (*.f64 z y))
Calls

7 calls:

7.0ms
x
6.0ms
(*.f64 (+.f64 x y) z)
6.0ms
(+.f64 x y)
6.0ms
y
6.0ms
(+.f64 x y)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1z
0.0b1(*.f64 (+.f64 x y) z)
0.0b1(*.f64 (+.f64 x y) z)
0.0b1(+.f64 x y)
0.0b1(+.f64 x y)
Compiler

Compiled 75 to 40 computations (46.7% saved)

regimes48.0ms (1.9%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 z x)
(*.f64 y z)
(*.f64 (+.f64 x y) z)
(+.f64 (*.f64 z y) (*.f64 z x))
Outputs
(+.f64 (*.f64 z y) (*.f64 z x))
Calls

5 calls:

12.0ms
(*.f64 (+.f64 x y) z)
11.0ms
y
10.0ms
z
10.0ms
x
5.0ms
(+.f64 x y)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1z
0.0b1(*.f64 (+.f64 x y) z)
0.0b1(+.f64 x y)
Compiler

Compiled 47 to 27 computations (42.6% saved)

regimes74.0ms (3%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 z x)
(*.f64 y z)
(*.f64 (+.f64 x y) z)
Outputs
(*.f64 (+.f64 x y) z)
Calls

5 calls:

36.0ms
(+.f64 x y)
10.0ms
x
9.0ms
z
9.0ms
(*.f64 (+.f64 x y) z)
9.0ms
y
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1z
0.0b1(*.f64 (+.f64 x y) z)
0.0b1(+.f64 x y)
Compiler

Compiled 40 to 25 computations (37.5% saved)

regimes82.0ms (3.3%)

Accuracy

Total -50.9b remaining (-630.4%)

Threshold costs -50.9b (-630.4%)

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

3 calls:

61.0ms
z
12.0ms
y
8.0ms
x
Results
ErrorSegmentsBranch
9.2b2x
8.1b2y
19.1b8z
Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch17.0ms (0.7%)

Algorithm
1×binary-search
Steps
TimeLeftRight
17.0ms
1.3769338521398656e-77
7.979274454904568e-74
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
2×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01543
12043
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(fma.f64 z x (*.f64 z y))
(+.f64 (*.f64 z y) (*.f64 z x))
(*.f64 (+.f64 x y) z)
(if (<=.f64 y 1795112828058711/130370302485407109521180524058200202307293977194619920040712988758680403184853549195737432064) (*.f64 z x) (*.f64 y z))
(*.f64 z x)
Outputs
(fma.f64 z x (*.f64 z y))
(+.f64 (*.f64 z y) (*.f64 z x))
(*.f64 (+.f64 x y) z)
(*.f64 z (+.f64 x y))
(if (<=.f64 y 1795112828058711/130370302485407109521180524058200202307293977194619920040712988758680403184853549195737432064) (*.f64 z x) (*.f64 y z))
(if (<=.f64 y 1795112828058711/130370302485407109521180524058200202307293977194619920040712988758680403184853549195737432064) (*.f64 z x) (*.f64 z y))
(*.f64 z x)
Compiler

Compiled 46 to 28 computations (39.1% saved)

soundness0.0ms (0%)

end49.0ms (2%)

Compiler

Compiled 52 to 22 computations (57.7% saved)

Profiling

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