Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Time bar (total: 7.5s)

analyze88.0ms (1.2%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
50%49.9%49.9%0.1%0%0%0%4
50%49.9%49.9%0.1%0%0%0%5
50%49.9%49.9%0.1%0%0%0%6
66.7%49.9%25%0.1%0%25%0%7
66.7%49.9%25%0.1%0%25%0%8
66.7%49.9%25%0.1%0%25%0%9
80%49.9%12.5%0.1%0%37.4%0%10
80%49.9%12.5%0.1%0%37.4%0%11
80%49.9%12.5%0.1%0%37.4%0%12
Compiler

Compiled 14 to 11 computations (21.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-div: 7.0ms (32.2% of total)
ival-mult: 6.0ms (27.6% of total)
ival-sqrt: 4.0ms (18.4% of total)
ival-add: 3.0ms (13.8% of total)
const: 1.0ms (4.6% of total)
backward-pass: 0.0ms (0% of total)

sample1.5s (19.5%)

Results
856.0ms8256×0valid
170.0ms1999×0invalid
Precisions
Click to see histograms. Total time spent on operations: 630.0ms
ival-mult: 312.0ms (49.5% of total)
ival-div: 118.0ms (18.7% of total)
ival-sqrt: 91.0ms (14.4% of total)
ival-add: 85.0ms (13.5% of total)
const: 20.0ms (3.2% of total)
backward-pass: 4.0ms (0.6% of total)
Bogosity

preprocess71.0ms (0.9%)

Algorithm
egg-herbie
Rules
2584×fnmadd-define
1704×sum3-define
1646×fmsub-define
1538×fnmsub-define
1244×fmm-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03786
111872
236872
381872
4186872
5416972
6630772
0118
1227
2377
3487
0487
Stop Event
iter limit
saturated
node limit
Calls
Call 1
Inputs
(* (/ 1 2) (+ x (* y (sqrt z))))
Outputs
(* (/ 1 2) (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
Call 2
Inputs
(* (/ 1 2) (+ x (* y (sqrt z))))
(* (/ 1 2) (+ (neg x) (* y (sqrt z))))
(* (/ 1 2) (+ x (* (neg y) (sqrt z))))
(* (/ 1 2) (+ x (* y (sqrt (neg z)))))
(neg (* (/ 1 2) (+ (neg x) (* y (sqrt z)))))
(neg (* (/ 1 2) (+ x (* (neg y) (sqrt z)))))
(neg (* (/ 1 2) (+ x (* y (sqrt (neg z))))))
(* (/ 1 2) (+ y (* x (sqrt z))))
(* (/ 1 2) (+ z (* y (sqrt x))))
(* (/ 1 2) (+ x (* z (sqrt y))))
Outputs
(* (/ 1 2) (+ x (* y (sqrt z))))
(* 1/2 (fma y (sqrt z) x))
(* (/ 1 2) (+ (neg x) (* y (sqrt z))))
(* 1/2 (fmsub y (sqrt z) x))
(* (/ 1 2) (+ x (* (neg y) (sqrt z))))
(* 1/2 (fnmadd y (sqrt z) x))
(* (/ 1 2) (+ x (* y (sqrt (neg z)))))
(* 1/2 (fma y (sqrt (neg z)) x))
(neg (* (/ 1 2) (+ (neg x) (* y (sqrt z)))))
(* 1/2 (fnmadd y (sqrt z) x))
(neg (* (/ 1 2) (+ x (* (neg y) (sqrt z)))))
(* 1/2 (fmsub y (sqrt z) x))
(neg (* (/ 1 2) (+ x (* y (sqrt (neg z))))))
(* 1/2 (fnmsub y (sqrt (neg z)) x))
(* (/ 1 2) (+ y (* x (sqrt z))))
(* 1/2 (fma x (sqrt z) y))
(* (/ 1 2) (+ z (* y (sqrt x))))
(* 1/2 (fma y (sqrt x) z))
(* (/ 1 2) (+ x (* z (sqrt y))))
(* 1/2 (fma z (sqrt y) x))

explain105.0ms (1.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
10-0-(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
00-0-x
00-0-(*.f64 y (sqrt.f64 z))
00-0-y
00-0-#s(literal 2 binary64)
00-0-(+.f64 x (*.f64 y (sqrt.f64 z)))
00-0-(sqrt.f64 z)
00-0-z
00-0-#s(literal 1 binary64)
00-0-(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
Results
71.0ms512×0valid
Compiler

Compiled 81 to 32 computations (60.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-mult: 7.0ms (34.5% of total)
ival-div: 4.0ms (19.7% of total)
ival-add: 4.0ms (19.7% of total)
ival-sqrt: 4.0ms (19.7% of total)
const: 1.0ms (4.9% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify24.0ms (0.3%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 z)
cost-diff0
(*.f64 y (sqrt.f64 z))
cost-diff0
(+.f64 x (*.f64 y (sqrt.f64 z)))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
20×fma-lowering-fma.f32
20×fma-define
20×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0824
11722
23422
34422
04422
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (sqrt z))))
1/2
(+ x (* y (sqrt z)))
x
(* y (sqrt z))
y
(sqrt z)
z
Outputs
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
1/2
#s(literal 1/2 binary64)
(+ x (* y (sqrt z)))
(+.f64 x (*.f64 y (sqrt.f64 z)))
x
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
y
(sqrt z)
(sqrt.f64 z)
z

localize37.0ms (0.5%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sqrt.f64 z)
accuracy100.0%
(+.f64 x (*.f64 y (sqrt.f64 z)))
accuracy99.7%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
accuracy99.7%
(*.f64 y (sqrt.f64 z))
Results
29.0ms256×0valid
Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 4.0ms (51.5% of total)
ival-sqrt: 2.0ms (25.8% of total)
ival-add: 1.0ms (12.9% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series7.0ms (0.1%)

Counts
4 → 108
Calls
Call 1
Inputs
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (sqrt z)>
Outputs
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* y (sqrt z))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt x>
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))>
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))>
#<alt (* x (+ 1 (* (/ y x) (sqrt z))))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt x>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (sqrt z))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
Calls

27 calls:

TimeVariablePointExpression
1.0ms
z
@-inf
(* 1/2 (+ x (* y (sqrt z))))
1.0ms
x
@0
(* 1/2 (+ x (* y (sqrt z))))
1.0ms
z
@0
(* 1/2 (+ x (* y (sqrt z))))
1.0ms
y
@0
(* 1/2 (+ x (* y (sqrt z))))
0.0ms
x
@inf
(* 1/2 (+ x (* y (sqrt z))))

rewrite278.0ms (3.7%)

Algorithm
batch-egg-rewrite
Rules
2916×*-lowering-*.f32
2916×*-lowering-*.f64
2390×/-lowering-/.f32
2390×/-lowering-/.f64
1382×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0820
13118
224318
3244518
0845318
Stop Event
iter limit
node limit
Counts
4 → 213
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(sqrt z)
Outputs
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))
(+.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) (/.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))))))
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))))))
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(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/4 binary64)))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
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(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 9/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) (neg.f64 (-.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (pow.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 y y) z))) #s(literal 3/2 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))) (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))) (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (*.f64 y (sqrt.f64 z)) x) (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x))) #s(literal -1 binary64))
(*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(*.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) #s(literal -1 binary64)))
(*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))) (+.f64 x (*.f64 y (sqrt.f64 z))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) #s(literal 3 binary64)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) (-.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) z)) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (+.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(*.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))))
(*.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) z))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 9/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z)))) (pow.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 y y) z))) #s(literal 3/2 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 (*.f64 y y) z) (*.f64 (*.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))))
(exp.f64 (log.f64 (*.f64 y (sqrt.f64 z))))
(exp.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 z))) #s(literal 1 binary64)))
(pow.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1 binary64))
(*.f64 y (sqrt.f64 z))
(*.f64 (sqrt.f64 z) y)
(*.f64 (sqrt.f64 z) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (sqrt.f64 z) (exp.f64 (log.f64 y)))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y))
(*.f64 (*.f64 y (pow.f64 z #s(literal 1/4 binary64))) (pow.f64 z #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) (sqrt.f64 z))
(*.f64 (pow.f64 (*.f64 y (pow.f64 z #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (sqrt.f64 z))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
(exp.f64 (*.f64 (log.f64 (pow.f64 z #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 z z)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 z) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 z) #s(literal 1/4 binary64)) (*.f64 (log.f64 z) #s(literal 1/4 binary64))))
(fabs.f64 (sqrt.f64 z))
(sqrt.f64 z)
(pow.f64 (sqrt.f64 z) #s(literal 1 binary64))
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 z #s(literal 1/2 binary64))
(pow.f64 (*.f64 z z) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))

simplify208.0ms (2.8%)

Algorithm
egg-herbie
Rules
3400×*-lowering-*.f32
3400×*-lowering-*.f64
1344×/-lowering-/.f32
1344×/-lowering-/.f64
1232×fma-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
075622
1264578
2891578
32789554
47950554
08118554
Stop Event
iter limit
node limit
Counts
108 → 108
Calls
Call 1
Inputs
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
Outputs
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)

eval36.0ms (0.5%)

Compiler

Compiled 7917 to 763 computations (90.4% saved)

prune70.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New31110321
Fresh000
Picked011
Done000
Total31111322
Accuracy
100.0%
Counts
322 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
47.7%
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
26.0%
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
99.3%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
46.7%
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
99.4%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y))))
94.6%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
99.3%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
75.7%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
99.4%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))))
99.5%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
54.2%
(*.f64 #s(literal 1/2 binary64) x)
Compiler

Compiled 329 to 228 computations (30.7% saved)

simplify17.0ms (0.2%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff0
(+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
cost-diff6528
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))
cost-diff0
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
cost-diff0
(*.f64 y (sqrt.f64 z))
cost-diff0
(+.f64 x (*.f64 y (sqrt.f64 z)))
cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
cost-diff128
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))
cost-diff0
(*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))
cost-diff0
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))))
Rules
270×*-lowering-*.f32
270×*-lowering-*.f64
168×fma-define
128×associate-*r*
120×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032174
172165
2158165
3303165
4365165
0365165
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
1/2
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))
x
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))
y
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))
(sqrt (pow z 3/4))
(pow z 3/4)
z
3/4
(sqrt (pow z 1/4))
(pow z 1/4)
1/4
(* 1/2 x)
1/2
x
(/ 1/2 (/ 1 (+ x (* y (sqrt z)))))
1/2
(/ 1 (+ x (* y (sqrt z))))
1
(+ x (* y (sqrt z)))
x
(* y (sqrt z))
y
(sqrt z)
z
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))
1/2
(+ x (* (sqrt (/ 1 z)) (* y z)))
x
(* (sqrt (/ 1 z)) (* y z))
(sqrt (/ 1 z))
(/ 1 z)
1
z
(* y z)
y
(* 1/2 (+ x (* y (pow (pow z 1/4) 2))))
1/2
(+ x (* y (pow (pow z 1/4) 2)))
x
(* y (pow (pow z 1/4) 2))
y
(pow (pow z 1/4) 2)
(pow z 1/4)
z
1/4
2
Outputs
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))
(+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))))
x
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))
(*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))
y
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))
(sqrt (pow z 3/4))
(sqrt.f64 (pow.f64 z #s(literal 3/4 binary64)))
(pow z 3/4)
(pow.f64 z #s(literal 3/4 binary64))
z
3/4
#s(literal 3/4 binary64)
(sqrt (pow z 1/4))
(sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))
(pow z 1/4)
(pow.f64 z #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
(/ 1/2 (/ 1 (+ x (* y (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
1/2
#s(literal 1/2 binary64)
(/ 1 (+ x (* y (sqrt z))))
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
1
#s(literal 1 binary64)
(+ x (* y (sqrt z)))
(+.f64 x (*.f64 y (sqrt.f64 z)))
x
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
y
(sqrt z)
(sqrt.f64 z)
z
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
1/2
#s(literal 1/2 binary64)
(+ x (* (sqrt (/ 1 z)) (* y z)))
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
x
(* (sqrt (/ 1 z)) (* y z))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
1
#s(literal 1 binary64)
z
(* y z)
(*.f64 y z)
y
(* 1/2 (+ x (* y (pow (pow z 1/4) 2))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
1/2
#s(literal 1/2 binary64)
(+ x (* y (pow (pow z 1/4) 2)))
(+.f64 x (*.f64 y (sqrt.f64 z)))
x
(* y (pow (pow z 1/4) 2))
(*.f64 y (sqrt.f64 z))
y
(pow (pow z 1/4) 2)
(sqrt.f64 z)
(pow z 1/4)
(pow.f64 z #s(literal 1/4 binary64))
z
1/4
#s(literal 1/4 binary64)
2
#s(literal 2 binary64)

localize211.0ms (2.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))
accuracy99.7%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
accuracy99.7%
(*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy99.3%
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy100.0%
(+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z)))
accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy99.7%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
accuracy90.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))
accuracy100.0%
(+.f64 x (*.f64 y (sqrt.f64 z)))
accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
accuracy99.7%
(*.f64 y (sqrt.f64 z))
accuracy98.7%
(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
accuracy99.8%
(sqrt.f64 (pow.f64 z #s(literal 3/4 binary64)))
accuracy99.7%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))))
accuracy99.7%
(*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))
accuracy99.5%
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))
Results
167.0ms256×0valid
Compiler

Compiled 198 to 33 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 55.0ms
ival-mult: 19.0ms (34.4% of total)
ival-pow: 16.0ms (29% of total)
ival-sqrt: 8.0ms (14.5% of total)
ival-div: 5.0ms (9% of total)
ival-add: 5.0ms (9% of total)
const: 1.0ms (1.8% of total)
backward-pass: 0.0ms (0% of total)

series144.0ms (1.9%)

Counts
18 → 480
Calls
Call 1
Inputs
#<alt (* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))>
#<alt (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))>
#<alt (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))>
#<alt (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))>
#<alt (* 1/2 x)>
#<alt (/ 1/2 (/ 1 (+ x (* y (sqrt z)))))>
#<alt (/ 1 (+ x (* y (sqrt z))))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))>
#<alt (+ x (* (sqrt (/ 1 z)) (* y z)))>
#<alt (* (sqrt (/ 1 z)) (* y z))>
#<alt (sqrt (/ 1 z))>
#<alt (pow (pow z 1/4) 2)>
#<alt (* 1/2 (+ x (* y (pow (pow z 1/4) 2))))>
#<alt (+ x (* y (pow (pow z 1/4) 2)))>
#<alt (* y (pow (pow z 1/4) 2))>
#<alt (sqrt (pow z 3/4))>
Outputs
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (+ x (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
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#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))>
#<alt x>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (+ (sqrt z) (/ x y)))>
#<alt (* y (sqrt z))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (pow (* 1 (pow z 3)) 1/8)>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))>
#<alt (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))>
Calls

120 calls:

TimeVariablePointExpression
56.0ms
x
@0
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
16.0ms
z
@0
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
12.0ms
z
@-inf
(sqrt (pow z 3/4))
12.0ms
y
@0
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
10.0ms
z
@0
(sqrt (pow z 3/4))

rewrite742.0ms (9.9%)

Algorithm
batch-egg-rewrite
Rules
4716×*-lowering-*.f32
4716×*-lowering-*.f64
1706×/-lowering-/.f32
1706×/-lowering-/.f64
904×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032162
116882
2105982
0920282
Stop Event
iter limit
node limit
Counts
18 → 1434
Calls
Call 1
Inputs
(* 1/2 (+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))))
(+ x (* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))))
(* y (* (sqrt (pow z 3/4)) (sqrt (pow z 1/4))))
(* (sqrt (pow z 3/4)) (sqrt (pow z 1/4)))
(* 1/2 x)
(/ 1/2 (/ 1 (+ x (* y (sqrt z)))))
(/ 1 (+ x (* y (sqrt z))))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))
(+ x (* (sqrt (/ 1 z)) (* y z)))
(* (sqrt (/ 1 z)) (* y z))
(sqrt (/ 1 z))
(pow (pow z 1/4) 2)
(* 1/2 (+ x (* y (pow (pow z 1/4) 2))))
(+ x (* y (pow (pow z 1/4) 2)))
(* y (pow (pow z 1/4) 2))
(sqrt (pow z 3/4))
Outputs
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal -1/2 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)) (*.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))
(fma.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (sqrt.f64 z) (*.f64 y #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 y (*.f64 z #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 y z) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 y (pow.f64 z #s(literal 3/8 binary64))) (*.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 y (sqrt.f64 z)) (*.f64 z #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal 3/8 binary64))) (pow.f64 z #s(literal 1/8 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (*.f64 y z) (*.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64))))
(/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) #s(literal 2 binary64))
(/.f64 (/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (+.f64 (*.f64 z (*.f64 y y)) (*.f64 x (-.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 z (*.f64 y y)) (*.f64 x (-.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64)) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (neg.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (*.f64 (-.f64 (*.f64 y (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (*.f64 x x)) (*.f64 z (*.f64 y y)))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 z (*.f64 y y)) (*.f64 x x))) (-.f64 (*.f64 y (sqrt.f64 z)) x))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 (sqrt.f64 z) #s(literal 1/2 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 z (*.f64 y y))))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64))))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (neg.f64 (*.f64 x x)) (*.f64 z (*.f64 y y)))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 z (*.f64 y y)) #s(literal 3/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z)))))))
(/.f64 (*.f64 (+.f64 (neg.f64 (*.f64 x x)) (*.f64 z (*.f64 y y))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
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(*.f64 (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))) (/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) (+.f64 (*.f64 z (*.f64 y y)) (*.f64 x (-.f64 x (*.f64 y (sqrt.f64 z)))))))
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(/.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1 binary64))
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(/.f64 (*.f64 y #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))
(/.f64 (*.f64 (/.f64 y (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) z))
(*.f64 y (sqrt.f64 z))
(*.f64 z (/.f64 y (sqrt.f64 z)))
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(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y))
(*.f64 (pow.f64 z #s(literal 1/8 binary64)) (*.f64 y (pow.f64 z #s(literal 3/8 binary64))))
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(*.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
(*.f64 (sqrt.f64 z) y)
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(*.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1 binary64))
(*.f64 (*.f64 y (pow.f64 z #s(literal 3/8 binary64))) (pow.f64 z #s(literal 1/8 binary64)))
(*.f64 (/.f64 y (sqrt.f64 z)) z)
(*.f64 (pow.f64 z #s(literal 3/16 binary64)) (*.f64 (pow.f64 z #s(literal 3/16 binary64)) (*.f64 (pow.f64 z #s(literal 1/8 binary64)) y)))
(*.f64 (pow.f64 z #s(literal 1/16 binary64)) (*.f64 (pow.f64 z #s(literal 1/16 binary64)) (*.f64 y (pow.f64 z #s(literal 3/8 binary64)))))
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(*.f64 (/.f64 z (pow.f64 z #s(literal 1/8 binary64))) (/.f64 y (pow.f64 z #s(literal 3/8 binary64))))
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(*.f64 (/.f64 z (pow.f64 z #s(literal 1/4 binary64))) (/.f64 y (pow.f64 z #s(literal 1/4 binary64))))
(*.f64 (/.f64 y (pow.f64 z #s(literal 1/8 binary64))) (/.f64 z (pow.f64 z #s(literal 3/8 binary64))))
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(*.f64 (*.f64 (*.f64 y (pow.f64 z #s(literal 1/8 binary64))) (pow.f64 z #s(literal 3/16 binary64))) (pow.f64 z #s(literal 3/16 binary64)))
(exp.f64 (*.f64 (log.f64 z) #s(literal 3/8 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 z) #s(literal 1/8 binary64)) #s(literal 3 binary64)))
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(fabs.f64 (pow.f64 z #s(literal 3/8 binary64)))
(fabs.f64 (neg.f64 (pow.f64 z #s(literal 3/8 binary64))))
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(pow.f64 z #s(literal 3/8 binary64))
(pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 z #s(literal 3/8 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 z #s(literal 1/8 binary64)) #s(literal 3 binary64))
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 z #s(literal 3/16 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 z #s(literal 3/2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 z z) #s(literal 3/16 binary64))
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(*.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/16 binary64))) (pow.f64 z #s(literal 1/16 binary64)))

simplify381.0ms (5.1%)

Algorithm
egg-herbie
Rules
4492×*-lowering-*.f32
4492×*-lowering-*.f64
1916×/-lowering-/.f32
1916×/-lowering-/.f64
1576×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03033816
110453484
236653429
083833429
Stop Event
iter limit
node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* -1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z))))))))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt (/ 1 z)))))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))
(* -1 (* (pow -1 1/4) (* (* y (sqrt -1)) (sqrt z))))
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(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 3) z) (* (pow y 4) (pow (sqrt -1) 4))) (* -1 (* (/ (pow x 2) (* (pow y 3) (pow (sqrt -1) 2))) (sqrt (pow z 3))))) z)) (* -1 (/ (* x z) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* (/ 1 y) (sqrt z))) z))
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x
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(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
x
(+ x (* y (sqrt z)))
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(* 1/2 x)
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x
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x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
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x
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(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
x
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(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
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(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(pow (* 1 (pow z 3)) 1/8)
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
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Outputs
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
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(* 1/2 x)
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(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
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(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
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(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
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(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
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(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
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(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
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(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(*.f64 (*.f64 z #s(literal 1/2 binary64)) (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
(* x (+ 1 (* (/ y x) (sqrt z))))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
(* x (+ 1 (* (/ y x) (sqrt z))))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(*.f64 x (+.f64 (*.f64 y (/.f64 (sqrt.f64 z) x)) #s(literal 1 binary64)))
x
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (+ (sqrt z) (/ x y)))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (sqrt z) (/ x y)))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (+ (sqrt z) (/ x y)))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y)))
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(*.f64 z (+.f64 (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (/.f64 x z)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(pow (* 1 (pow z 3)) 1/8)
(pow.f64 (*.f64 z (*.f64 z z)) #s(literal 1/8 binary64))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)))
(exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 z))))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -3/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/8 binary64)))

eval227.0ms (3%)

Compiler

Compiled 37579 to 2270 computations (94% saved)

prune147.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New190861914
Fresh415
Picked415
Done011
Total191691925
Accuracy
100.0%
Counts
1925 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
94.6%
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x))
46.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
46.3%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
54.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
88.2%
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
46.7%
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
94.3%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (/.f64 y (sqrt.f64 z)) z)))
99.5%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
54.2%
(*.f64 #s(literal 1/2 binary64) x)
Compiler

Compiled 175 to 131 computations (25.1% saved)

simplify31.0ms (0.4%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) z)
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
cost-diff0
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
cost-diff0
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
cost-diff0
(sqrt.f64 z)
cost-diff0
(*.f64 y (sqrt.f64 z))
cost-diff0
(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
cost-diff128
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
cost-diff0
(sqrt.f64 z)
cost-diff0
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))
cost-diff0
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff128
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
cost-diff0
(sqrt.f64 z)
cost-diff0
(*.f64 #s(literal 1/2 binary64) y)
cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z))
cost-diff6400
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x))
Rules
272×*-lowering-*.f32
272×*-lowering-*.f64
156×times-frac
150×/-lowering-/.f32
150×/-lowering-/.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02294
14794
27492
311391
415091
518891
624591
734191
838191
943991
1048991
1153391
1253491
053491
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))
(/ (* 1/2 y) (sqrt z))
(* 1/2 y)
1/2
y
(sqrt z)
z
(* 1/2 x)
x
(/ 1/2 (/ 1 x))
1/2
(/ 1 x)
1
x
(* y (* 1/2 (sqrt z)))
y
(* 1/2 (sqrt z))
1/2
(sqrt z)
z
(/ 1/2 (/ 1 (* y (sqrt z))))
1/2
(/ 1 (* y (sqrt z)))
1
(* y (sqrt z))
y
(sqrt z)
z
(/ 1/2 (/ (sqrt (/ 1 z)) y))
1/2
(/ (sqrt (/ 1 z)) y)
(sqrt (/ 1 z))
(/ 1 z)
1
z
y
Outputs
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y))))
(/ (* 1/2 y) (sqrt z))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y))
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
1/2
#s(literal 1/2 binary64)
y
(sqrt z)
(sqrt.f64 z)
z
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(/ 1/2 (/ 1 x))
(*.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* y (* 1/2 (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
y
(* 1/2 (sqrt z))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))
1/2
#s(literal 1/2 binary64)
(sqrt z)
(sqrt.f64 z)
z
(/ 1/2 (/ 1 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
1/2
#s(literal 1/2 binary64)
(/ 1 (* y (sqrt z)))
(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
1
#s(literal 1 binary64)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
y
(sqrt z)
(sqrt.f64 z)
z
(/ 1/2 (/ (sqrt (/ 1 z)) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
1/2
#s(literal 1/2 binary64)
(/ (sqrt (/ 1 z)) y)
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
1
#s(literal 1 binary64)
z
y

localize196.0ms (2.6%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(/.f64 #s(literal 1 binary64) z)
accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy99.6%
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
accuracy99.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
accuracy100.0%
(sqrt.f64 z)
accuracy99.7%
(*.f64 y (sqrt.f64 z))
accuracy99.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
accuracy98.5%
(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))
accuracy100.0%
(sqrt.f64 z)
accuracy99.7%
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
accuracy100.0%
(sqrt.f64 z)
accuracy99.7%
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z))
accuracy94.7%
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x))
Results
164.0ms256×0valid
Compiler

Compiled 108 to 22 computations (79.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-div: 15.0ms (43% of total)
ival-mult: 10.0ms (28.7% of total)
ival-sqrt: 4.0ms (11.5% of total)
compiled-spec: 4.0ms (11.5% of total)
ival-add: 1.0ms (2.9% of total)
const: 1.0ms (2.9% of total)
backward-pass: 0.0ms (0% of total)

series14.0ms (0.2%)

Counts
16 → 300
Calls
Call 1
Inputs
#<alt (+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))>
#<alt (/ (* 1/2 y) (sqrt z))>
#<alt (* 1/2 y)>
#<alt (sqrt z)>
#<alt (/ 1/2 (/ 1 x))>
#<alt (/ 1 x)>
#<alt (* y (* 1/2 (sqrt z)))>
#<alt (* 1/2 (sqrt z))>
#<alt (/ 1/2 (/ 1 (* y (sqrt z))))>
#<alt (/ 1 (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (/ 1/2 (/ (sqrt (/ 1 z)) y))>
#<alt (/ (sqrt (/ 1 z)) y)>
#<alt (sqrt (/ 1 z))>
#<alt (/ 1 z)>
#<alt (* 1/2 x)>
Outputs
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))>
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))>
#<alt (* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 (* y (sqrt (/ 1 z))))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* 1/2 (sqrt z))>
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* y (sqrt z))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (/ 1 z)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
Calls

75 calls:

TimeVariablePointExpression
3.0ms
y
@0
(/ (* 1/2 y) (sqrt z))
1.0ms
z
@-inf
(/ 1 (* y (sqrt z)))
1.0ms
z
@-inf
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))
1.0ms
z
@-inf
(/ (sqrt (/ 1 z)) y)
1.0ms
z
@-inf
(/ (* 1/2 y) (sqrt z))

rewrite657.0ms (8.7%)

Algorithm
batch-egg-rewrite
Rules
4668×*-lowering-*.f32
4668×*-lowering-*.f64
3126×/-lowering-/.f32
3126×/-lowering-/.f64
958×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02271
111668
274665
0864365
Stop Event
iter limit
node limit
Counts
16 → 748
Calls
Call 1
Inputs
(+ (* (/ (* 1/2 y) (sqrt z)) z) (* 1/2 x))
(/ (* 1/2 y) (sqrt z))
(* 1/2 y)
(sqrt z)
(/ 1/2 (/ 1 x))
(/ 1 x)
(* y (* 1/2 (sqrt z)))
(* 1/2 (sqrt z))
(/ 1/2 (/ 1 (* y (sqrt z))))
(/ 1 (* y (sqrt z)))
(* y (sqrt z))
(/ 1/2 (/ (sqrt (/ 1 z)) y))
(/ (sqrt (/ 1 z)) y)
(sqrt (/ 1 z))
(/ 1 z)
(* 1/2 x)
Outputs
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 x #s(literal 2 binary64)))
(+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 x #s(literal -1/2 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))))
(-.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (/.f64 x #s(literal 2 binary64)))
(fma.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y)) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 z) y)) z (/.f64 x #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) (/.f64 x #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) z) (/.f64 y (sqrt.f64 z)) (/.f64 x #s(literal 2 binary64)))
(neg.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x))))))
(neg.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64)))) (+.f64 (*.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 z)) (/.f64 x #s(literal 2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) (/.f64 #s(literal 2 binary64) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) y)) z) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) x))) #s(literal 1 binary64)))
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(pow.f64 (*.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (/.f64 y (pow.f64 z #s(literal -1/2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) #s(literal 1 binary64))
(*.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) y))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) (/.f64 #s(literal -1 binary64) y))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) y) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(*.f64 (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 z #s(literal -1/4 binary64)) (*.f64 (pow.f64 z #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 z #s(literal 1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) (pow.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 z #s(literal -1/4 binary64))) (pow.f64 z #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 z) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 z)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 z) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 z) #s(literal 1/2 binary64))))
(fabs.f64 (pow.f64 z #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 z))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) z)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) z))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 1/4 binary64))) (pow.f64 z #s(literal 1/4 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) z)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) z)))
(pow.f64 z #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 z) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) z) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 #s(literal 1 binary64) z)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 z #s(literal -1/2 binary64)))
(*.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 z #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) z)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 0 binary64) z))))
(*.f64 (pow.f64 z #s(literal -1/4 binary64)) (pow.f64 z #s(literal -1/4 binary64)))
(*.f64 (pow.f64 z #s(literal -1/4 binary64)) (*.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 z) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 z #s(literal -1/4 binary64))) (pow.f64 z #s(literal -1/4 binary64)))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) z)))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) z))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 #s(literal 1 binary64) z)))
(neg.f64 (/.f64 #s(literal -1 binary64) z))
(/.f64 #s(literal 1 binary64) z)
(/.f64 (/.f64 #s(literal 1 binary64) z) #s(literal 1 binary64))
(/.f64 (pow.f64 z #s(literal -1/2 binary64)) (sqrt.f64 z))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) z))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 z)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))
(/.f64 (*.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))
(/.f64 (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) z)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 z #s(literal -1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) z)))
(pow.f64 z #s(literal -1 binary64))
(pow.f64 (sqrt.f64 z) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) z) #s(literal 1 binary64))
(pow.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 z z) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) z))
(*.f64 (/.f64 #s(literal 1 binary64) z) #s(literal 1 binary64))
(*.f64 (pow.f64 z #s(literal -1/2 binary64)) (pow.f64 z #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) z))
(*.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))
(*.f64 (pow.f64 z #s(literal -1/4 binary64)) (*.f64 (pow.f64 z #s(literal -1/4 binary64)) (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (pow.f64 z #s(literal -1/4 binary64))) (pow.f64 z #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(literal 2 binary64))
(/.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))

simplify223.0ms (3%)

Algorithm
egg-herbie
Rules
3060×*-lowering-*.f32
3060×*-lowering-*.f64
2120×fma-lowering-fma.f32
2120×fma-lowering-fma.f64
2076×fmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0621601
11941521
25991497
316621497
449721497
080541497
Stop Event
iter limit
node limit
Counts
300 → 300
Calls
Call 1
Inputs
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* 1/2 (* y (sqrt z)))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 (* y (sqrt (/ 1 z))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* 1/2 (sqrt z))
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt z) (pow (sqrt -1) 2)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(/ 1 z)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (sqrt z)))
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(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (sqrt.f64 z))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(/ 1 z)
(/.f64 #s(literal 1 binary64) z)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)

eval132.0ms (1.8%)

Compiler

Compiled 13920 to 1645 computations (88.2% saved)

prune94.0ms (1.2%)

Pruning

9 alts after pruning (4 fresh and 5 done)

PrunedKeptTotal
New114131144
Fresh112
Picked235
Done022
Total114491153
Accuracy
100.0%
Counts
1153 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.7%
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
46.6%
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
46.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
46.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
54.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
88.2%
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
46.7%
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
99.5%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
54.2%
(*.f64 #s(literal 1/2 binary64) x)
Compiler

Compiled 87 to 68 computations (21.8% saved)

simplify343.0ms (4.6%)

Algorithm
egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(pow.f64 z #s(literal -1/2 binary64))
cost-diff0
(*.f64 #s(literal 1/2 binary64) y)
cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
cost-diff0
(/.f64 #s(literal 2 binary64) y)
cost-diff0
(sqrt.f64 z)
cost-diff0
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
cost-diff0
(pow.f64 z #s(literal -1/2 binary64))
cost-diff0
(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)
cost-diff0
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
cost-diff0
(sqrt.f64 z)
cost-diff0
(+.f64 (sqrt.f64 z) (/.f64 x y))
cost-diff0
(*.f64 #s(literal 1/2 binary64) y)
cost-diff128
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
Rules
6268×*-lowering-*.f32
6268×*-lowering-*.f64
2920×cube-prod
2396×pow-lowering-pow.f64
2396×pow-lowering-pow.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01778
13478
27478
313278
415577
517975
624275
744475
8149375
9214875
10266175
11295975
12330775
13375575
14442175
15529475
16574975
17591575
18598875
19606575
20614475
21715075
22778175
23794775
0801975
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
(* 1/2 y)
1/2
y
(+ (sqrt z) (/ x y))
(sqrt z)
z
(/ x y)
x
(/ 1/2 (/ (pow z -1/2) y))
1/2
(/ (pow z -1/2) y)
(pow z -1/2)
z
-1/2
y
(/ (sqrt z) (/ 2 y))
(sqrt z)
z
(/ 2 y)
2
y
(/ (* 1/2 y) (pow z -1/2))
(* 1/2 y)
1/2
y
(pow z -1/2)
z
-1/2
Outputs
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 y)
(/.f64 y #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)
y
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(sqrt z)
(sqrt.f64 z)
z
(/ x y)
(/.f64 x y)
x
(/ 1/2 (/ (pow z -1/2) y))
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
1/2
#s(literal 1/2 binary64)
(/ (pow z -1/2) y)
(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)
(pow z -1/2)
(pow.f64 z #s(literal -1/2 binary64))
z
-1/2
#s(literal -1/2 binary64)
y
(/ (sqrt z) (/ 2 y))
(/.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2 binary64))
(sqrt z)
(sqrt.f64 z)
z
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
y
(/ (* 1/2 y) (pow z -1/2))
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(* 1/2 y)
(/.f64 y #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)
y
(pow z -1/2)
(pow.f64 z #s(literal -1/2 binary64))
z
-1/2
#s(literal -1/2 binary64)

localize101.0ms (1.3%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(pow.f64 z #s(literal -1/2 binary64))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) y)
accuracy99.7%
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
accuracy100.0%
(/.f64 #s(literal 2 binary64) y)
accuracy100.0%
(sqrt.f64 z)
accuracy99.5%
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
accuracy100.0%
(pow.f64 z #s(literal -1/2 binary64))
accuracy99.6%
(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)
accuracy99.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) y)
accuracy100.0%
(sqrt.f64 z)
accuracy100.0%
(+.f64 (sqrt.f64 z) (/.f64 x y))
accuracy88.2%
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
Results
77.0ms256×0valid
Compiler

Compiled 82 to 18 computations (78% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-div: 11.0ms (40.4% of total)
ival-pow: 6.0ms (22% of total)
ival-sqrt: 5.0ms (18.4% of total)
ival-mult: 4.0ms (14.7% of total)
ival-add: 1.0ms (3.7% of total)
const: 1.0ms (3.7% of total)
backward-pass: 0.0ms (0% of total)

series24.0ms (0.3%)

Counts
10 → 216
Calls
Call 1
Inputs
#<alt (* (* 1/2 y) (+ (sqrt z) (/ x y)))>
#<alt (* 1/2 y)>
#<alt (+ (sqrt z) (/ x y))>
#<alt (sqrt z)>
#<alt (/ 1/2 (/ (pow z -1/2) y))>
#<alt (/ (pow z -1/2) y)>
#<alt (pow z -1/2)>
#<alt (/ (sqrt z) (/ 2 y))>
#<alt (/ 2 y)>
#<alt (/ (* 1/2 y) (pow z -1/2))>
Outputs
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))>
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))>
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))>
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))>
#<alt (* 1/2 (* y (+ (sqrt z) (/ x y))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (sqrt z)>
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))>
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))>
#<alt (* z (+ (sqrt (/ 1 z)) (/ x (* y z))))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))>
#<alt (sqrt z)>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (/ x y)>
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))>
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))>
#<alt (* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))>
#<alt (/ x y)>
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))>
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))>
#<alt (* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))>
#<alt (/ x y)>
#<alt (/ (+ x (* y (sqrt z))) y)>
#<alt (/ (+ x (* y (sqrt z))) y)>
#<alt (/ (+ x (* y (sqrt z))) y)>
#<alt (sqrt z)>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (sqrt z)>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (+ (sqrt z) (/ x y))>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (* (/ 1 y) (sqrt (/ 1 z)))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (sqrt (/ 1 z))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* 1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
#<alt (* -1/2 (* y (sqrt z)))>
Calls

54 calls:

TimeVariablePointExpression
16.0ms
y
@-inf
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
1.0ms
z
@0
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
1.0ms
y
@0
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
0.0ms
x
@inf
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
0.0ms
y
@inf
(* (* 1/2 y) (+ (sqrt z) (/ x y)))

rewrite238.0ms (3.2%)

Algorithm
batch-egg-rewrite
Rules
3730×*-lowering-*.f32
3730×*-lowering-*.f64
2784×/-lowering-/.f32
2784×/-lowering-/.f64
826×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01753
19350
265348
3749348
0806648
Stop Event
iter limit
node limit
Counts
10 → 651
Calls
Call 1
Inputs
(* (* 1/2 y) (+ (sqrt z) (/ x y)))
(* 1/2 y)
(+ (sqrt z) (/ x y))
(sqrt z)
(/ 1/2 (/ (pow z -1/2) y))
(/ (pow z -1/2) y)
(pow z -1/2)
(/ (sqrt z) (/ 2 y))
(/ 2 y)
(/ (* 1/2 y) (pow z -1/2))
Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(+.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(-.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(-.f64 (/.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 (sqrt.f64 z) (/.f64 x y)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x)))) (*.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 (sqrt.f64 z) (/.f64 x y)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y (/.f64 y x)) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (/.f64 y #s(literal 2 binary64)) (sqrt.f64 z) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 x y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (sqrt.f64 z) (/.f64 y #s(literal 2 binary64)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 x (/.f64 (/.f64 y #s(literal 2 binary64)) y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (/.f64 x y) (/.f64 y #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 y #s(literal -2 binary64)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) y (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 y (/.f64 y x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) y (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(fma.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) y) (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y))
(/.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 z) (/.f64 x y))))
(/.f64 (+.f64 (sqrt.f64 z) (/.f64 x y)) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (-.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))))) (+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64))))) (*.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 (sqrt.f64 z) (/.f64 x y))) (-.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 z (/.f64 (-.f64 (/.f64 x y) (sqrt.f64 z)) (/.f64 y x))) (/.f64 (+.f64 (pow.f64 z #s(literal 3/2 binary64)) (/.f64 (/.f64 x y) (/.f64 (/.f64 y (/.f64 x y)) x))) (/.f64 #s(literal 2 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 z) (/.f64 x y)) (/.f64 (-.f64 z (/.f64 x (/.f64 y (/.f64 x y)))) (/.f64 #s(literal 2 binary64) y))))
(/.f64 (*.f64 y (+.f64 (sqrt.f64 z) (/.f64 x y))) #s(literal 2 binary64))
(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64))))) (*.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x)))))) (+.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (-.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))))))
(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64))))) (*.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x)))))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x)))) (-.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (/.f64 (/.f64 (*.f64 y (*.f64 #s(literal 1/2 binary64) x)) y) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64)))))))
(/.f64 (-.f64 (*.f64 z (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 y (/.f64 y x)) (/.f64 y (/.f64 y x))))) (*.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 (sqrt.f64 z) (/.f64 x y))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 z) (/.f64 x y))) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 (+.f64 (pow.f64 z #s(literal 3/2 binary64)) (/.f64 (/.f64 x y) (/.f64 (/.f64 y (/.f64 x y)) x))) (/.f64 #s(literal 2 binary64) y)) (+.f64 z (/.f64 (-.f64 (/.f64 x y) (sqrt.f64 z)) (/.f64 y x))))
(/.f64 (/.f64 (-.f64 z (/.f64 x (/.f64 y (/.f64 x y)))) (/.f64 #s(literal 2 binary64) y)) (-.f64 (sqrt.f64 z) (/.f64 x y)))
(/.f64 (/.f64 (+.f64 (sqrt.f64 z) (/.f64 x y)) (/.f64 #s(literal 2 binary64) y)) (*.f64 (/.f64 #s(literal 1 binary64) y) y))
(/.f64 (/.f64 (+.f64 (sqrt.f64 z) (/.f64 x y)) (/.f64 #s(literal 2 binary64) y)) (*.f64 y (/.f64 #s(literal 1 binary64) y)))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (/.f64 y x)))
(/.f64 (+.f64 (/.f64 y #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) y))
(/.f64 (+.f64 (/.f64 y #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 y x)) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64)))) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y x)))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) y) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) y)) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (pow.f64 z #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (*.f64 (sqrt.f64 z) (/.f64 y x)) (*.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 y x)))
(/.f64 (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (*.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 #s(literal 2 binary64) y) y))
(/.f64 (+.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (/.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (/.f64 y #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (/.f64 y x)))
(/.f64 (+.f64 (/.f64 y #s(literal -2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) y))
(/.f64 (+.f64 (/.f64 y #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal -2 binary64)) (/.f64 y x)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 y #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 y x)))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal -2 binary64)) y) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) y))
(/.f64 (+.f64 (*.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 y x)) (*.f64 (/.f64 #s(literal -2 binary64) y) (/.f64 y #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal -2 binary64) y) (/.f64 y x)))
(/.f64 (+.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) (*.f64 (/.f64 #s(literal -2 binary64) y) (*.f64 (/.f64 y #s(literal -2 binary64)) x))) (*.f64 (/.f64 #s(literal -2 binary64) y) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (+.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal -2 binary64) y) (*.f64 y (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 #s(literal -2 binary64) y) y))
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(*.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) y)
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 y #s(literal -2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1 binary64)) y)
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(exp.f64 (*.f64 (log.f64 (/.f64 y #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) y))
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(neg.f64 (/.f64 (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
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(/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) y))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)))
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(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
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(/.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64))
(pow.f64 (/.f64 y #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
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(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) y))
(*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -2 binary64))
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(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
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(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) y)) (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
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(/.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))))
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(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal -2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y))
(/.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
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(/.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (/.f64 #s(literal 2 binary64) y) (pow.f64 z #s(literal -1/4 binary64))))
(/.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal -1/4 binary64)))
(/.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))
(/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) y))
(/.f64 (neg.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) y))
(/.f64 (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y #s(literal 2 binary64))) (pow.f64 z #s(literal -1/4 binary64)))
(/.f64 (*.f64 (/.f64 y #s(literal -2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) y) (pow.f64 z #s(literal -1/4 binary64)))
(/.f64 (*.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 z #s(literal -1/4 binary64)))
(/.f64 (/.f64 (/.f64 y #s(literal -2 binary64)) (pow.f64 z #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64))))
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal -1/8 binary64))) (pow.f64 z #s(literal -1/8 binary64)))
(pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 y (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 (/.f64 y #s(literal 2 binary64)) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (/.f64 y #s(literal 2 binary64)))
(*.f64 #s(literal -1/2 binary64) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))))
(*.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 (sqrt.f64 z) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 y #s(literal -2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(*.f64 (/.f64 y (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) y)
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 y (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (/.f64 y (pow.f64 z #s(literal -1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/2 binary64)))) #s(literal -1/2 binary64))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 (/.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) y)))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 y #s(literal 2 binary64))))
(*.f64 (/.f64 y (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (pow.f64 z #s(literal 1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y))
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) y))
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/4 binary64)) y) #s(literal -1 binary64)))
(*.f64 (/.f64 (sqrt.f64 z) #s(literal -1 binary64)) (/.f64 y #s(literal -2 binary64)))
(*.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))))
(*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))))
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal -2 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) y)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 z #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 z #s(literal -1/4 binary64))) (/.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 z #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) (/.f64 y #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 y (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 z #s(literal -1/4 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) y))
(*.f64 (*.f64 (/.f64 (sqrt.f64 z) #s(literal -2 binary64)) #s(literal -1 binary64)) y)
(*.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) y)
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal 1 binary64)) (/.f64 y #s(literal -2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal 1 binary64)) y)
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))

simplify185.0ms (2.5%)

Algorithm
egg-herbie
Rules
4746×*-lowering-*.f32
4746×*-lowering-*.f64
1484×times-frac
1466×fnmadd-define
1334×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0821260
12691185
28631177
326821159
088241159
Stop Event
iter limit
node limit
Counts
216 → 216
Calls
Call 1
Inputs
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(sqrt z)
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(sqrt z)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(/ x y)
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(/ x y)
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(/ x y)
(/ (+ x (* y (sqrt z))) y)
(/ (+ x (* y (sqrt z))) y)
(/ (+ x (* y (sqrt z))) y)
(sqrt z)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(sqrt z)
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(+ (sqrt z) (/ x y))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(sqrt (/ 1 z))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
(* -1/2 (* y (sqrt z)))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (+ (sqrt z) (/ x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 z (*.f64 #s(literal 1/2 binary64) y))))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(sqrt z)
(sqrt.f64 z)
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(* z (+ (sqrt (/ 1 z)) (/ x (* y z))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2)))))
(+.f64 (/.f64 x y) (*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(sqrt z)
(sqrt.f64 z)
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(/ x y)
(/.f64 x y)
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y)))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(/ x y)
(/.f64 x y)
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y))))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(/ x y)
(/.f64 x y)
(/ (+ x (* y (sqrt z))) y)
(/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) y)
(/ (+ x (* y (sqrt z))) y)
(/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) y)
(/ (+ x (* y (sqrt z))) y)
(/.f64 (+.f64 x (*.f64 y (sqrt.f64 z))) y)
(sqrt z)
(sqrt.f64 z)
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(sqrt z)
(sqrt.f64 z)
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(+ (sqrt z) (/ x y))
(+.f64 (sqrt.f64 z) (/.f64 x y))
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(sqrt z)
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(sqrt.f64 z)
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (-.f64 #s(literal 0 binary64) y))
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(* (/ 1 y) (sqrt (/ 1 z)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(sqrt (/ 1 z))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* (sqrt (/ 1 z)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* 1/2 (* y (sqrt z)))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))
(* -1/2 (* y (sqrt z)))
(*.f64 y (*.f64 (sqrt.f64 z) #s(literal -1/2 binary64)))

eval114.0ms (1.5%)

Compiler

Compiled 13602 to 1500 computations (89% saved)

prune93.0ms (1.2%)

Pruning

10 alts after pruning (1 fresh and 9 done)

PrunedKeptTotal
New9951996
Fresh000
Picked044
Done055
Total995101005
Accuracy
100.0%
Counts
1005 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.7%
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
46.6%
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
46.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
46.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
54.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
42.5%
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y))
88.2%
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
46.7%
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
99.5%
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
54.2%
(*.f64 #s(literal 1/2 binary64) x)
Compiler

Compiled 326 to 162 computations (50.3% saved)

regimes48.0ms (0.6%)

Counts
22 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (/.f64 y (sqrt.f64 z)) z)))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (+.f64 (sqrt.f64 z) (/.f64 x y)))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 y y) z) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z)) z (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 y z) (*.f64 x (sqrt.f64 z))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64)))))))
Outputs
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
Calls

7 calls:

7.0ms
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
7.0ms
(sqrt.f64 z)
7.0ms
z
6.0ms
x
6.0ms
y
Results
AccuracySegmentsBranch
99.5%1x
99.5%1y
99.5%1z
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z))))
99.5%1(+.f64 x (*.f64 y (sqrt.f64 z)))
99.5%1(*.f64 y (sqrt.f64 z))
99.5%1(sqrt.f64 z)
Compiler

Compiled 46 to 34 computations (26.1% saved)

regimes12.0ms (0.2%)

Counts
7 → 3
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
Outputs
(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
Calls

4 calls:

3.0ms
x
3.0ms
(sqrt.f64 z)
3.0ms
z
3.0ms
y
Results
AccuracySegmentsBranch
74.8%3x
77.4%3y
63.1%4z
63.1%4(sqrt.f64 z)
Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes3.0ms (0%)

Counts
6 → 3
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y))
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
Outputs
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
Calls

1 calls:

3.0ms
y
Results
AccuracySegmentsBranch
77.4%3y
Compiler

Compiled 4 to 3 computations (25% saved)

regimes6.0ms (0.1%)

Accuracy

Total -7.6b remaining (-25.8%)

Threshold costs -7.6b (-25.8%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 x y))
Outputs
(*.f64 #s(literal 1/2 binary64) x)
Calls

3 calls:

2.0ms
x
2.0ms
y
2.0ms
z
Results
AccuracySegmentsBranch
54.2%1z
54.2%1x
54.2%1y
Compiler

Compiled 12 to 9 computations (25% saved)

bsearch18.0ms (0.2%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
0.0ms
1.025349932504715e+22
1.0700200736056834e+22
16.0ms
-1.0773809055121578e+52
-3.1065192583820855e+49
Results
11.0ms128×0valid
Compiler

Compiled 163 to 135 computations (17.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 4.0ms (60.9% of total)
ival-div: 1.0ms (15.2% of total)
ival-add: 1.0ms (15.2% of total)
ival-sqrt: 1.0ms (15.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch17.0ms (0.2%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
0.0ms
1.025349932504715e+22
1.0700200736056834e+22
15.0ms
-1.0773809055121578e+52
-3.1065192583820855e+49
Results
10.0ms128×0valid
Compiler

Compiled 155 to 127 computations (18.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 2.0ms (42.5% of total)
ival-div: 1.0ms (21.2% of total)
ival-add: 1.0ms (21.2% of total)
ival-sqrt: 1.0ms (21.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
12×*-commutative_binary64
+-commutative_binary64
if-if-or-not_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02453
13453
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(if (<=.f64 y #s(literal -32000000000000001403066977442438315348289524858880 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))))
(if (<=.f64 y #s(literal -41000000000000000012827519726777094232637840556032 binary64)) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))))
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(*.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
(if (<=.f64 y #s(literal -32000000000000001403066977442438315348289524858880 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))))
(if (<=.f64 y #s(literal -41000000000000000012827519726777094232637840556032 binary64)) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (if (<=.f64 y #s(literal 10499999999999998951424 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))))
(*.f64 #s(literal 1/2 binary64) x)

soundness664.0ms (8.8%)

Rules
4668×*-lowering-*.f32
4668×*-lowering-*.f64
3400×*-lowering-*.f32
3400×*-lowering-*.f64
3126×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02271
111668
274665
0864365
075622
1264578
2891578
32789554
47950554
08118554
0118
1227
2377
3487
0487
Stop Event
fuel
iter limit
saturated
iter limit
node limit
iter limit
node limit
Compiler

Compiled 193 to 124 computations (35.8% saved)

preprocess31.0ms (0.4%)

Compiler

Compiled 148 to 68 computations (54.1% saved)

end0.0ms (0%)

Profiling

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