sqrt times

Time bar (total: 4.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory
3.7MiB live, 3.7MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%50%0%0%50%0%2
50%25%25%0%0%50%0%3
66.7%25%12.5%0%0%62.5%0%4
80%25%6.2%0%0%68.7%0%5
88.9%25%3.1%0%0%71.8%0%6
94.1%25%1.6%0%0%73.4%0%7
97%25%0.8%0%0%74.2%0%8
98.5%25%0.4%0%0%74.6%0%9
99.2%25%0.2%0%0%74.8%0%10
99.6%25%0.1%0%0%74.9%0%11
99.8%25%0%0%0%74.9%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample574.0ms (14.2%)

Memory
66.7MiB live, 740.5MiB allocated
Samples
376.0ms8 246×0valid
1.0ms10×1valid
0.0ms10×0invalid
Precisions
Click to see histograms. Total time spent on operations: 244.0ms
ival-sqrt: 130.0ms (53.3% of total)
ival-sub: 52.0ms (21.3% of total)
ival-mult: 50.0ms (20.5% of total)
ival-true: 5.0ms (2.1% of total)
exact: 4.0ms (1.6% of total)
ival-assert: 3.0ms (1.2% of total)
adjust: 0.0ms (0% of total)
Bogosity

explain86.0ms (2.1%)

Memory
-6.7MiB live, 117.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
00-0-(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
00-0-(sqrt.f64 x)
00-0-(-.f64 x #s(literal 1 binary64))
00-0-#s(literal 1 binary64)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
28.0ms512×0valid
Compiler

Compiled 48 to 22 computations (54.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-sqrt: 7.0ms (41.4% of total)
ival-mult: 6.0ms (35.5% of total)
ival-sub: 3.0ms (17.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess19.0ms (0.5%)

Memory
-9.7MiB live, 28.2MiB allocated
Algorithm
egg-herbie
Rules
36×sub-neg
20×+-commutative
12×associate-+l-
10×*-commutative
10×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
12219
23817
35917
47717
59717
611617
713117
813217
067
0107
1167
2177
0177
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory
5.8MiB live, 5.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(-.f64 x #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff0
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Rules
lift-sqrt.f64
lower-+.f64
lower-*.f32
lower-sqrt.f32
lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11618
21718
01718
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal 1 binary64))
(+.f64 x #s(literal -1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize24.0ms (0.6%)

Memory
-10.9MiB live, 33.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 x #s(literal 1 binary64))
accuracy0
(sqrt.f64 x)
accuracy0.00390625
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy0.4921875
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Samples
18.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-sqrt: 9.0ms (72% of total)
ival-sub: 2.0ms (16% of total)
ival-mult: 1.0ms (8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
7.1MiB live, 7.1MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(* (sqrt (- x 1)) (sqrt x))
1.0ms
x
@-inf
(sqrt x)
1.0ms
x
@-inf
(sqrt (- x 1))
1.0ms
x
@inf
(sqrt (- x 1))
0.0ms
x
@-inf
(* (sqrt (- x 1)) (sqrt x))

simplify361.0ms (9%)

Memory
-22.0MiB live, 209.3MiB allocated
Algorithm
egg-herbie
Rules
10 896×lower-fma.f64
10 896×lower-fma.f32
4 646×lower-*.f64
4 646×lower-*.f32
1 844×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150492
1442431
21553410
34080392
08296368
Stop Event
iter limit
node limit
Counts
48 → 45
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
-1
(- x 1)
(- x 1)
(- x 1)
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 x (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
-1
#s(literal -1 binary64)
(- x 1)
(+.f64 x #s(literal -1 binary64))
(- x 1)
(+.f64 x #s(literal -1 binary64))
(- x 1)
(+.f64 x #s(literal -1 binary64))
x
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
x
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite358.0ms (8.9%)

Memory
33.9MiB live, 359.0MiB allocated
Rules
4 558×lower-/.f64
4 558×lower-/.f32
3 416×lower-fma.f64
3 416×lower-fma.f32
3 070×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01015
13415
216115
3138815
0839315
Stop Event
iter limit
node limit
iter limit
Counts
4 → 368
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
(sqrt.f64 x)
Outputs
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (neg.f64 x))) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x #s(literal -1 binary64))))))
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 x))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (neg.f64 x))))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))))) (sqrt.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal -1 binary64) x)))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (sqrt.f64 (*.f64 x (neg.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))))) (sqrt.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 x (neg.f64 (fma.f64 x x #s(literal -1 binary64))))) (sqrt.f64 (-.f64 #s(literal -1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) x)) (sqrt.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (sqrt.f64 (-.f64 #s(literal -1 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))))) (neg.f64 (sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 x x (neg.f64 x)) (fma.f64 x x (neg.f64 x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (neg.f64 x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 x))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 x (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) x)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 x (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) x)))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) x)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x #s(literal -1 binary64)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64) (*.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64))))
(sqrt.f64 (+.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (neg.f64 x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
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(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log1p.f64 (+.f64 x (*.f64 x x))))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log1p.f64 x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))

eval55.0ms (1.4%)

Memory
-29.8MiB live, 125.5MiB allocated
Compiler

Compiled 11 188 to 1 524 computations (86.4% saved)

prune63.0ms (1.6%)

Memory
17.5MiB live, 179.6MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New4085413
Fresh000
Picked101
Done000
Total4095414
Accuracy
100.0%
Counts
414 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.2%
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
53.7%
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
99.5%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
99.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
97.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 74 to 46 computations (37.8% saved)

simplify318.0ms (7.9%)

Memory
-15.4MiB live, 347.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x x #s(literal -1 binary64))
cost-diff0
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
cost-diff0
(sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
cost-diff0
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(neg.f64 x)
cost-diff0
(fma.f64 x x (neg.f64 x))
cost-diff0
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
cost-diff0
(+.f64 x #s(literal -1/2 binary64))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
cost-diff0
(/.f64 #s(literal 1/8 binary64) x)
cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
cost-diff0
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
Rules
18 058×lower-fma.f32
18 054×lower-fma.f64
2 858×lower-*.f32
2 856×lower-*.f64
2 620×lower-+.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026112
040112
164109
2102109
3191109
4380109
5974109
61976109
73492109
84944109
96475109
107485109
117909109
08006109
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
x
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(fma.f64 x x (neg.f64 x))
x
(neg.f64 x)
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
x
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
x
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(fma.f64 x x (neg.f64 x))
x
(neg.f64 x)
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
x
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)

localize74.0ms (1.8%)

Memory
22.9MiB live, 104.6MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy0.08203125
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
accuracy18.386377218355953
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy20.70736078397709
(sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
accuracy0
(fma.f64 x x (neg.f64 x))
accuracy0
(neg.f64 x)
accuracy29.612254874702717
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
accuracy0
(+.f64 x #s(literal -1/2 binary64))
accuracy0.5277933730651704
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
accuracy1.676965612986999
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
accuracy0
(/.f64 #s(literal 1/8 binary64) x)
accuracy0
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
accuracy0.00390625
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
accuracy0.34192822316671295
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
Samples
53.0ms256×0valid
Compiler

Compiled 106 to 26 computations (75.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-sqrt: 19.0ms (46.2% of total)
ival-add: 10.0ms (24.3% of total)
ival-mult: 5.0ms (12.2% of total)
ival-div: 3.0ms (7.3% of total)
ival-sub: 3.0ms (7.3% of total)
exact: 1.0ms (2.4% of total)
ival-neg: 1.0ms (2.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series24.0ms (0.6%)

Memory
-18.2MiB live, 18.5MiB allocated
Counts
15 → 180
Calls
Call 1
Inputs
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/8 binary64) x) (patch (/.f64 #s(literal 1/8 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal -1/2 binary64)) (patch (+.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 x x (neg.f64 x))) (patch (sqrt.f64 (fma.f64 x x (neg.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 x x (neg.f64 x)) (patch (fma.f64 x x (neg.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (patch (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 x) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (patch (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
Calls

45 calls:

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

simplify246.0ms (6.1%)

Memory
33.9MiB live, 302.9MiB allocated
Algorithm
egg-herbie
Rules
8 186×lower-fma.f64
8 186×lower-fma.f32
4 496×lower-*.f64
4 496×lower-*.f32
2 726×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02671999
17871821
227881619
375591601
081821524
Stop Event
iter limit
node limit
Counts
180 → 171
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(/ 1/8 x)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 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 x)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
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(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 5)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/8 (sqrt (/ 1 (pow x 9)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 (pow x 9)))) (* -1/16 (sqrt (/ 1 (pow x 13))))))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (pow x 3))) (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 x)
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(pow x 3)
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
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(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
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(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* -1/2 x) 1/8) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
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(/ 1/8 x)
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(/ 1/8 x)
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(/ 1/8 x)
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(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
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(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
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(*.f64 (neg.f64 x) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

rewrite308.0ms (7.6%)

Memory
-19.4MiB live, 465.8MiB allocated
Rules
4 840×lower-fma.f32
4 836×lower-fma.f64
3 866×lower-/.f32
3 862×lower-/.f64
2 952×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02699
04090
116288
2116581
0937276
Stop Event
iter limit
node limit
iter limit
Counts
15 → 757
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(/.f64 #s(literal 1/8 binary64) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(fma.f64 x x (neg.f64 x))
(neg.f64 x)
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
(+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x)
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x))) (neg.f64 (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (neg.f64 (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))))
(+.f64 (+.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal -1/2 binary64))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))))
(-.f64 (+.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/2 binary64))
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (/.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal 8 binary64)))))) (/.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (/.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal 8 binary64)))))))
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))))
(fma.f64 x #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 x #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/2 binary64)) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1 binary64) x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (neg.f64 (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))))
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x))) (neg.f64 (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x)))))
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x x (*.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x x (*.f64 x #s(literal -1/2 binary64))))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))) x)
(fma.f64 (fma.f64 x x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (fma.f64 x x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) x)
(fma.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 x x #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 x x #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (neg.f64 (fma.f64 x x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (neg.f64 (fma.f64 x x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x #s(literal 1/2 binary64)))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(fma.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) x)
(fma.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) x)
(fma.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/8 binary64) x))
(fma.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/2 binary64))) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))) (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (/.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal 8 binary64))))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x)))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))) (fma.f64 x x (fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))))
(/.f64 (*.f64 (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))) (neg.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))) (neg.f64 (fma.f64 x x (fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))) (neg.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))))
(/.f64 (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (/.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal 8 binary64))))))
(/.f64 (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (/.f64 (+.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal 8 binary64))))))
(/.f64 (fma.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/64 binary64) (*.f64 x x))) (+.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
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(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 x #s(literal 1 binary64)) x) (-.f64 (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) (pow.f64 (neg.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (fma.f64 x x x) (fma.f64 x x x) (-.f64 (*.f64 (neg.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (fma.f64 x x x) (neg.f64 (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 x #s(literal 1 binary64)) x)) (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) (*.f64 (neg.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 (fma.f64 x x x) (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(*.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(*.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (/.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64))))

eval147.0ms (3.7%)

Memory
-3.0MiB live, 277.2MiB allocated
Compiler

Compiled 18 724 to 2 347 computations (87.5% saved)

prune140.0ms (3.5%)

Memory
9.6MiB live, 239.9MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New9271928
Fresh000
Picked235
Done000
Total9294933
Accuracy
100.0%
Counts
933 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.7%
(sqrt.f64 (-.f64 (*.f64 x x) x))
99.5%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
99.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
97.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 24 to 14 computations (41.7% saved)

simplify9.0ms (0.2%)

Memory
14.4MiB live, 14.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) x)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) x))
Rules
144×lower-fma.f64
144×lower-fma.f32
88×lower-*.f32
86×lower-*.f64
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0415
0715
1915
21415
32415
43615
55515
611415
720415
823615
923615
023615
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
x
Outputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
x

localize17.0ms (0.4%)

Memory
-2.4MiB live, 35.3MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0.0078125
(-.f64 (*.f64 x x) x)
accuracy29.612254874702717
(sqrt.f64 (-.f64 (*.f64 x x) x))
Samples
11.0ms256×0valid
Compiler

Compiled 17 to 6 computations (64.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sub: 3.0ms (44.4% of total)
ival-mult: 2.0ms (29.6% of total)
ival-sqrt: 2.0ms (29.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
3.1MiB live, 3.1MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())
#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (*.f64 x x) x)) (patch (sqrt.f64 (-.f64 (*.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) x) (patch (-.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(* x x)
0.0ms
x
@0
(* x x)
0.0ms
x
@0
(sqrt (- (* x x) x))
0.0ms
x
@inf
(sqrt (- (* x x) x))
0.0ms
x
@-inf
(sqrt (- (* x x) x))

simplify453.0ms (11.2%)

Memory
-33.0MiB live, 346.0MiB allocated
Algorithm
egg-herbie
Rules
7 260×lower-fma.f64
7 260×lower-fma.f32
3 920×lower-*.f64
3 920×lower-*.f32
2 256×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075279
1209263
2661257
32067232
44858224
57636224
08865218
Stop Event
iter limit
node limit
Counts
36 → 35
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/8 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(+.f64 (-.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (-.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(* -1 x)
(neg.f64 x)
(* x (- x 1))
(-.f64 (*.f64 x x) x)
(* x (- x 1))
(-.f64 (*.f64 x x) x)
(* x (- x 1))
(-.f64 (*.f64 x x) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(* (pow x 2) (- 1 (/ 1 x)))
(-.f64 (*.f64 x x) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite266.0ms (6.6%)

Memory
-11.3MiB live, 344.3MiB allocated
Rules
7 082×lower-fma.f64
7 082×lower-fma.f32
3 072×lower-/.f64
3 072×lower-/.f32
2 656×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0414
0714
12514
216714
3156714
0967411
Stop Event
iter limit
node limit
iter limit
Counts
3 → 404
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x x))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 x x) x))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/4 binary64))))
(hypot.f64 x (sqrt.f64 x))
(hypot.f64 x (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (sqrt.f64 x))
(hypot.f64 (neg.f64 x) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 x) x)
(hypot.f64 (sqrt.f64 x) (neg.f64 x))
(hypot.f64 (sqrt.f64 x) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (sqrt.f64 x))
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x x x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) (sqrt.f64 (fma.f64 x x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) x))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 x (fma.f64 x (*.f64 x x) x)))) (sqrt.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (fma.f64 x x x))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) (sqrt.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) (sqrt.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) (sqrt.f64 (*.f64 (fma.f64 x x x) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) (neg.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)))) (neg.f64 (sqrt.f64 (fma.f64 x x x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 x (fma.f64 x (*.f64 x x) x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 x (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))) (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (*.f64 x (*.f64 x x))))) (sqrt.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x x)) (*.f64 (fma.f64 x x x) (*.f64 x x)))) (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x x) x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))))
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(*.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))) (*.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))))))
(*.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) (*.f64 x x)) (*.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) (*.f64 x x))) (*.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (*.f64 x (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) (*.f64 x x) (*.f64 x (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))))
(*.f64 (neg.f64 (+.f64 x #s(literal 1 binary64))) x)
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))))
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))))
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 x (fma.f64 x (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x x) x))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 x (fma.f64 x (*.f64 x x) x))) (fma.f64 x x x))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (pow.f64 (/.f64 x (*.f64 x (fma.f64 x (*.f64 x x) x))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (fma.f64 x x x)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (fma.f64 x x x)) (-.f64 (*.f64 x (fma.f64 x x x)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))) (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))))
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x x)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)) (*.f64 x (fma.f64 x (*.f64 x x) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x x) x))))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))))
(*.f64 (pow.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x))) (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x))))
(*.f64 (exp.f64 (log.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (*.f64 x x)) x)))) (exp.f64 (neg.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 x x) (fma.f64 x x x)))))))
(*.f64 (exp.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 x x) x)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x x)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (-.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) (log.f64 x)))
(neg.f64 (neg.f64 (*.f64 x x)))
(/.f64 (*.f64 x (*.f64 x x)) x)
(/.f64 (*.f64 x (*.f64 x x)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x (*.f64 x x))))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x x)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)

eval60.0ms (1.5%)

Memory
27.4MiB live, 99.5MiB allocated
Compiler

Compiled 15 293 to 1 276 computations (91.7% saved)

prune67.0ms (1.7%)

Memory
-9.6MiB live, 146.4MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New4390439
Fresh000
Picked011
Done033
Total4394443
Accuracy
100.0%
Counts
443 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.7%
(sqrt.f64 (-.f64 (*.f64 x x) x))
99.5%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
99.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
97.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 70 to 40 computations (42.9% saved)

regimes6.0ms (0.1%)

Memory
11.4MiB live, 11.4MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(sqrt.f64 (-.f64 (*.f64 x x) x))
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
Calls

2 calls:

3.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0.1%)

Memory
8.1MiB live, 8.0MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
Calls

2 calls:

2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0.1%)

Memory
6.6MiB live, 6.6MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Calls

2 calls:

1.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
97.4%1x
97.4%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 10 to 7 computations (30% saved)

simplify25.0ms (0.6%)

Memory
-30.6MiB live, 23.2MiB allocated
Algorithm
egg-herbie
Rules
16×+-commutative_binary64
12×sub-neg_binary64
10×*-commutative_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01635
12335
23135
34335
45235
55835
66035
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 x #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

soundness285.0ms (7.1%)

Memory
-3.4MiB live, 148.1MiB allocated
Rules
10 896×lower-fma.f64
10 896×lower-fma.f32
4 646×lower-*.f64
4 646×lower-*.f32
1 844×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150492
1442431
21553410
34080392
08296368
Stop Event
done
iter limit
node limit
Compiler

Compiled 18 to 10 computations (44.4% saved)

preprocess22.0ms (0.6%)

Memory
17.0MiB live, 54.7MiB allocated
Compiler

Compiled 46 to 28 computations (39.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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