Numeric.Log:$clog1p from log-domain-0.10.2.1, B

Time bar (total: 7.3s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory
2.7MiB live, 2.7MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
66.7%50%25%0%0%25%0%3
83.3%62.5%12.5%0%0%25%0%4
91.7%68.7%6.2%0%0%25%0%5
95.8%71.8%3.1%0%0%25%0%6
97.9%73.4%1.6%0%0%25%0%7
99%74.2%0.8%0%0%25%0%8
99.5%74.6%0.4%0%0%25%0%9
99.7%74.8%0.2%0%0%25%0%10
99.9%74.9%0.1%0%0%25%0%11
99.9%74.9%0%0%0%25%0%12
Compiler

Compiled 10 to 8 computations (20% saved)

sample713.0ms (9.8%)

Memory
12.6MiB live, 1 284.1MiB allocated
Samples
441.0ms8 251×0valid
1.0ms5×2valid
0.0ms1×0invalid
Precisions
Click to see histograms. Total time spent on operations: 282.0ms
ival-add: 148.0ms (52.5% of total)
ival-div: 61.0ms (21.6% of total)
ival-sqrt: 59.0ms (20.9% of total)
ival-true: 5.0ms (1.8% of total)
exact: 5.0ms (1.8% of total)
ival-assert: 3.0ms (1.1% of total)
adjust: 0.0ms (0% of total)
Bogosity

explain69.0ms (0.9%)

Memory
6.2MiB live, 167.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
00-0-(+.f64 x #s(literal 1 binary64))
00-0-(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
00-0-#s(literal 1 binary64)
00-0-(sqrt.f64 (+.f64 x #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
24.0ms510×0valid
0.0ms2×2valid
Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-add: 5.0ms (38.4% of total)
ival-sqrt: 4.0ms (30.8% of total)
ival-div: 3.0ms (23.1% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess20.0ms (0.3%)

Memory
1.6MiB live, 40.5MiB allocated
Algorithm
1×egg-herbie
Rules
44×associate-*l*
42×distribute-lft-neg-in
42×times-frac
38×unsub-neg
36×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
12317
25116
311016
422116
533316
636116
737716
839016
068
0108
1148
0148
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.7%
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory
8.1MiB live, 8.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Rules
8×lower-+.f32
4×lift-+.f64
4×lower-+.f64
4×+-commutative
2×lift-sqrt.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0623
01023
11423
01423
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
x
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
x
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)

localize19.0ms (0.3%)

Memory
-2.0MiB live, 36.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x #s(literal 1 binary64))
accuracy0.00390625
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy0.0234375
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy0.16796875
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Samples
12.0ms255×0valid
0.0ms1×2valid
Compiler

Compiled 25 to 8 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-add: 3.0ms (43.8% of total)
ival-div: 2.0ms (29.2% of total)
ival-sqrt: 2.0ms (29.2% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory
-27.7MiB live, 13.6MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 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>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation:binary64>) () ())
Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* 1/2 x)) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt 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 (+ 1 (* 1/2 x)) (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 (+ 1 (* x (+ 1/2 (* -1/8 x)))) (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 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (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 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (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)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 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)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 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 (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 (* -1 (sqrt x)) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (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)))) (* (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))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))
2.0ms
x
@inf
((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))
0.0ms
x
@0
((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))

simplify202.0ms (2.8%)

Memory
24.1MiB live, 291.2MiB allocated
Algorithm
1×egg-herbie
Rules
18 662×lower-fma.f64
18 662×lower-fma.f32
3 776×lower-*.f64
3 776×lower-*.f32
2 642×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0161600
1485505
21630483
35408474
08354430
Stop Event
1×iter limit
1×node limit
Counts
48 → 46
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(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))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/2 binary64))) x) x) (neg.f64 x)) (sqrt.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal -1 binary64)))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)

rewrite184.0ms (2.5%)

Memory
-14.3MiB live, 265.8MiB allocated
Rules
3 950×lower-fma.f64
3 950×lower-fma.f32
3 308×lower-/.f32
3 306×lower-/.f64
2 908×lower-*.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0621
01021
14621
231520
3340020
0827820
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 474
Calls
Call 1
Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
Outputs
(*.f64 (/.f64 x (+.f64 x #s(literal 0 binary64))) (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))))
(*.f64 (/.f64 x x) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 x (fma.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (neg.f64 x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 x #s(literal 1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x))
(*.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (pow.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x))
(*.f64 (/.f64 (neg.f64 x) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) x)
(*.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 x (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (log.f64 x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 (neg.f64 x) x) (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (/.f64 (neg.f64 x) x) (neg.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) x (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (*.f64 (neg.f64 x) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
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(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 (log1p.f64 x)))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (exp.f64 (neg.f64 (log1p.f64 x)))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (neg.f64 (exp.f64 (neg.f64 (log1p.f64 x))))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (exp.f64 (neg.f64 (log1p.f64 x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log1p.f64 x))))
(neg.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fabs.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(fabs.f64 (-.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))))))
(fabs.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(fabs.f64 (+.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1 binary64)))
(exp.f64 (log1p.f64 x))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

eval122.0ms (1.7%)

Memory
10.6MiB live, 167.2MiB allocated
Compiler

Compiled 9 774 to 2 141 computations (78.1% saved)

prune14.0ms (0.2%)

Memory
15.6MiB live, 54.2MiB allocated
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New50911520
Fresh000
Picked011
Done000
Total50912521
Accuracy
100.0%
Counts
521 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
51.2%
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
66.0%
(/.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
✓99.7%
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
67.7%
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))
▶40.0%
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
33.7%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
▶67.0%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
▶65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
▶66.8%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
34.3%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
Compiler

Compiled 196 to 152 computations (22.4% saved)

simplify165.0ms (2.3%)

Memory
-16.3MiB live, 111.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff128
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff0
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
cost-diff0
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
cost-diff0
(*.f64 x #s(literal 1/2 binary64))
cost-diff0
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff0
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff12928
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
Rules
1 792×lower-fma.f32
1 786×lower-fma.f64
816×lower-*.f32
810×lower-*.f64
760×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027148
044148
164147
2103145
3172143
4268143
5435143
6660143
7993143
81879143
92544143
103198143
113465143
123473143
133473143
143475143
03475143
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
x
Outputs
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 x (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
#s(literal -1 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
x

localize136.0ms (1.9%)

Memory
11.6MiB live, 283.0MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 #s(literal 1 binary64) x)
accuracy0
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy0.00390625
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy38.214244232242436
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy0
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
accuracy0
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
accuracy0.0625
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
accuracy21.103306590891716
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
accuracy0
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
accuracy0.015625
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
accuracy22.055715173484717
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
accuracy0
(*.f64 x #s(literal 1/2 binary64))
accuracy21.230214451449456
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
accuracy0.00390625
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.0234375
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy0.09375
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy0.26171875
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
Samples
56.0ms58×2valid
38.0ms101×1valid
20.0ms96×0valid
1.0ms1×5exit
Compiler

Compiled 136 to 29 computations (78.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 86.0ms
ival-mult: 28.0ms (32.5% of total)
ival-add: 22.0ms (25.5% of total)
adjust: 13.0ms (15.1% of total)
ival-pow: 8.0ms (9.3% of total)
ival-sqrt: 6.0ms (7% of total)
ival-div: 5.0ms (5.8% of total)
ival-sub: 2.0ms (2.3% of total)
ival-neg: 2.0ms (2.3% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory
-4.5MiB live, 32.9MiB allocated
Counts
16 → 192
Calls
Call 1
Inputs
#s(alt (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation:binary64>) () ())
#s(alt (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation:binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.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 #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())
#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())
#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation:binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())
Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation:binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/8))) (taylor 0 x) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))) (taylor 0 x) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* 1/2 x)) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/8))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/8))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt -1/8 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/16 x) 1/8) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
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#s(alt (* 1/16 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/16 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation:binary64>) () ())) ())
#s(alt (* (sqrt x) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation:binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (pow (+ (sqrt (+ 1 x)) 1) -1) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))
2.0ms
x
@inf
((/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (pow (+ (sqrt (+ 1 x)) 1) -1) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))
2.0ms
x
@0
((/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (pow (+ (sqrt (+ 1 x)) 1) -1) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))

simplify269.0ms (3.7%)

Memory
-24.0MiB live, 281.7MiB allocated
Algorithm
1×egg-herbie
Rules
18 038×lower-fma.f64
18 038×lower-fma.f32
4 690×lower-+.f64
4 690×lower-+.f32
3 728×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02932209
19231882
232691791
083821658
Stop Event
1×iter limit
1×node limit
Counts
192 → 190
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
-1/8
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* -1/2 x)
(* x (- (* 1/8 x) 1/2))
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2))
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(sqrt (/ 1 x))
(/ (- (sqrt x) 1) x)
(/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) x)
(/ (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) x)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(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))))))))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (+ (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ (pow x 2) (pow (sqrt -1) 4))) (* -1 (* (sqrt x) (+ (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))))) x)) (+ (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(* 1/16 x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
-1/8
#s(literal -1/8 binary64)
(- (* 1/16 x) 1/8)
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(- (* 1/16 x) 1/8)
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(- (* 1/16 x) 1/8)
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/8 x) 1/2))
(*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal -1/2 binary64)) x)
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64)) x)
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) x #s(literal -1/16 binary64)) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (- (sqrt x) 1) x)
(/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)
(/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) x)
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) x)
(/ (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) x)
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* -1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* 1/16 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/16 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) x)
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x x))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x x))
(* 1/16 x)
(*.f64 #s(literal 1/16 binary64) x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal -1 binary64))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal -1 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal 1 binary64))
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x) x) x) (sqrt.f64 x))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))
(/.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) x)
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (+ (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ (pow x 2) (pow (sqrt -1) 4))) (* -1 (* (sqrt x) (+ (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))))) x)) (+ (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (*.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) x) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/2 binary64))) x) x) x) (sqrt.f64 x)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)) x) (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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(*.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x) x) x) (sqrt.f64 x))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x) x) x) (sqrt.f64 x))
(* -1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x) x) x) (sqrt.f64 x))
(* 1/16 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/16 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) x)
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x x))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x x))
(* 1/16 x)
(*.f64 #s(literal 1/16 binary64) x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64)) x) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)

rewrite275.0ms (3.8%)

Memory
37.7MiB live, 267.5MiB allocated
Rules
4 032×lower-/.f32
4 030×lower-/.f64
3 848×lower-*.f32
3 842×lower-*.f64
3 322×lower-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027124
044124
1188119
21191119
08448119
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
16 → 573
Calls
Call 1
Inputs
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 (/.f64 (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)) x))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)))
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(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(-.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(-.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(+.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))
(+.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(*.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (fma.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (fma.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fabs.f64 (+.f64 x #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (log1p.f64 x))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)

eval181.0ms (2.5%)

Memory
-16.0MiB live, 218.2MiB allocated
Compiler

Compiled 16 308 to 2 717 computations (83.3% saved)

prune38.0ms (0.5%)

Memory
23.9MiB live, 62.5MiB allocated
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New8776883
Fresh516
Picked235
Done011
Total88411895
Accuracy
100.0%
Counts
895 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
51.2%
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
✓99.7%
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
▶40.0%
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶33.7%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
▶34.3%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
▶65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
✓67.0%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓66.8%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
Compiler

Compiled 147 to 116 computations (21.1% saved)

simplify161.0ms (2.2%)

Memory
-0.1MiB live, 39.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(*.f64 #s(literal -1/8 binary64) x)
cost-diff0
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
cost-diff320
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
cost-diff0
(sqrt.f64 x)
cost-diff0
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff0
(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
cost-diff1408
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
Rules
624×lower-fma.f32
622×lower-fma.f64
416×lower-*.f32
412×lower-*.f64
256×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030132
043130
166130
292124
3140118
4209118
5441118
6835118
71170118
81331118
91443118
101458118
111460118
01460116
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(literal -1 binary64)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(sqrt.f64 x)
x
#s(literal 1 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
Outputs
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 x (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
#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))) #s(literal -1 binary64))
(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)
(/.f64 #s(literal -1 binary64) x)
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(sqrt.f64 x)
x
#s(literal 1 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
#s(literal -1 binary64)
(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)

localize281.0ms (3.9%)

Memory
-25.5MiB live, 109.3MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x #s(literal 1 binary64))
accuracy0.00390625
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy18.182889993579757
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy0
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0
(*.f64 #s(literal -1/8 binary64) x)
accuracy21.758785274944007
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
accuracy0
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
accuracy0
(sqrt.f64 x)
accuracy20.169301874478037
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
accuracy0
(sqrt.f64 x)
accuracy19.83447672323337
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
accuracy0.00390625
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy0.01171875
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy0.08984375
(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
accuracy0.171875
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
Samples
106.0ms88×0invalid
48.0ms92×0valid
16.0ms46×1valid
14.0ms29×2valid
1.0ms1×5exit
Compiler

Compiled 118 to 28 computations (76.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 135.0ms
ival-pow: 81.0ms (60.1% of total)
ival-div: 25.0ms (18.5% of total)
ival-add: 10.0ms (7.4% of total)
adjust: 6.0ms (4.5% of total)
ival-sqrt: 6.0ms (4.5% of total)
ival-mult: 4.0ms (3% of total)
ival-sub: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series21.0ms (0.3%)

Memory
-21.5MiB live, 16.8MiB allocated
Counts
14 → 168
Calls
Call 1
Inputs
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #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>) () ())
#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())
#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation:binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 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 (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal -1 binary64) (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>) () ())
Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/8 x) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* x (+ 1/8 (* -1/16 x))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* 1/2 x)) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt 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 (+ 1 (* 1/2 x)) (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 (+ 1 (* x (+ 1/2 (* -1/8 x)))) (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 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (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 (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x)) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (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 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
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Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (+ (sqrt (+ x 1)) 1) (sqrt (+ x 1)) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt x) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (- (sqrt x) 1) (+ (* (* -1/8 x) x) (* 1/2 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* -1/8 x) (* 1/2 x) (+ -1 (sqrt (+ x 1))) (+ x 1))
2.0ms
x
@inf
((/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (+ (sqrt (+ x 1)) 1) (sqrt (+ x 1)) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt x) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (- (sqrt x) 1) (+ (* (* -1/8 x) x) (* 1/2 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* -1/8 x) (* 1/2 x) (+ -1 (sqrt (+ x 1))) (+ x 1))
1.0ms
x
@0
((/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (+ (sqrt (+ x 1)) 1) (sqrt (+ x 1)) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt x) (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (- (sqrt x) 1) (+ (* (* -1/8 x) x) (* 1/2 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* -1/8 x) (* 1/2 x) (+ -1 (sqrt (+ x 1))) (+ x 1))

simplify407.0ms (5.6%)

Memory
38.0MiB live, 276.2MiB allocated
Algorithm
1×egg-herbie
Rules
21 890×lower-fma.f64
21 890×lower-fma.f32
4 566×lower-*.f64
4 566×lower-*.f32
3 510×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02251817
16891529
223201423
082601314
Stop Event
1×iter limit
1×node limit
Counts
168 → 166
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
-1/2
(- (* 1/8 x) 1/2)
(- (* x (+ 1/8 (* -1/16 x))) 1/2)
(- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(- (sqrt x) 1)
(- (sqrt x) 1)
(- (sqrt x) 1)
(- (sqrt x) 1)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1 (sqrt (/ 1 x)))
(/ (+ 1 (* -1 (sqrt x))) x)
(/ (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))) (pow x 2))))) x)
(/ (- (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (* (sqrt x) (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))))) (* 1/2 (pow x 2))) (pow x 3))))) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 x))))) x)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(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))))))))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(sqrt (/ 1 x))
(* -1 (/ (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) 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)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 x) 1/2)
(fma.f64 #s(literal 1/8 binary64) x #s(literal -1/2 binary64))
(- (* x (+ 1/8 (* -1/16 x))) 1/2)
(fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64))
(- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) x #s(literal -1/16 binary64)) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 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)
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ 1 (* -1 (sqrt x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)
(/ (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(/ (- (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (* (sqrt x) (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))))) (* 1/2 (pow x 2))) (pow x 3))))) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 x x))) (pow.f64 x #s(literal 3 binary64))))) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(* -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)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal -1 binary64))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x #s(literal -1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) x)) (neg.f64 x)) (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* -1 (/ (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) x))
(/.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) x))
(/.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x) (sqrt.f64 x)) x)
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) x))
(/.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) x)) x) (sqrt.f64 x)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (neg.f64 (*.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) x)) (neg.f64 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)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) x)) (neg.f64 x)) (sqrt.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1/8 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) x)) (neg.f64 x)) (sqrt.f64 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)
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)))
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)

rewrite317.0ms (4.4%)

Memory
-12.7MiB live, 347.7MiB allocated
Rules
5 222×lower-fma.f32
5 220×lower-fma.f64
3 872×lower-*.f32
3 868×lower-*.f64
3 774×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030108
043106
120294
2126394
0839191
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 530
Calls
Call 1
Inputs
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 #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))) #s(literal 1 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal -1/8 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 x #s(literal 1 binary64))
Outputs
(*.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #s(literal -1/2 binary64)))
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(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fabs.f64 (+.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (log1p.f64 x))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

eval175.0ms (2.4%)

Memory
-7.7MiB live, 228.3MiB allocated
Compiler

Compiled 14 677 to 2 291 computations (84.4% saved)

prune23.0ms (0.3%)

Memory
5.9MiB live, 82.7MiB allocated
Pruning

13 alts after pruning (5 fresh and 8 done)

PrunedKeptTotal
New8534857
Fresh112
Picked145
Done044
Total85513868
Accuracy
100.0%
Counts
868 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶51.2%
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
▶66.6%
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
✓99.7%
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
✓40.0%
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶7.6%
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
▶4.5%
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
✓33.7%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓34.3%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
✓65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
✓67.0%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓66.8%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
Compiler

Compiled 134 to 115 computations (14.2% saved)

simplify125.0ms (1.7%)

Memory
6.0MiB live, 167.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 x (neg.f64 x))
cost-diff128
(*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
cost-diff768
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
cost-diff0
(/.f64 #s(literal -1 binary64) x)
cost-diff0
#s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64))
cost-diff960
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
cost-diff0
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
cost-diff0
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
cost-diff0
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
Rules
3 574×lower-*.f32
3 570×lower-*.f64
2 884×lower-fma.f32
2 882×lower-fma.f64
1 244×cube-prod
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027152
043148
185148
2175143
3679142
42336142
54371142
65521142
76300142
86860142
97708142
08015142
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
#s(literal 1 binary64)
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(literal -1 binary64)
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(literal -1 binary64)
#s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(*.f64 x (neg.f64 x))
x
(neg.f64 x)
(*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
(/.f64 x (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(literal 1 binary64)
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)
(/.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(+.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (neg.f64 x) #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)))
#s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(/.f64 x (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 x (neg.f64 x))
(*.f64 (neg.f64 x) x)
x
(neg.f64 x)
(*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) x)
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)

localize208.0ms (2.9%)

Memory
-9.0MiB live, 236.8MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.0234375
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy0.0546875
(*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy30.630930060253238
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
accuracy0
(/.f64 #s(literal -1 binary64) x)
accuracy0.26171875
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
accuracy21.228534018826792
#s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64))
accuracy0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy20.697010880558505
#s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
accuracy38.214244232242436
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
accuracy21.272250753418014
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy38.214244232242436
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
accuracy0.00390625
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy0.0234375
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
accuracy0.09765625
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)
accuracy0.21875
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
Samples
130.0ms101×1valid
35.0ms58×2valid
17.0ms96×0valid
3.0ms1×5exit
Compiler

Compiled 137 to 26 computations (81% saved)

Precisions
Click to see histograms. Total time spent on operations: 114.0ms
ival-div: 80.0ms (70% of total)
ival-add: 11.0ms (9.6% of total)
adjust: 10.0ms (8.7% of total)
ival-sqrt: 6.0ms (5.2% of total)
ival-mult: 5.0ms (4.4% of total)
ival-sub: 2.0ms (1.7% of total)
exact: 1.0ms (0.9% of total)
ival-neg: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory
-4.7MiB live, 33.6MiB allocated
Counts
17 → 204
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) #<representation:binary64>) () ())
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #<representation:binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))) (patch (+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #<representation:binary64>) () ())
#s(alt #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (patch #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation:binary64>) () ())
#s(alt (/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation:binary64>) () ())
#s(alt (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation:binary64>) () ())
#s(alt (*.f64 x (neg.f64 x)) (patch (*.f64 x (neg.f64 x)) #<representation:binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation:binary64>) () ())
Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 x)) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x) #<representation:binary64>) () ())) ())
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Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((/ 1 (/ (- (sqrt (+ 1 x)) -1) x)) (/ (- (sqrt (+ 1 x)) -1) x) (- (sqrt (+ 1 x)) -1) (sqrt (+ 1 x)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ (* x 1/2) 1) (/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x) (/ (* x (neg x)) (* (neg x) (+ (sqrt (+ 1 x)) 1))) (* (neg x) (+ (sqrt (+ 1 x)) 1)) (* x (neg x)) (neg x) (+ (sqrt (+ 1 x)) 1))
1.0ms
x
@inf
((/ 1 (/ (- (sqrt (+ 1 x)) -1) x)) (/ (- (sqrt (+ 1 x)) -1) x) (- (sqrt (+ 1 x)) -1) (sqrt (+ 1 x)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ (* x 1/2) 1) (/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x) (/ (* x (neg x)) (* (neg x) (+ (sqrt (+ 1 x)) 1))) (* (neg x) (+ (sqrt (+ 1 x)) 1)) (* x (neg x)) (neg x) (+ (sqrt (+ 1 x)) 1))
1.0ms
x
@0
((/ 1 (/ (- (sqrt (+ 1 x)) -1) x)) (/ (- (sqrt (+ 1 x)) -1) x) (- (sqrt (+ 1 x)) -1) (sqrt (+ 1 x)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ -1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ (* x 1/2) 1) (/ (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x)) (/ -1 (+ (sqrt (+ x 1)) 1)) (/ -1 x) (/ (* x (neg x)) (* (neg x) (+ (sqrt (+ 1 x)) 1))) (* (neg x) (+ (sqrt (+ 1 x)) 1)) (* x (neg x)) (neg x) (+ (sqrt (+ 1 x)) 1))

simplify246.0ms (3.4%)

Memory
20.0MiB live, 295.7MiB allocated
Algorithm
1×egg-herbie
Rules
21 782×lower-fma.f64
21 782×lower-fma.f32
4 254×lower-+.f64
4 254×lower-+.f32
3 870×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02692604
18052214
227292108
081561927
Stop Event
1×iter limit
1×node limit
Counts
204 → 204
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(/ 2 x)
(/ (+ 2 (* 1/2 x)) x)
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
-1/2
(- (* 1/8 x) 1/2)
(- (* x (+ 1/8 (* -1/16 x))) 1/2)
(- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(* -2 x)
(* x (- (* -1/2 x) 2))
(* x (- (* x (- (* 1/8 x) 1/2)) 2))
(* x (- (* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (/ 1 x))
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))
(+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(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))))))))
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
(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))))))))
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))
(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))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1 (sqrt (/ 1 x)))
(/ (+ 1 (* -1 (sqrt x))) x)
(/ (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))) (pow x 2))))) x)
(/ (- (+ 1 (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (* (sqrt x) (+ (sqrt (pow x 3)) (* -1/2 (sqrt (pow x 3)))))) (* 1/2 (pow x 2))) (pow x 3))))) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 x))))) x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1 (sqrt (pow x 3)))
(* (pow x 2) (- (* -1 (sqrt (/ 1 x))) (/ 1 x)))
(* (pow x 2) (- (+ (* -1 (sqrt (/ 1 x))) (* -1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))
(* (pow x 2) (- (+ (* -1 (sqrt (/ 1 x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 (pow x 5)))))) (/ 1 x)))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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)))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(sqrt (/ 1 x))
(* -1 (/ (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) x))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/2 x)) x)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 x) 1/2)
(fma.f64 #s(literal 1/8 binary64) x #s(literal -1/2 binary64))
(- (* x (+ 1/8 (* -1/16 x))) 1/2)
(fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64))
(- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/128 binary64) x #s(literal -1/16 binary64)) x #s(literal 1/8 binary64)) x #s(literal -1/2 binary64))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* x (- (* -1/2 x) 2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -2 binary64)) x)
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(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (fma.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (*.f64 x x)) x #s(literal -1 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(*.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x (fma.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (*.f64 x x)) x #s(literal -1 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(*.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x)) (neg.f64 x)) (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* -1 (/ (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) x))
(/.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) x))
(/.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x) (sqrt.f64 x)) x)
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) x))
(/.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x)) x) (sqrt.f64 x)) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x)) (neg.f64 x)) (sqrt.f64 x))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) #s(literal -1 binary64)) x)
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (*.f64 (-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) x)) x)

rewrite482.0ms (6.6%)

Memory
6.0MiB live, 208.9MiB allocated
Rules
3 596×lower-fma.f32
3 594×lower-fma.f64
3 464×lower-/.f32
3 454×lower-/.f64
3 216×lower-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
027128
043124
1210119
21320118
08827118
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
17 → 699
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) x)
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 x (neg.f64 x))
(neg.f64 x)
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
Outputs
(*.f64 (/.f64 (*.f64 (neg.f64 x) x) (expm1.f64 (log1p.f64 x))) (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 (neg.f64 x) x) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 (neg.f64 x) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 x (expm1.f64 (log1p.f64 x))) (/.f64 #s(literal 1 binary64) (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 x (expm1.f64 (log1p.f64 x))) (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))))
(*.f64 (/.f64 x (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))))
(*.f64 (/.f64 x (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (neg.f64 x) (expm1.f64 (log1p.f64 x))) (/.f64 #s(literal -1 binary64) (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (neg.f64 x) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (expm1.f64 (log1p.f64 x)) #s(literal -1 binary64)) (/.f64 x (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 x (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 (log1p.f64 x))) (/.f64 (neg.f64 x) (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))) (/.f64 (neg.f64 x) (pow.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x x) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 x (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) x)
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x x)) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x x)) (*.f64 (neg.f64 x) x))
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eval326.0ms (4.5%)

Memory
-15.7MiB live, 175.6MiB allocated
Compiler

Compiled 17 954 to 2 505 computations (86% saved)

prune67.0ms (0.9%)

Memory
22.3MiB live, 60.4MiB allocated
Pruning

14 alts after pruning (2 fresh and 12 done)

PrunedKeptTotal
New9962998
Fresh000
Picked145
Done088
Total997141 011
Accuracy
100.0%
Counts
1 011 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.3%
(/.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x x))
✓66.6%
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
✓99.7%
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
✓40.0%
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓7.6%
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
4.9%
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
✓4.5%
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
✓33.7%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓34.3%
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
✓65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
✓67.0%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓65.5%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓66.8%
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
Compiler

Compiled 289 to 163 computations (43.6% saved)

regimes31.0ms (0.4%)

Memory
-29.9MiB live, 19.1MiB allocated
Counts
24 → 1
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) x))
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Calls

2 calls:

22.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
7.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes11.0ms (0.1%)

Memory
15.9MiB live, 15.9MiB allocated
Counts
15 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (/ -1 (+ (sqrt (+ x 1)) 1)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Calls

2 calls:

5.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
5.0ms
x
Results
AccuracySegmentsBranch
99.6%2x
99.6%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes67.0ms (0.9%)

Memory
-23.4MiB live, 13.1MiB allocated
Counts
11 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Calls

2 calls:

62.0ms
x
4.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
99.5%2x
99.5%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes8.0ms (0.1%)

Memory
12.1MiB live, 12.1MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
Calls

2 calls:

4.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms
x
Results
AccuracySegmentsBranch
98.3%2x
98.3%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes7.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB allocated
Counts
9 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
Calls

2 calls:

3.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms
x
Results
AccuracySegmentsBranch
98.3%2x
98.3%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory
9.1MiB live, 9.1MiB allocated
Counts
7 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
Calls

2 calls:

3.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms
x
Results
AccuracySegmentsBranch
97.4%2x
97.4%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes66.0ms (0.9%)

Memory
-30.2MiB live, 7.2MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ (pow (+ (sqrt (+ 1 x)) 1) -1) (pow x -1)) (sqrt.f64 x))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
Calls

2 calls:

62.0ms
x
3.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
96.6%2x
96.6%2(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
Calls

2 calls:

2.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
2.0ms
x
Results
AccuracySegmentsBranch
66.8%1x
66.8%1(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory
6.7MiB live, 6.7MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
Outputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
Calls

2 calls:

1.0ms
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
1.0ms
x
Results
AccuracySegmentsBranch
4.5%1x
4.5%1(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.2985711082010155e-8
0.009363156606290477
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.2985711082010155e-8
0.009363156606290477
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.009363156606290477
10.992660359392636
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.009363156606290477
10.992660359392636
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.009363156606290477
10.992660359392636
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.009363156606290477
10.992660359392636
Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify103.0ms (1.4%)

Memory
-23.6MiB live, 63.8MiB allocated
Algorithm
1×egg-herbie
Rules
12×+-commutative-binary64-+.f64
10×*-commutative-binary64-*.f64
4×sub-neg-binary64-neg.f64-+.f64--.f64
2×*-rgt-identity-binary64-*.f64
2×1-exp-binary32-exp.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044248
157248
260248
365248
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64))

soundness1.2s (16.9%)

Memory
28.2MiB live, 740.9MiB allocated
Rules
21 890×lower-fma.f64
21 890×lower-fma.f32
18 662×lower-fma.f64
18 662×lower-fma.f32
4 566×lower-*.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02251817
16891529
223201423
082601314
0161600
1485505
21630483
35408474
08354430
027124
044124
1188119
21191119
08448119
0621
01021
14621
231520
3340020
0827820
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 347 to 169 computations (51.3% saved)

preprocess464.0ms (6.4%)

Memory
-13.7MiB live, 145.6MiB allocated
Compiler

Compiled 328 to 90 computations (72.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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