Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G

Time bar (total: 4.9s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 7 to 7 computations (0% saved)

sample1.4s (28.6%)

Memory
-14.2MiB live, 746.5MiB allocated
Samples
1.1s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 152.0ms
ival-div: 94.0ms (61.9% of total)
ival-sub: 42.0ms (27.7% of total)
exact: 7.0ms (4.6% of total)
ival-true: 6.0ms (4% of total)
ival-assert: 3.0ms (2% of total)
Bogosity

explain167.0ms (3.4%)

Memory
14.4MiB live, 92.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-#s(literal 1 binary64)
00-0-#s(literal 3 binary64)
00-0-(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
00-0-(/.f64 #s(literal 1 binary64) #s(literal 3 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
138.0ms512×0valid
Compiler

Compiled 32 to 19 computations (40.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-div: 4.0ms (54% of total)
ival-sub: 2.0ms (27% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess137.0ms (2.8%)

Memory
-11.2MiB live, 30.4MiB allocated
Algorithm
egg-herbie
Rules
16×distribute-lft-neg-in
14×sub-neg
12×cancel-sign-sub-inv
10×associate--r+
10×distribute-neg-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1189
2396
3636
4966
51046
61066
053
083
1133
2143
0143
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Outputs
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(-.f64 x #s(literal 1/3 binary64))
Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory
7.3MiB live, 7.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
cost-diff704
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
Rules
lower-+.f64
lower-+.f32
lift-/.f64
1-exp
lift--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
087
1137
2147
0147
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
x
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 3 binary64)
Outputs
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(-.f64 x #s(literal 1/3 binary64))
x
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(literal 3 binary64)

localize12.0ms (0.3%)

Memory
26.9MiB live, 26.9MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
accuracy0.015625
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Samples
8.0ms256×0valid
Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-div: 2.0ms (53.5% of total)
ival-sub: 1.0ms (26.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
-35.1MiB live, 4.1MiB allocated
Counts
2 → 12
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())
Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
5.0ms
x
@0
((/ 1 3) (- x (/ 1 3)))
1.0ms
x
@inf
((/ 1 3) (- x (/ 1 3)))
0.0ms
x
@-inf
((/ 1 3) (- x (/ 1 3)))

simplify15.0ms (0.3%)

Memory
18.8MiB live, 18.8MiB allocated
Algorithm
egg-herbie
Rules
192×lower-fma.f64
192×lower-fma.f32
144×lower-*.f64
144×lower-*.f32
96×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01330
13230
27530
315830
441230
552330
657630
759930
860130
060130
Stop Event
iter limit
saturated
Counts
12 → 10
Calls
Call 1
Inputs
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
Outputs
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))

rewrite264.0ms (5.4%)

Memory
14.4MiB live, 160.7MiB allocated
Rules
6 912×lower-fma.f64
6 912×lower-fma.f32
4 474×lower-*.f64
4 474×lower-*.f32
3 944×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054
084
1274
21294
39794
085574
Stop Event
iter limit
node limit
iter limit
Counts
2 → 313
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Outputs
#s(literal 1/3 binary64)
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (+.f64 #s(literal 1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 binary64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1/3 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 #s(literal -1/3 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1/3 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 binary64)))))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))))))
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(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #s(literal 1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/81 binary64) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) (/.f64 #s(literal 1/729 binary64) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 #s(literal 1/729 binary64) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64))))) (/.f64 #s(literal 1/19683 binary64) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x)) (-.f64 #s(literal 1/3 binary64) x))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (-.f64 #s(literal 1/3 binary64) x))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal -1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (-.f64 x #s(literal -1/3 binary64))) (/.f64 (/.f64 #s(literal 1/729 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (-.f64 x #s(literal -1/3 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 (/.f64 #s(literal 1/729 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 (/.f64 #s(literal 1/19683 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 (*.f64 x x) (-.f64 #s(literal -1/3 binary64) x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) x))
(-.f64 x #s(literal 1/3 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64)))
(+.f64 (*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64))) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) (*.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal -1/9 binary64)) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))))
(+.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (*.f64 (*.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))))
(+.f64 (*.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal -1/3 binary64))
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64)))) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (*.f64 x x)))
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (*.f64 x x)) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (-.f64 #s(literal 1/9 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(+.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (*.f64 x x)) (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 #s(literal -1/3 binary64) x #s(literal -1/9 binary64))))
(+.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))) (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(+.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #s(literal -1/9 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (*.f64 x x)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (*.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #s(literal -1/9 binary64)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1/27 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1/27 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal -1/3 binary64))
(+.f64 (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 #s(literal -1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal -1/3 binary64) (*.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal -1/3 binary64) x)
(+.f64 x #s(literal -1/3 binary64))

eval38.0ms (0.8%)

Memory
16.3MiB live, 52.9MiB allocated
Compiler

Compiled 10 409 to 757 computations (92.7% saved)

prune304.0ms (6.2%)

Memory
-213.4MiB live, 120.6MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3194323
Fresh000
Picked101
Done000
Total3204324
Accuracy
100.0%
Counts
324 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.5%
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
100.0%
(-.f64 x #s(literal 1/3 binary64))
77.0%
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
49.9%
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify87.0ms (1.8%)

Memory
-0.2MiB live, 77.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
cost-diff0
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
cost-diff0
(-.f64 x #s(literal 1/3 binary64))
cost-diff0
(-.f64 #s(literal -1/3 binary64) x)
cost-diff0
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))
cost-diff0
(fma.f64 x x #s(literal -1/9 binary64))
cost-diff320
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
cost-diff0
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Rules
1 128×lower-fma.f32
1 122×lower-fma.f64
632×lower-*.f32
628×lower-*.f64
362×distribute-rgt-in
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02272
03372
14970
26969
310269
412669
516968
632668
779768
8152168
9169468
10175668
11186568
12215068
13235668
14246668
15269668
16271668
17271668
0271668
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(fma.f64 x x #s(literal -1/9 binary64))
x
#s(literal -1/9 binary64)
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))
#s(literal -1 binary64)
(-.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(-.f64 x #s(literal 1/3 binary64))
x
#s(literal 1/3 binary64)
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(*.f64 x x)
x
#s(literal -1/27 binary64)
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(-.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
Outputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64)))
(fma.f64 x x #s(literal -1/9 binary64))
x
#s(literal -1/9 binary64)
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))
#s(literal -1 binary64)
(-.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
(-.f64 x #s(literal 1/3 binary64))
x
#s(literal 1/3 binary64)
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(*.f64 x x)
x
#s(literal -1/27 binary64)
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
(-.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)

localize75.0ms (1.5%)

Memory
0.4MiB live, 120.8MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(-.f64 x #s(literal -1/3 binary64))
accuracy0.0234375
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy0.04296875
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
accuracy20.3105395498375
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy0.015625
(-.f64 x #s(literal 1/3 binary64))
accuracy0.00390625
(fma.f64 x x #s(literal -1/9 binary64))
accuracy0.00390625
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))
accuracy0.00390625
(-.f64 #s(literal -1/3 binary64) x)
accuracy14.698514384628556
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
accuracy32.04278354006126
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Samples
63.0ms256×0valid
Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
const: 14.0ms (30% of total)
ival-sub: 12.0ms (25.7% of total)
ival-mult: 10.0ms (21.4% of total)
ival-div: 7.0ms (15% of total)
ival-add: 3.0ms (6.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory
-20.9MiB live, 17.8MiB allocated
Counts
11 → 132
Calls
Call 1
Inputs
#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())
Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1/9 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* 27 x) 9))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/27 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@inf
((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
2.0ms
x
@-inf
((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
2.0ms
x
@0
((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3))

simplify152.0ms (3.1%)

Memory
-5.7MiB live, 151.0MiB allocated
Algorithm
egg-herbie
Rules
8 024×lower-fma.f64
8 024×lower-fma.f32
3 062×lower-*.f64
3 062×lower-*.f32
1 470×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
091515
1257507
2639490
31857486
44563486
08216464
Stop Event
iter limit
node limit
Counts
132 → 122
Calls
Call 1
Inputs
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/9
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
3
(+ 3 (* -9 x))
(+ 3 (* x (- (* 27 x) 9)))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
-1/3
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
(- (* -1 x) 1/3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/27
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/9
(+ 1/9 (* 1/3 x))
(+ 1/9 (* x (+ 1/3 x)))
(+ 1/9 (* x (+ 1/3 x)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 3)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
Outputs
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/9
#s(literal -1/9 binary64)
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* x (- (* 27 x) 9)))
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
(- (* -1 x) 1/3)
(-.f64 #s(literal -1/3 binary64) x)
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/27
#s(literal -1/27 binary64)
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* 1/3 x))
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
(+ 1/3 x)
(-.f64 x #s(literal -1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -1/3 binary64)) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
(* -1 (* x (+ 1 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal -1/3 binary64) x)
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -1/3 binary64)) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))
(* x (+ 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal -1/3 binary64))

rewrite237.0ms (4.8%)

Memory
8.9MiB live, 456.3MiB allocated
Rules
5 516×lower-fma.f32
5 510×lower-fma.f64
4 694×lower-*.f32
4 690×lower-*.f64
3 668×lower-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02261
03364
113161
289843
0914243
Stop Event
iter limit
node limit
iter limit
Counts
11 → 1 404
Calls
Call 1
Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(fma.f64 x x #s(literal -1/9 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 #s(literal -1/3 binary64) x)
(-.f64 x #s(literal 1/3 binary64))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(*.f64 x x)
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(-.f64 x #s(literal -1/3 binary64))
Outputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal -1/3 binary64) x) x #s(literal -1/9 binary64))) (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal -1/3 binary64) x) x #s(literal -1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -1/19683 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (-.f64 #s(literal 1/729 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/27 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x)) (-.f64 x #s(literal -1/3 binary64))) x #s(literal 1/729 binary64)))) (fma.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 #s(literal 1/9 binary64) x) (-.f64 x #s(literal -1/3 binary64))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal -1/3 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 x x) #s(literal -1/9 binary64))))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))))
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(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 x x) #s(literal -1/9 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))))
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(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))))
(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1/3 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1/3 binary64))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64))))
(-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))))
(-.f64 (/.f64 #s(literal -1/27 binary64) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1 binary64)))
(-.f64 #s(literal 1/3 binary64) (neg.f64 x))
(-.f64 x #s(literal -1/3 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(+.f64 (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))))
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64))
(+.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1/3 binary64))
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 x x #s(literal 1/9 binary64))) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 #s(literal 1/3 binary64) x)))
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x)))
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x)) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))))
(+.f64 #s(literal 0 binary64) (-.f64 x #s(literal -1/3 binary64)))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal 1/3 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 #s(literal 1/3 binary64) (neg.f64 (*.f64 x #s(literal -1 binary64))))
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 x #s(literal 1/3 binary64))

eval257.0ms (5.3%)

Memory
30.4MiB live, 328.8MiB allocated
Compiler

Compiled 42 231 to 2 333 computations (94.5% saved)

prune138.0ms (2.8%)

Memory
-34.3MiB live, 261.0MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1 52421 526
Fresh000
Picked134
Done000
Total1 52551 530
Accuracy
100.0%
Counts
1 530 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.5%
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
50.3%
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
100.0%
(-.f64 x #s(literal 1/3 binary64))
49.2%
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
49.9%
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify11.0ms (0.2%)

Memory
18.5MiB live, 18.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 x #s(literal -1/3 binary64))
cost-diff0
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
cost-diff0
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
cost-diff0
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
cost-diff0
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
cost-diff0
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
cost-diff0
(fma.f64 x x #s(literal -1/9 binary64))
cost-diff0
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
Rules
132×lower-+.f64
132×lower-+.f32
98×lower-fma.f32
92×lower-fma.f64
50×lower-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02175
02975
14271
26071
37971
49471
510271
611871
716071
821571
922971
1023271
1123571
023571
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(fma.f64 x x #s(literal -1/9 binary64))
x
#s(literal -1/9 binary64)
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
#s(literal -9 binary64)
#s(literal 3 binary64)
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
#s(literal -1/27 binary64)
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
x
(-.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)
Outputs
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (fma.f64 x x #s(literal -1/9 binary64)))
(fma.f64 x x #s(literal -1/9 binary64))
x
#s(literal -1/9 binary64)
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
#s(literal -9 binary64)
#s(literal 3 binary64)
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
#s(literal -1/27 binary64)
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))
x
(-.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
#s(literal 1/9 binary64)

localize156.0ms (3.2%)

Memory
15.9MiB live, 88.3MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(-.f64 x #s(literal -1/3 binary64))
accuracy0.0234375
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
accuracy20.3105395498375
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
accuracy31.82102830291946
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
accuracy0
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
accuracy0.00390625
(fma.f64 x x #s(literal -1/9 binary64))
accuracy14.698514384628556
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
accuracy32.12210910256336
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
Samples
143.0ms248×0valid
1.0ms1valid
1.0ms2valid
Compiler

Compiled 68 to 23 computations (66.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
const: 13.0ms (36.9% of total)
ival-mult: 8.0ms (22.7% of total)
ival-div: 7.0ms (19.9% of total)
ival-add: 5.0ms (14.2% of total)
ival-sub: 2.0ms (5.7% 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)

series23.0ms (0.5%)

Memory
-23.0MiB live, 18.2MiB allocated
Counts
8 → 96
Calls
Call 1
Inputs
#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())
Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1/9 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* 27 x) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
18.0ms
x
@inf
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
1.0ms
x
@-inf
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
1.0ms
x
@0
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))

simplify171.0ms (3.5%)

Memory
2.3MiB live, 200.0MiB allocated
Algorithm
egg-herbie
Rules
7 720×lower-fma.f64
7 720×lower-fma.f32
3 206×lower-*.f64
3 206×lower-*.f32
1 476×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
094430
1270422
2659414
31994410
44709410
08237379
Stop Event
iter limit
node limit
Counts
96 → 90
Calls
Call 1
Inputs
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/9
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
3
(+ 3 (* -9 x))
(+ 3 (* x (- (* 27 x) 9)))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
3
(+ 3 (* -9 x))
(+ 3 (* -9 x))
(+ 3 (* -9 x))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/27
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
1/9
(+ 1/9 (* 1/3 x))
(+ 1/9 (* x (+ 1/3 x)))
(+ 1/9 (* x (+ 1/3 x)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(* -9 x)
(* x (- (* 3 (/ 1 x)) 9))
(* x (- (* 3 (/ 1 x)) 9))
(* x (- (* 3 (/ 1 x)) 9))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 3)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(* -9 x)
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
Outputs
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/9
#s(literal -1/9 binary64)
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* x (- (* 27 x) 9)))
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/27
#s(literal -1/27 binary64)
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* 1/3 x))
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -9 x)
(*.f64 #s(literal -9 binary64) x)
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -9 x)
(*.f64 #s(literal -9 binary64) x)
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)

rewrite214.0ms (4.4%)

Memory
15.5MiB live, 170.4MiB allocated
Rules
6 318×lower-fma.f32
6 312×lower-fma.f64
4 722×lower-*.f32
4 720×lower-*.f64
3 878×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02167
02963
113163
286763
0851563
Stop Event
iter limit
node limit
iter limit
Counts
8 → 498
Calls
Call 1
Inputs
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(fma.f64 x x #s(literal -1/9 binary64))
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))
(-.f64 x #s(literal -1/3 binary64))
Outputs
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 (*.f64 x x) #s(literal -1/9 binary64) #s(literal 1/81 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64))) (fma.f64 x x #s(literal -1/9 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)) (-.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 #s(literal 1/9 binary64) (*.f64 x x))))) (-.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 #s(literal 1/9 binary64) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x)) x (*.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) x (*.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (-.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (*.f64 (*.f64 (*.f64 x x) x) x)))))
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))))
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(fma.f64 #s(literal 1 binary64) x #s(literal 1/3 binary64))
(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1/3 binary64))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1/9 binary64)))) (-.f64 x #s(literal 1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))
(-.f64 (/.f64 #s(literal -1/27 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)) (/.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x))
(-.f64 #s(literal 1/3 binary64) (neg.f64 x))
(-.f64 x #s(literal -1/3 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(+.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1/3 binary64))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))))
(+.f64 #s(literal 0 binary64) (-.f64 x #s(literal -1/3 binary64)))
(+.f64 #s(literal 1/3 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 #s(literal 1/3 binary64) x)
(+.f64 x #s(literal 1/3 binary64))

eval145.0ms (3%)

Memory
6.2MiB live, 167.8MiB allocated
Compiler

Compiled 15 692 to 1 732 computations (89% saved)

prune75.0ms (1.5%)

Memory
6.2MiB live, 204.6MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New5862588
Fresh000
Picked202
Done033
Total5885593
Accuracy
100.0%
Counts
593 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.5%
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
49.8%
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
100.0%
(-.f64 x #s(literal 1/3 binary64))
99.7%
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
49.9%
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Compiler

Compiled 39 to 26 computations (33.3% saved)

simplify11.0ms (0.2%)

Memory
-13.8MiB live, 24.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (- x -1/3) #s(literal 1/3 binary64))
cost-diff0
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
cost-diff0
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
cost-diff0
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
cost-diff0
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
cost-diff0
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
cost-diff0
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
cost-diff0
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
Rules
80×lower-+.f64
80×lower-+.f32
44×lower-fma.f32
40×lower-fma.f64
30×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02487
03087
14283
24883
35283
45983
56783
68383
711483
813483
914483
1014783
1115083
015081
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
#s(literal -9 binary64)
x
#s(literal 3 binary64)
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
#s(literal -1/27 binary64)
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
x
#s(approx (- x -1/3) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(literal 1/9 binary64)
Outputs
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)))
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
#s(literal -9 binary64)
x
#s(literal 3 binary64)
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
#s(literal -1/27 binary64)
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))
x
#s(approx (- x -1/3) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(literal 1/9 binary64)

localize93.0ms (1.9%)

Memory
10.0MiB live, 91.2MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0234375
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
accuracy20.3105395498375
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
accuracy31.82102830291946
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
accuracy32.03160924390678
#s(approx (- x -1/3) #s(literal 1/3 binary64))
accuracy0
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
accuracy14.698514384628556
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
accuracy32.12210910256336
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
accuracy32.348081041745836
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
Samples
78.0ms248×0valid
1.0ms1valid
1.0ms2valid
Compiler

Compiled 68 to 24 computations (64.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 71.0ms
ival-mult: 43.0ms (60.8% of total)
const: 14.0ms (19.8% of total)
ival-div: 5.0ms (7.1% of total)
ival-add: 5.0ms (7.1% of total)
ival-sub: 2.0ms (2.8% 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)

series9.0ms (0.2%)

Memory
-26.2MiB live, 11.5MiB allocated
Counts
8 → 96
Calls
Call 1
Inputs
#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())
Outputs
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1/9 (taylor 0 x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* 27 x) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
1.0ms
x
@inf
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))
1.0ms
x
@0
((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3))

simplify163.0ms (3.3%)

Memory
14.1MiB live, 128.9MiB allocated
Algorithm
egg-herbie
Rules
7 720×lower-fma.f64
7 720×lower-fma.f32
3 206×lower-*.f64
3 206×lower-*.f32
1 476×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
094430
1270422
2659414
31994410
44709410
08237379
Stop Event
iter limit
node limit
Counts
96 → 90
Calls
Call 1
Inputs
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/9
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
(- (pow x 2) 1/9)
3
(+ 3 (* -9 x))
(+ 3 (* x (- (* 27 x) 9)))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
3
(+ 3 (* -9 x))
(+ 3 (* -9 x))
(+ 3 (* -9 x))
-1/3
(- x 1/3)
(- x 1/3)
(- x 1/3)
-1/27
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
(- (pow x 3) 1/27)
1/9
(+ 1/9 (* 1/3 x))
(+ 1/9 (* x (+ 1/3 x)))
(+ 1/9 (* x (+ 1/3 x)))
1/3
(+ 1/3 x)
(+ 1/3 x)
(+ 1/3 x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(* -9 x)
(* x (- (* 3 (/ 1 x)) 9))
(* x (- (* 3 (/ 1 x)) 9))
(* x (- (* 3 (/ 1 x)) 9))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(* x (- 1 (* 1/3 (/ 1 x))))
(pow x 3)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 2)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(/ 1 x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(* -9 x)
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
(* x (+ 1 (* 1/3 (/ 1 x))))
Outputs
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/9
#s(literal -1/9 binary64)
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
(- (pow x 2) 1/9)
(fma.f64 x x #s(literal -1/9 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* x (- (* 27 x) 9)))
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64))
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(+ 3 (* -9 x))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
-1/3
#s(literal -1/3 binary64)
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
(- x 1/3)
(-.f64 x #s(literal 1/3 binary64))
-1/27
#s(literal -1/27 binary64)
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(- (pow x 3) 1/27)
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* 1/3 x))
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(+ 1/9 (* x (+ 1/3 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
(+ 1/3 x)
(+.f64 #s(literal 1/3 binary64) x)
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x)
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -9 x)
(*.f64 #s(literal -9 binary64) x)
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* x (- (* 3 (/ 1 x)) 9))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
x
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(* x (- 1 (* 1/3 (/ 1 x))))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3)))))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/9 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x))
(* -9 x)
(*.f64 #s(literal -9 binary64) x)
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(* -1 (* x (- 9 (* 3 (/ 1 x)))))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
x
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/3 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/3 binary64))
(pow x 3)
(*.f64 (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1)))
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x))))
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x)
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x)))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))
x
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)
(* x (+ 1 (* 1/3 (/ 1 x))))
(+.f64 #s(literal 1/3 binary64) x)

rewrite230.0ms (4.7%)

Memory
19.8MiB live, 211.2MiB allocated
Rules
5 924×lower-fma.f32
5 920×lower-fma.f64
4 190×lower-*.f32
4 188×lower-*.f64
3 446×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02479
03075
113175
283275
3746975
0839173
Stop Event
iter limit
node limit
iter limit
Counts
8 → 218
Calls
Call 1
Inputs
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64))
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
#s(approx (- x -1/3) #s(literal 1/3 binary64))
Outputs
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)))
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) (fma.f64 #s(literal -27 binary64) x #s(literal 9 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (*.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)) (-.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (*.f64 x #s(literal 27 binary64))))) (-.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (*.f64 x #s(literal 27 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))) (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (-.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (*.f64 #s(literal 81 binary64) (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 9 binary64) (*.f64 #s(literal 81 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (*.f64 #s(literal -9 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)))
(*.f64 (neg.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) x #s(literal 3 binary64))))
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(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))) (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x) #s(literal 1/387420489 binary64)) (*.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))) (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (-.f64 #s(literal 1/531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal 1/729 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (*.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(/.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))
(/.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)) (neg.f64 (fma.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))
(/.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64)) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x #s(literal 1/729 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x #s(literal 1/729 binary64)) (neg.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x #s(literal 1/729 binary64)) (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))
(/.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(/.f64 (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))
(neg.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)))
(fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/729 binary64))) (fma.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64)) (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal 1/9 binary64) #s(literal 1/81 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal -1/81 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) (/.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x) (/.f64 x (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (/.f64 (*.f64 x x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (/.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) (/.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 x (/.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))
(-.f64 (/.f64 #s(literal 1/81 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x))) (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))) #s(literal 1/9 binary64))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))))
(+.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal 1/9 binary64))
(+.f64 #s(literal 1/9 binary64) (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))))
(+.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x))
#s(approx (- x -1/3) #s(literal 1/3 binary64))

eval41.0ms (0.8%)

Memory
9.1MiB live, 95.1MiB allocated
Compiler

Compiled 7 112 to 719 computations (89.9% saved)

prune40.0ms (0.8%)

Memory
7.7MiB live, 119.8MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New3080308
Fresh000
Picked022
Done033
Total3085313
Accuracy
100.0%
Counts
313 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.5%
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
49.8%
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
100.0%
(-.f64 x #s(literal 1/3 binary64))
99.7%
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
49.9%
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Compiler

Compiled 108 to 54 computations (50% saved)

regimes11.0ms (0.2%)

Memory
-24.2MiB live, 20.4MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
(-.f64 x #s(literal 1/3 binary64))
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))
Outputs
(-.f64 x #s(literal 1/3 binary64))
Calls

2 calls:

7.0ms
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory
8.3MiB live, 8.3MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Outputs
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Results
AccuracySegmentsBranch
49.9%1x
49.9%1(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0.1%)

Memory
13.6MiB live, 13.6MiB allocated
Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
1-exp_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
098
1148
2188
3208
4218
Stop Event
saturated
Calls
Call 1
Inputs
(-.f64 x #s(literal 1/3 binary64))
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))
Outputs
(-.f64 x #s(literal 1/3 binary64))
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64))

soundness161.0ms (3.3%)

Memory
-26.7MiB live, 128.1MiB allocated
Rules
6 912×lower-fma.f64
6 912×lower-fma.f32
4 474×lower-*.f64
4 474×lower-*.f32
3 944×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01330
13230
27530
315830
441230
552330
657630
759930
860130
060130
054
084
1274
21294
39794
085574
Stop Event
done
iter limit
node limit
iter limit
iter limit
saturated
Compiler

Compiled 17 to 13 computations (23.5% saved)

preprocess21.0ms (0.4%)

Memory
15.9MiB live, 55.1MiB allocated
Compiler

Compiled 24 to 18 computations (25% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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