x / (x^2 + 1)

Time bar (total: 6.2s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample698.0ms (11.2%)

Memory
36.7MiB live, 645.1MiB allocated
Samples
324.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 191.0ms
ival-mult: 64.0ms (33.6% of total)
ival-div: 59.0ms (31% of total)
ival-add: 55.0ms (28.9% of total)
ival-true: 5.0ms (2.6% of total)
exact: 4.0ms (2.1% of total)
ival-assert: 3.0ms (1.6% of total)
Bogosity

explain108.0ms (1.7%)

Memory
0.7MiB live, 91.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
700-0-(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
00-0-#s(literal 1 binary64)
00-0-(+.f64 (*.f64 x x) #s(literal 1 binary64))
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
/.f64(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))n/o700
(*.f64 x x)overflow70
(+.f64 (*.f64 x x) #s(literal 1 binary64))overflow70
Confusion
Predicted +Predicted -
+700
-0186
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+7000
-00186
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0186
170
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
71.0ms512×0valid
Compiler

Compiled 46 to 19 computations (58.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 4.0ms (38.4% of total)
ival-div: 3.0ms (28.8% of total)
ival-add: 2.0ms (19.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess21.0ms (0.3%)

Memory
-14.4MiB live, 23.3MiB allocated
Algorithm
egg-herbie
Rules
46×associate-*l*
42×times-frac
30×unsub-neg
28×distribute-lft-neg-in
26×distribute-neg-frac2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
12615
26214
312814
423214
533114
634414
734614
835014
057
087
1117
0116
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
Symmetry

(negabs x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.4%
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff128
(+.f64 (*.f64 x x) #s(literal 1 binary64))
Rules
lower-+.f32
lift-+.f64
lift-/.f64
lower-fma.f64
lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0517
0817
11117
01115
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

localize18.0ms (0.3%)

Memory
-9.8MiB live, 27.8MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy0
(*.f64 x x)
accuracy16.35784292098552
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Samples
12.0ms256×0valid
Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 2.0ms (40.7% of total)
ival-mult: 2.0ms (40.7% of total)
ival-add: 1.0ms (20.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
4.5MiB live, 4.6MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 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 (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

9 calls:

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

simplify253.0ms (4.1%)

Memory
27.7MiB live, 261.7MiB allocated
Algorithm
egg-herbie
Rules
12 662×lower-fma.f64
12 662×lower-fma.f32
2 988×lower-*.f64
2 988×lower-*.f32
1 640×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045226
1131224
2312216
3888212
42381210
55550210
67627210
08047197
Stop Event
iter limit
node limit
Counts
36 → 35
Calls
Call 1
Inputs
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1 (pow x 2))))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))))) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite341.0ms (5.5%)

Memory
-13.5MiB live, 433.3MiB allocated
Rules
4 942×lower-/.f32
4 940×lower-/.f64
4 762×lower-fma.f64
4 762×lower-fma.f32
3 572×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0515
0815
13315
220215
3176615
0856213
Stop Event
iter limit
node limit
iter limit
Counts
3 → 327
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 x x)
Outputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)))
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(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(*.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))))
(*.f64 (*.f64 x (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))))
(*.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x))))
(*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (neg.f64 x)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 x (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))

eval264.0ms (4.2%)

Memory
-7.4MiB live, 68.6MiB allocated
Compiler

Compiled 12 336 to 1 050 computations (91.5% saved)

prune55.0ms (0.9%)

Memory
-3.4MiB live, 115.1MiB allocated
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3566362
Fresh000
Picked101
Done000
Total3576363
Accuracy
100.0%
Counts
363 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.4%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
47.4%
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
74.4%
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
47.3%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
46.4%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
55.4%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 96 to 50 computations (47.9% saved)

simplify601.0ms (9.6%)

Memory
8.6MiB live, 510.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
cost-diff0
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) (neg.f64 x) x)
cost-diff0
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
cost-diff0
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
cost-diff0
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
cost-diff0
(fma.f64 x x #s(literal 1 binary64))
cost-diff0
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
Rules
29 084×lower-fma.f32
29 076×lower-fma.f64
3 328×lower-*.f32
3 324×lower-*.f64
2 354×lower--.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
020114
032114
157107
2127107
3274105
4671105
51701105
63677105
75738105
87647105
08113105
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
x
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(*.f64 x x)
x
(neg.f64 x)
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(*.f64 x x)
x
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
Outputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
x
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (*.f64 x (*.f64 x x))))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(-.f64 x (*.f64 x (*.f64 x x)))
(*.f64 x x)
x
(neg.f64 x)
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(*.f64 x x)
x
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)

localize254.0ms (4.1%)

Memory
9.5MiB live, 118.1MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0.03515625
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
accuracy0.046875
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
accuracy33.75825627323028
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
accuracy0
(*.f64 x x)
accuracy0
(neg.f64 x)
accuracy0.03125
(fma.f64 (*.f64 x x) (neg.f64 x) x)
accuracy34.293742822799786
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
accuracy16.35784292098552
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy33.472205925571735
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy0
(/.f64 #s(literal 1 binary64) x)
accuracy28.561925913073072
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy0
(fma.f64 x x #s(literal 1 binary64))
accuracy16.35784292098552
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
Samples
232.0ms256×0valid
Compiler

Compiled 100 to 16 computations (84% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 6.0ms (39.3% of total)
ival-add: 4.0ms (26.2% of total)
ival-div: 3.0ms (19.7% of total)
ival-neg: 1.0ms (6.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory
18.7MiB live, 18.6MiB allocated
Counts
13 → 156
Calls
Call 1
Inputs
#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)) (patch #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) (patch (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) (neg.f64 x) x) (patch (fma.f64 (*.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())
#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ 1 x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) (patch #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (pow x 5) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (pow x 5) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) (patch (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (patch (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
Calls

39 calls:

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

simplify531.0ms (8.5%)

Memory
11.0MiB live, 500.2MiB allocated
Algorithm
egg-herbie
Rules
17 574×lower-fma.f64
17 574×lower-fma.f32
4 114×lower-*.f64
4 114×lower-*.f32
1 558×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0621173
11741100
24431071
314471047
458861047
082961029
Stop Event
iter limit
node limit
Counts
156 → 149
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(pow x 5)
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 x)
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(pow x 3)
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* -1 (pow x 3))
(*.f64 x (*.f64 x (neg.f64 x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(-.f64 x (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(-.f64 x (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(-.f64 x (*.f64 x (*.f64 x x)))
(* -1 (pow x 3))
(*.f64 x (*.f64 x (neg.f64 x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (*.f64 x (*.f64 x x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(pow x 5)
(*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(pow x 5)
(*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(* -1 x)
(neg.f64 x)
(* x (- (pow x 2) 1))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* x (- (pow x 2) 1))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* x (- (pow x 2) 1))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(pow x 3)
(*.f64 x (*.f64 x x))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(pow x 3)
(*.f64 x (*.f64 x x))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))

rewrite405.0ms (6.5%)

Memory
-33.7MiB live, 418.6MiB allocated
Rules
11 206×lower-fma.f32
11 198×lower-fma.f64
5 362×lower-*.f32
5 358×lower-*.f64
4 004×lower-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02098
03298
112091
280689
0879989
Stop Event
iter limit
node limit
iter limit
Counts
13 → 673
Calls
Call 1
Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(*.f64 x x)
(neg.f64 x)
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x)) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(+.f64 (*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(exp.f64 (*.f64 (log.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(fma.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x)))
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
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(/.f64 (*.f64 (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (neg.f64 x)) (*.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) x) (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x)) (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) x) (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (neg.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (neg.f64 x)) (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(/.f64 (*.f64 (neg.f64 x) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))))) (neg.f64 (fma.f64 x x (*.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x x) x))))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x)) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))) (fma.f64 x x (*.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x x) x)))))
(/.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x x) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) x)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
(*.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) x))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) x)))
(*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) x))
(*.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 x x x) (+.f64 x #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x x) x))))))
(*.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))))
(*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) (*.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) (-.f64 #s(literal -1 binary64) (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) x) (fma.f64 x (*.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) x) (*.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) (-.f64 #s(literal -1 binary64) (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 (*.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (fma.f64 (neg.f64 x) (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))))))
(*.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))

eval109.0ms (1.8%)

Memory
31.2MiB live, 251.6MiB allocated
Compiler

Compiled 21 107 to 1 644 computations (92.2% saved)

prune364.0ms (5.8%)

Memory
-23.9MiB live, 217.3MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New8640864
Fresh011
Picked055
Done000
Total8646870
Accuracy
100.0%
Counts
870 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.4%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
47.4%
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
74.4%
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
47.3%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
46.4%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
55.4%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 48 to 25 computations (47.9% saved)

simplify5.0ms (0.1%)

Memory
7.1MiB live, 7.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x x #s(literal 1 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
cost-diff320
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
Rules
26×lower-*.f32
24×lower-*.f64
12×lower-/.f32
10×lower-/.f64
*-commutative
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0520
0920
11518
21918
32818
42918
53518
63618
73718
03718
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 x x #s(literal 1 binary64))
x
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 x x #s(literal 1 binary64))
x

localize20.0ms (0.3%)

Memory
-7.6MiB live, 30.3MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 x x #s(literal 1 binary64))
accuracy0.49327961426286226
(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
accuracy15.777813735667067
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
Samples
11.0ms256×0valid
Compiler

Compiled 25 to 8 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult: 3.0ms (47.6% of total)
ival-div: 2.0ms (31.8% of total)
ival-add: 1.0ms (15.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
2.3MiB live, 2.3MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) (patch (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (pow x 2) 1))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
Calls

9 calls:

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

simplify227.0ms (3.6%)

Memory
21.9MiB live, 350.0MiB allocated
Algorithm
egg-herbie
Rules
12 228×lower-fma.f64
12 228×lower-fma.f32
2 786×lower-*.f64
2 786×lower-*.f32
1 868×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048338
1140334
2335322
3977314
42695312
56838312
08367301
Stop Event
iter limit
node limit
Counts
36 → 35
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x x)) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))

rewrite296.0ms (4.7%)

Memory
17.4MiB live, 545.4MiB allocated
Rules
4 580×lower-fma.f32
4 578×lower-fma.f64
4 570×lower-/.f32
4 568×lower-/.f64
3 446×lower-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0518
0918
13816
221816
3176916
0856116
Stop Event
iter limit
node limit
iter limit
Counts
3 → 510
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
Outputs
(+.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x)) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 x) (neg.f64 (log1p.f64 (*.f64 x x)))))
(exp.f64 (+.f64 (neg.f64 (log1p.f64 (*.f64 x x))) (log.f64 x)))
(exp.f64 (-.f64 (log.f64 x) (log1p.f64 (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x x) (*.f64 (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) x))
(neg.f64 (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 x (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
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(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))))
(*.f64 (-.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
(*.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 (*.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (exp.f64 (neg.f64 (log1p.f64 (*.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x (*.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))))))

eval121.0ms (1.9%)

Memory
17.4MiB live, 171.9MiB allocated
Compiler

Compiled 20 531 to 1 878 computations (90.9% saved)

prune215.0ms (3.4%)

Memory
-12.4MiB live, 254.3MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New5441545
Fresh000
Picked011
Done145
Total5456551
Accuracy
100.0%
Counts
551 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.4%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
74.4%
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
47.4%
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
47.3%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
46.4%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
55.4%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 48 to 25 computations (47.9% saved)

simplify4.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0722
0822
11222
01220
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
x
Outputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
(*.f64 x #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)))
#s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
x

localize18.0ms (0.3%)

Memory
3.9MiB live, 43.2MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy15.777813735667067
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
accuracy33.491138967578706
#s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))
Samples
12.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 3.0ms (45.7% of total)
ival-div: 2.0ms (30.4% of total)
ival-add: 1.0ms (15.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
2.0MiB live, 2.0MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) (patch (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (pow x 2) 1))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify246.0ms (3.9%)

Memory
-10.1MiB live, 285.0MiB allocated
Algorithm
egg-herbie
Rules
11 374×lower-fma.f64
11 374×lower-fma.f32
2 438×lower-*.f64
2 438×lower-*.f32
1 828×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045286
1130282
2316270
3921262
42625260
56598260
08288258
Stop Event
iter limit
node limit
Counts
24 → 23
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (*.f64 x (*.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x x)) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 1 binary64)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))) (*.f64 x x))

rewrite257.0ms (4.1%)

Memory
-18.9MiB live, 389.2MiB allocated
Rules
4 998×lower-fma.f64
4 998×lower-fma.f32
4 196×lower-/.f64
4 196×lower-/.f32
3 158×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
0820
13520
219520
3158620
0826318
Stop Event
iter limit
node limit
iter limit
Counts
2 → 3
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))
Outputs
(*.f64 x #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)))
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))

eval3.0ms (0%)

Memory
8.7MiB live, 8.7MiB allocated
Compiler

Compiled 331 to 39 computations (88.2% saved)

prune7.0ms (0.1%)

Memory
-19.2MiB live, 20.5MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New26026
Fresh000
Picked011
Done055
Total26632
Accuracy
100.0%
Counts
32 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
74.4%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
74.4%
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
47.4%
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
47.3%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
46.4%
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
55.4%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 102 to 43 computations (57.8% saved)

regimes6.0ms (0.1%)

Memory
18.9MiB live, 18.9MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))) x))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
Outputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Calls

2 calls:

3.0ms
x
3.0ms
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
100.0%2x
99.8%2(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Compiler

Compiled 10 to 6 computations (40% saved)

regimes4.0ms (0.1%)

Memory
13.0MiB live, 13.0MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
Outputs
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Calls

2 calls:

2.0ms
x
2.0ms
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
80.9%4(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
99.3%2x
Compiler

Compiled 10 to 6 computations (40% saved)

regimes3.0ms (0.1%)

Memory
-32.7MiB live, 6.6MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
Outputs
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.0%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory
8.7MiB live, 8.7MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

2 calls:

1.0ms
x
1.0ms
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
47.4%1(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
47.4%1x
Compiler

Compiled 10 to 6 computations (40% saved)

bsearch5.0ms (0.1%)

Memory
13.3MiB live, 13.3MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
5.0ms
57101184.41235557
91215664.04990576
Samples
2.0ms64×0valid
Compiler

Compiled 67 to 45 computations (32.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-div: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch11.0ms (0.2%)

Memory
-13.3MiB live, 25.5MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
10.0ms
0.2779191921325004
13189.367918759615
Samples
6.0ms128×0valid
Compiler

Compiled 139 to 81 computations (41.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-div: 1.0ms (41.7% of total)
ival-add: 1.0ms (41.7% of total)
ival-mult: 1.0ms (41.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch3.0ms (0%)

Memory
6.9MiB live, 6.9MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
3.0ms
0.2779191921325004
13189.367918759615
Samples
1.0ms32×0valid
Compiler

Compiled 107 to 73 computations (31.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-div: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify6.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated
Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
1-exp_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02488
13188
23388
33488
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 x #s(literal 90000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
Outputs
(if (<=.f64 x #s(literal 90000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (*.f64 x #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)) x)
(*.f64 x #s(approx (/ 1 (+ (* x x) 1)) #s(literal 1 binary64)))

soundness631.0ms (10.1%)

Memory
-9.9MiB live, 414.8MiB allocated
Rules
12 662×lower-fma.f64
12 662×lower-fma.f32
12 228×lower-fma.f64
12 228×lower-fma.f32
4 942×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045226
1131224
2312216
3888212
42381210
55550210
67627210
08047197
048338
1140334
2335322
3977314
42695312
56838312
08367301
0515
0815
13315
220215
3176615
0856213
Stop Event
done
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 139 to 63 computations (54.7% saved)

preprocess114.0ms (1.8%)

Memory
3.6MiB live, 227.9MiB allocated
Compiler

Compiled 186 to 86 computations (53.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...