invcot (example 3.9)

Time bar (total: 15.2s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze5.0ms (0%)

Memory
6.1MiB live, 6.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.7%50.3%0%0%0%0
0%0%49.7%50.3%0%0%0%1
0%0%49.7%50.3%0%0%0%2
25%12.4%37.3%50.3%0%0%0%3
62.5%31.1%18.6%50.3%0%0%0%4
81.3%40.4%9.3%50.3%0%0%0%5
90.6%45%4.7%50.3%0%0%0%6
95.3%47.4%2.3%50.3%0%0%0%7
97.7%48.5%1.2%50.3%0%0%0%8
98.8%49.1%0.6%50.3%0%0%0%9
99.4%49.4%0.3%50.3%0%0%0%10
99.7%49.5%0.1%50.3%0%0%0%11
99.9%49.6%0.1%50.3%0%0%0%12
Compiler

Compiled 16 to 12 computations (25% saved)

sample10.2s (67%)

Memory
51.0MiB live, 8 334.9MiB allocated
Samples
7.9s3 906×2valid
1.8s4 256×1valid
8.0ms94×0valid
Precisions
Click to see histograms. Total time spent on operations: 9.4s
ival-tan: 7.9s (84.6% of total)
ival-div: 503.0ms (5.4% of total)
adjust: 347.0ms (3.7% of total)
const: 334.0ms (3.6% of total)
ival-sub: 197.0ms (2.1% of total)
ival-<: 44.0ms (0.5% of total)
ival-and: 12.0ms (0.1% of total)
exact: 5.0ms (0.1% of total)
ival-assert: 3.0ms (0% of total)
Bogosity

explain510.0ms (3.3%)

Memory
-17.3MiB live, 859.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2560-0-(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-(tan.f64 x)
00-0-(/.f64 #s(literal 1 binary64) (tan.f64 x))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))cancellation2560
Confusion
Predicted +Predicted -
+2560
-00
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25600
-000
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
1256
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
366.0ms252×2valid
82.0ms254×1valid
0.0ms6×0valid
Compiler

Compiled 50 to 22 computations (56% saved)

Precisions
Click to see histograms. Total time spent on operations: 423.0ms
ival-tan: 382.0ms (90.2% of total)
ival-div: 24.0ms (5.7% of total)
adjust: 11.0ms (2.6% of total)
ival-sub: 6.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess21.0ms (0.1%)

Memory
15.7MiB live, 15.7MiB allocated
Algorithm
1×egg-herbie
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
12119
25416
313116
420416
522816
623016
068
0108
1148
2228
3318
4438
5638
61028
71348
81928
92258
102478
02478
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
Symmetry

(negabs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶6.3%
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

Memory
4.9MiB live, 4.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(/.f64 #s(literal 1 binary64) (tan.f64 x))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
01019
11419
22219
33119
44319
56319
610219
713419
819219
922519
1024719
024719
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

localize305.0ms (2%)

Memory
-23.5MiB live, 90.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 #s(literal 1 binary64) x)
accuracy0
(tan.f64 x)
accuracy0.0078125
(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy59.9460429831848
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Samples
266.0ms126×2valid
32.0ms127×1valid
0.0ms3×0valid
Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 287.0ms
ival-tan: 269.0ms (93.7% of total)
ival-div: 10.0ms (3.5% of total)
adjust: 6.0ms (2.1% of total)
ival-sub: 3.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory
3.4MiB live, 3.4MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/3 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms
x
@inf
((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms
x
@0
((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))

simplify255.0ms (1.7%)

Memory
17.1MiB live, 92.9MiB allocated
Algorithm
1×egg-herbie
Rules
18 970×lower-fma.f64
18 970×lower-fma.f32
3 656×lower-*.f64
3 656×lower-*.f32
3 436×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067324
1179324
2458318
31332318
42094318
53093318
63682318
73949318
85089318
97269318
08431300
Stop Event
1×iter limit
1×node limit
Counts
48 → 47
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 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 (* -1/3 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite115.0ms (0.8%)

Memory
7.9MiB live, 83.6MiB allocated
Rules
3 072×lower-fma.f64
3 072×lower-fma.f32
2 002×lower-*.f64
2 002×lower-*.f32
1 374×frac-times
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0617
01017
14917
245417
3570617
0920317
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 277
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)
Outputs
(*.f64 (/.f64 (-.f64 (tan.f64 x) x) (*.f64 x (sin.f64 x))) (cos.f64 x))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (/.f64 (-.f64 (tan.f64 x) x) x)) (tan.f64 x))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (-.f64 (pow.f64 x #s(literal -4 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -4 binary64)) (pow.f64 (*.f64 x (tan.f64 x)) #s(literal -2 binary64))))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal -6 binary64)))) (fma.f64 (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) (-.f64 (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (tan.f64 x) x)) (*.f64 x (tan.f64 x)))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (sin.f64 x)) (cos.f64 x))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))))
(*.f64 (*.f64 (-.f64 (tan.f64 x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (tan.f64 x) x)) (-.f64 (tan.f64 x) x))
(*.f64 (*.f64 (-.f64 (tan.f64 x) x) #s(literal 1 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(*.f64 (-.f64 (tan.f64 x) x) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))))
(*.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))))
(*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))))
(*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x) (-.f64 (tan.f64 x) x))
(*.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(pow.f64 (/.f64 (tan.f64 x) (/.f64 (-.f64 (tan.f64 x) x) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) #s(literal -1 binary64))
(/.f64 (/.f64 (-.f64 (tan.f64 x) x) (tan.f64 x)) x)
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))))
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (tan.f64 x) x)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(/.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 (tan.f64 x) #s(literal -4 binary64))) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x)))) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 (tan.f64 x) #s(literal -6 binary64))) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x)))) (-.f64 (pow.f64 x #s(literal -4 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -4 binary64)) (pow.f64 (*.f64 x (tan.f64 x)) #s(literal -2 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 (tan.f64 x) #s(literal -6 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -9 binary64)) (pow.f64 (tan.f64 x) #s(literal -9 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (*.f64 x (tan.f64 x)) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -6 binary64))) (pow.f64 x #s(literal -6 binary64))))
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 x x)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x)) (-.f64 (tan.f64 x) x))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x)) (fma.f64 x (-.f64 (tan.f64 x) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (tan.f64 x) x) #s(literal -1 binary64)) (*.f64 x (tan.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) x) x)) (tan.f64 x))
(/.f64 (*.f64 (-.f64 (tan.f64 x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) x)
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64))) (fma.f64 (pow.f64 x #s(literal -2 binary64)) (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 x #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))))))
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(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x (tan.f64 x)) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 0 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(+.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 0 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 x (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) x))))))
(+.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 x) (/.f64 x (-.f64 (tan.f64 x) x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (tan.f64 x) (*.f64 x (sin.f64 x))) (cos.f64 x))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))
(*.f64 (/.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (tan.f64 x) x) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (sin.f64 x) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (*.f64 x (tan.f64 x))))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (/.f64 (tan.f64 x) x))
(*.f64 (tan.f64 x) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (/.f64 (*.f64 x (tan.f64 x)) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (*.f64 x (tan.f64 x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 (tan.f64 x) x) (tan.f64 x))
(/.f64 #s(literal -1 binary64) x)
(/.f64 (sin.f64 x) (*.f64 (*.f64 x (tan.f64 x)) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 (*.f64 x (tan.f64 x)) (cos.f64 x)))
(/.f64 (tan.f64 x) (*.f64 (*.f64 x (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 (tan.f64 x) (*.f64 x (tan.f64 x)))
(/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (tan.f64 x)) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (pow.f64 x #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (neg.f64 (log.f64 (*.f64 x (tan.f64 x))))))
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (*.f64 (log.f64 (*.f64 x (tan.f64 x))) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(*.f64 (/.f64 x (*.f64 x (sin.f64 x))) (cos.f64 x))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (cos.f64 x))
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (cos.f64 x))
(*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 x (tan.f64 x)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (cos.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 x (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) x))
(*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(*.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x (tan.f64 x)))
(*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (*.f64 x (tan.f64 x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 x (tan.f64 x)) (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x (tan.f64 x)) x) #s(literal -1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow.f64 (tan.f64 x) #s(literal -1 binary64))
(/.f64 (/.f64 x (tan.f64 x)) x)
(/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(/.f64 x (*.f64 (*.f64 x (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 x (*.f64 x (tan.f64 x)))
(/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))))
(/.f64 #s(literal -1 binary64) (tan.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (tan.f64 x)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (tan.f64 x)) x))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64) (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (log.f64 x) (neg.f64 (log.f64 (*.f64 x (tan.f64 x))))))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 x (tan.f64 x))) #s(literal -1 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 (tan.f64 x))))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (tan.f64 x))
(*.f64 (sin.f64 x) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (sin.f64 x) (neg.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64))))
(*.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (sin.f64 x) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (tan.f64 x) #s(literal -1 binary64))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (tan.f64 x)))

eval87.0ms (0.6%)

Memory
-13.3MiB live, 67.1MiB allocated
Compiler

Compiled 5 442 to 762 computations (86% saved)

prune5.0ms (0%)

Memory
18.6MiB live, 18.6MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3213324
Fresh000
Picked101
Done000
Total3223325
Accuracy
99.5%
Counts
325 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
▶99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
▶98.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify72.0ms (0.5%)

Memory
-1.5MiB live, 37.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff0
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
cost-diff0
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
cost-diff0
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
cost-diff0
(*.f64 x #s(literal 1/3 binary64))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Rules
2 368×lower-fma.f32
2 362×lower-fma.f64
1 024×lower-*.f32
1 016×lower-*.f64
650×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019113
029113
148113
283113
3145113
4237113
5263113
6305113
7337113
8588113
91987113
102697113
112789113
122789113
132791113
142792113
02792113
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x #s(literal 1/3 binary64))
x
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
x
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize721.0ms (4.7%)

Memory
-22.8MiB live, 411.7MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
accuracy0.00390625
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
accuracy0.00390625
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy0.3359375
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
accuracy0
(*.f64 x x)
accuracy0.0078125
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
accuracy0.3359375
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
accuracy0.337648094888529
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
accuracy0.33984375
(*.f64 x #s(literal 1/3 binary64))
Samples
537.0ms126×2valid
83.0ms127×1valid
0.0ms3×0valid
Compiler

Compiled 95 to 21 computations (77.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 549.0ms
ival-tan: 422.0ms (76.9% of total)
adjust: 44.0ms (8% of total)
ival-mult: 42.0ms (7.7% of total)
const: 22.0ms (4% of total)
ival-div: 10.0ms (1.8% of total)
ival-add: 6.0ms (1.1% of total)
ival-sub: 3.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
19.7MiB live, 19.7MiB allocated
Counts
10 → 120
Calls
Call 1
Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/45 (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 5)) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) (patch (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@0
((- (/ 1 x) (/ 1 (tan x))) (* x 1/3) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))
2.0ms
x
@inf
((- (/ 1 x) (/ 1 (tan x))) (* x 1/3) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))
2.0ms
x
@-inf
((- (/ 1 x) (/ 1 (tan x))) (* x 1/3) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))

simplify164.0ms (1.1%)

Memory
-10.7MiB live, 184.2MiB allocated
Algorithm
1×egg-herbie
Rules
15 606×lower-fma.f64
15 606×lower-fma.f32
3 878×lower-*.f64
3 878×lower-*.f32
1 934×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
060908
1185908
2477908
31163908
42339908
55675908
08126833
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
1/45
#s(literal 1/45 binary64)
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(* 2/945 (pow x 2))
(*.f64 #s(literal 2/945 binary64) (*.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(* 2/945 (pow x 2))
(*.f64 #s(literal 2/945 binary64) (*.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

rewrite158.0ms (1%)

Memory
23.9MiB live, 212.7MiB allocated
Rules
8 520×lower-fma.f32
8 514×lower-fma.f64
5 256×lower-*.f32
5 248×lower-*.f64
3 582×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019101
029101
1123101
2933101
08743101
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
10 → 309
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x #s(literal 1/3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))
(*.f64 (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #s(literal 1 binary64)) x)
(*.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (pow.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (*.f64 (pow.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #s(literal -1 binary64)) x))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) (*.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))) #s(literal -1 binary64)) x))
(*.f64 (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x))
(/.f64 (*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64))) x) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(/.f64 (*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) x) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 (*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) x) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))
(/.f64 (*.f64 (neg.f64 x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 x (-.f64 #s(literal 1/9 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(/.f64 (*.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 (*.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) (*.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))) (-.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64))) (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (-.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x) (-.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) (*.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (+.f64 #s(literal 1/9 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (+.f64 #s(literal 1/9 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) #s(literal 1 binary64))
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(/.f64 (neg.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64))) (neg.f64 (+.f64 #s(literal 1/2025 binary64) (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64))) (neg.f64 (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/2025 binary64) (*.f64 #s(literal 2/42525 binary64) (*.f64 x x))))))
(/.f64 (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2025 binary64)) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64)))
(/.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64)) (+.f64 #s(literal 1/2025 binary64) (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64)))))
(/.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64)) (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/2025 binary64) (*.f64 #s(literal 2/42525 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/45 binary64) (*.f64 #s(literal 2/945 binary64) (*.f64 x x))) (-.f64 #s(literal 1/2025 binary64) (*.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2025 binary64) (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64)))) (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2025 binary64))) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64))) (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/2025 binary64) (*.f64 #s(literal 2/42525 binary64) (*.f64 x x))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2025 binary64)) (fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 8/843908625 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64)) (neg.f64 (fma.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/2025 binary64) (*.f64 #s(literal 2/42525 binary64) (*.f64 x x)))))))
(fma.f64 (*.f64 #s(literal 2/945 binary64) x) x #s(literal 1/45 binary64))
(fma.f64 (*.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/2025 binary64) (fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 (*.f64 #s(literal 2/945 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64))
(fma.f64 x (*.f64 #s(literal 2/945 binary64) x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/945 binary64) (*.f64 x x)) #s(literal 1/45 binary64))
(-.f64 (/.f64 #s(literal 1/2025 binary64) (-.f64 #s(literal 1/45 binary64) (*.f64 #s(literal 2/945 binary64) (*.f64 x x)))) (/.f64 (*.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/45 binary64) (*.f64 #s(literal 2/945 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (*.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64))) (/.f64 #s(literal -1/2025 binary64) (fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))))
(+.f64 (/.f64 (*.f64 #s(literal 4/893025 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64))) (neg.f64 (/.f64 #s(literal -1/2025 binary64) (fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)))))
(+.f64 (*.f64 #s(literal 2/945 binary64) (*.f64 x x)) #s(literal 1/45 binary64))
(+.f64 #s(literal 1/45 binary64) (*.f64 #s(literal 2/945 binary64) (*.f64 x x)))

eval62.0ms (0.4%)

Memory
-9.9MiB live, 151.2MiB allocated
Compiler

Compiled 9 610 to 1 398 computations (85.5% saved)

prune16.0ms (0.1%)

Memory
6.0MiB live, 45.3MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New4763479
Fresh000
Picked033
Done000
Total4766482
Accuracy
100.0%
Counts
482 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
▶99.4%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
▶99.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓98.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Compiler

Compiled 58 to 45 computations (22.4% saved)

simplify37.0ms (0.2%)

Memory
-2.0MiB live, 41.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 1/45 binary64) x)
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
cost-diff320
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
cost-diff0
(pow.f64 x #s(literal 3 binary64))
cost-diff0
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
cost-diff6144
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
cost-diff0
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
cost-diff1088
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
Rules
552×lower-fma.f32
546×lower-fma.f64
376×lower-*.f32
368×lower-*.f64
168×associate-*r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022128
035132
157120
275120
399120
4117120
5141120
6176120
7199120
8350120
9807120
101074120
111105120
121107120
131110120
141111120
01111120
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
x
#s(literal 1/3 binary64)
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
#s(literal 1/45 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
x
#s(literal 1/3 binary64)
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
#s(literal 1/45 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)

localize308.0ms (2%)

Memory
8.8MiB live, 519.1MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
accuracy0.22265625
(*.f64 #s(literal 1/45 binary64) x)
accuracy0.33984375
(*.f64 #s(literal 1/3 binary64) x)
accuracy0
(pow.f64 x #s(literal 3 binary64))
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
accuracy0.15625
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
accuracy0.33203125
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
accuracy0.00390625
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
accuracy0.0078125
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy0.01171875
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
Samples
225.0ms126×2valid
62.0ms127×1valid
1.0ms3×0valid
Compiler

Compiled 104 to 24 computations (76.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 260.0ms
ival-tan: 180.0ms (69.2% of total)
const: 21.0ms (8.1% of total)
ival-div: 19.0ms (7.3% of total)
adjust: 15.0ms (5.8% of total)
ival-mult: 14.0ms (5.4% of total)
ival-add: 6.0ms (2.3% of total)
ival-sub: 3.0ms (1.2% of total)
ival-pow: 3.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series14.0ms (0.1%)

Memory
-8.5MiB live, 29.8MiB allocated
Counts
13 → 156
Calls
Call 1
Inputs
#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (patch (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/45 binary64) x) (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) 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 (* 1/45 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/45 binary64) x) (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/45 binary64) x) (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/45 binary64) x) (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/45 binary64) x) (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@0
((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* x 1/3) (* (pow x 3) 1/45)) (- (/ 1 x) (/ 1 (tan x))) (* (pow x 3) 1/45) (pow x 3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (* 1/3 x))
2.0ms
x
@-inf
((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* x 1/3) (* (pow x 3) 1/45)) (- (/ 1 x) (/ 1 (tan x))) (* (pow x 3) 1/45) (pow x 3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (* 1/3 x))
2.0ms
x
@inf
((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* x 1/3) (* (pow x 3) 1/45)) (- (/ 1 x) (/ 1 (tan x))) (* (pow x 3) 1/45) (pow x 3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (* 1/3 x))

simplify120.0ms (0.8%)

Memory
32.8MiB live, 188.5MiB allocated
Algorithm
1×egg-herbie
Rules
10 150×lower-fma.f64
10 150×lower-fma.f32
3 108×lower-*.f64
3 108×lower-*.f32
2 516×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0771054
11981054
24941054
311581054
424231054
553331054
08386994
Stop Event
1×iter limit
1×node limit
Counts
156 → 156
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (*.f64 x x) #s(literal 1/75 binary64)) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (*.f64 x x)) #s(literal 45 binary64))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (*.f64 x x)) #s(literal 45 binary64))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* 1/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (*.f64 x x)) #s(literal 45 binary64))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (*.f64 x x)) #s(literal 45 binary64))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* 1/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))

rewrite218.0ms (1.4%)

Memory
-31.2MiB live, 330.9MiB allocated
Rules
13 802×lower-fma.f32
13 796×lower-fma.f64
5 970×lower-*.f32
5 962×lower-*.f64
2 776×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022114
035118
1154106
21107106
09073106
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
13 → 565
Calls
Call 1
Inputs
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow.f64 x #s(literal 3 binary64))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
Outputs
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (pow.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (-.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/135 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) x) (/.f64 (*.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #s(literal -1 binary64))) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) #s(literal -1 binary64))) (/.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))
(*.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x (pow.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 x (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 x (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/9 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(*.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (*.f64 #s(literal -1/2025 binary64) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(*.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))))
(*.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (-.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/135 binary64)))))))
(*.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (*.f64 #s(literal -1/2025 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)) #s(literal -1 binary64)) x))
(*.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/9 binary64) (*.f64 x x))) (pow.f64 (*.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (-.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/135 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))) #s(literal -1 binary64))))
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(neg.f64 (/.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/9 binary64) (*.f64 x x))) (*.f64 x (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (*.f64 #s(literal -1/2025 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(neg.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (neg.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal 1/135 binary64) (*.f64 x x))))))))
(neg.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/91125 binary64) #s(literal 1/27 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/9 binary64) x) x (-.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/135 binary64)))))))
(neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) #s(literal 1 binary64)))
(neg.f64 (*.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x))
(fma.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64)) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/45 binary64)) x) x) (/.f64 (*.f64 #s(literal 1/45 binary64) x) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/45 binary64)) x) (/.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/45 binary64)) x) (/.f64 #s(literal 1/45 binary64) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 3 binary64))) x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) x) (/.f64 #s(literal 1/2025 binary64) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (*.f64 x x)) x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) x) (/.f64 (*.f64 #s(literal 1/2025 binary64) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 #s(literal 1/2025 binary64) x) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64)) x) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) x) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/45 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/45 binary64) x) x) (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/45 binary64)) x) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) x) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) x) (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 #s(literal 1/45 binary64) x) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/45 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) x) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64)) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (/.f64 x x) (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64)) x) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 #s(literal -1/45 binary64) (*.f64 x x)) (neg.f64 x) (*.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) (*.f64 (*.f64 #s(literal -1/45 binary64) (*.f64 x x)) (neg.f64 x)))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(fma.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) #s(literal -1 binary64)) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(fma.f64 (neg.f64 x) (*.f64 #s(literal -1/45 binary64) (*.f64 x x)) (*.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/3 binary64) (*.f64 (neg.f64 x) (*.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))) (*.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x))
(-.f64 (/.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) x) (/.f64 #s(literal 1/2025 binary64) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) #s(literal 1 binary64)))
(-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) x) (/.f64 #s(literal 1/2025 binary64) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)))) (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x))
(+.f64 (*.f64 (*.f64 #s(literal -1/45 binary64) (*.f64 x x)) (neg.f64 x)) (*.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(+.f64 (*.f64 #s(literal -1/3 binary64) (neg.f64 x)) (*.f64 (*.f64 #s(literal -1/45 binary64) (*.f64 x x)) (neg.f64 x)))
(+.f64 (*.f64 (neg.f64 x) (*.f64 #s(literal -1/45 binary64) (*.f64 x x))) (*.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(+.f64 (*.f64 (neg.f64 x) #s(literal -1/3 binary64)) (*.f64 (neg.f64 x) (*.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(+.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) x) (/.f64 #s(literal 1/2025 binary64) (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64)))) (neg.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) x) x) (/.f64 x (fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 x (pow.f64 x #s(literal -1 binary64)))
(neg.f64 (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1/45 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/45 binary64) x))
(*.f64 x #s(literal 1/45 binary64))
(/.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal -1 binary64)))

eval228.0ms (1.5%)

Memory
10.6MiB live, 209.5MiB allocated
Compiler

Compiled 15 060 to 1 336 computations (91.1% saved)

prune23.0ms (0.2%)

Memory
18.6MiB live, 58.1MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New7413744
Fresh000
Picked303
Done033
Total7446750
Accuracy
100.0%
Counts
750 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.4%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
▶99.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
▶99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓98.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify51.0ms (0.3%)

Memory
-7.8MiB live, 30.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))
cost-diff0
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
cost-diff0
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
cost-diff0
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
cost-diff0
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
cost-diff0
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
cost-diff0
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
Rules
824×lower-fma.f32
820×lower-fma.f64
600×lower-*.f32
594×lower-*.f64
226×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026168
035168
153160
273160
383160
497160
5117160
6156160
7188160
8351160
9853160
101208160
111375160
121543160
131607160
141666160
151687160
161692160
01692154
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))
x
#s(literal 1/3 binary64)
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
#s(literal 1/45 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
x
#s(literal 1/3 binary64)
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(*.f64 (*.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))
(*.f64 x x)
#s(literal 1/45 binary64)

localize397.0ms (2.6%)

Memory
-12.3MiB live, 421.6MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.0625
(*.f64 (*.f64 x x) x)
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
accuracy0.15625
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))
accuracy0.33203125
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))
accuracy0
(*.f64 x x)
accuracy0.00390625
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
accuracy0.07269017332901713
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
accuracy0.00390625
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
accuracy0.07642110654952644
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
accuracy0.338591740555907
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
Samples
315.0ms126×2valid
64.0ms127×1valid
1.0ms3×0valid
Compiler

Compiled 110 to 23 computations (79.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 356.0ms
ival-tan: 210.0ms (59% of total)
ival-div: 81.0ms (22.8% of total)
adjust: 30.0ms (8.4% of total)
const: 12.0ms (3.4% of total)
ival-mult: 12.0ms (3.4% of total)
ival-add: 5.0ms (1.4% of total)
ival-sub: 4.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
22.4MiB live, 22.4MiB allocated
Counts
12 → 144
Calls
Call 1
Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) (patch (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 x x) x) (patch (*.f64 (*.f64 x x) x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 45 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 45 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) (patch (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) (patch (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) (patch (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) (patch (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) (patch (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 (*.f64 x x) x) (patch (*.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 (*.f64 x x) x) (patch (*.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 (*.f64 x x) x) (patch (*.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 (*.f64 x x) x) (patch (*.f64 (*.f64 x x) x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (+ (* x 1/3) (* (* (* x x) x) 1/45)) (* (* (* x x) x) 1/45) (* x x) (* (* x x) x))
2.0ms
x
@inf
((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (+ (* x 1/3) (* (* (* x x) x) 1/45)) (* (* (* x x) x) 1/45) (* x x) (* (* x x) x))
1.0ms
x
@0
((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (+ (* x 1/3) (* (* (* x x) x) 1/45)) (* (* (* x x) x) 1/45) (* x x) (* (* x x) x))

simplify146.0ms (1%)

Memory
5.4MiB live, 121.4MiB allocated
Algorithm
1×egg-herbie
Rules
12 352×lower-fma.f64
12 352×lower-fma.f32
3 826×lower-*.f64
3 826×lower-*.f32
2 020×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0781134
11971134
24941134
311831134
422981134
539071134
664831134
080981068
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (*.f64 x x) #s(literal 1/75 binary64)) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (*.f64 x x) #s(literal 1/75 binary64)) (*.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* -1/5 (pow x 2))
(*.f64 #s(literal -1/5 binary64) (*.f64 x x))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal -10125 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x))
(* -1/5 (pow x 2))
(*.f64 #s(literal -1/5 binary64) (*.f64 x x))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))

rewrite150.0ms (1%)

Memory
2.0MiB live, 156.9MiB allocated
Rules
5 072×lower-fma.f32
5 068×lower-fma.f64
3 914×lower-*.f32
3 908×lower-*.f64
3 592×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026157
035149
1148149
21063149
08594143
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
12 → 196
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64)))
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))
(*.f64 x x)
(*.f64 (*.f64 x x) x)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)) x)
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 x (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1 binary64))
(/.f64 (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) x))
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64)) x)
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(*.f64 x (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x) #s(literal -1 binary64))
(/.f64 (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (neg.f64 x)))
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) #s(literal -1 binary64)))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(*.f64 (-.f64 #s(literal 9 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) #s(literal -1/5 binary64)))))
(*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) #s(literal -9 binary64)) (pow.f64 (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal -1/125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) (*.f64 (*.f64 x x) #s(literal 3/5 binary64))))))
(*.f64 (fma.f64 #s(literal -1/125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64)))) (*.f64 (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))) (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 9 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64)))) (neg.f64 (-.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) #s(literal -1/5 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) #s(literal -9 binary64)))) (neg.f64 (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/125 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/5 binary64)) #s(literal 4 binary64)) #s(literal 81 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/25 binary64) #s(literal 9 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/15625 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -729 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/5 binary64)) #s(literal 4 binary64)) (+.f64 #s(literal 81 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9/25 binary64)))) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal -3 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (*.f64 (*.f64 #s(literal -1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/91125 binary64) (*.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (*.f64 #s(literal -1/2025 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/91125 binary64) (*.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal -1/3 binary64) x))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (*.f64 #s(literal -1/2025 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/91125 binary64) (*.f64 #s(literal 1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal -1/3 binary64) x)))))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(fma.f64 x (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) (*.f64 #s(literal 1/3 binary64) x))
(-.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal -1/3 binary64) x))) (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64) (*.f64 #s(literal -1/3 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (/.f64 (*.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/3 binary64) x (*.f64 #s(literal -1/45 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 (*.f64 #s(literal 1/45 binary64) x) (*.f64 x x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(*.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x))
(*.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) x)
(*.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 x (*.f64 (*.f64 #s(literal 1/45 binary64) x) x))
(/.f64 (*.f64 (*.f64 #s(literal 1/45 binary64) x) x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 x) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 x (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) x)
(*.f64 x (*.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 x x) (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))

eval73.0ms (0.5%)

Memory
-15.0MiB live, 59.8MiB allocated
Compiler

Compiled 5 459 to 983 computations (82% saved)

prune10.0ms (0.1%)

Memory
28.1MiB live, 28.1MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New3670367
Fresh000
Picked033
Done033
Total3676373
Accuracy
100.0%
Counts
373 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.4%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
✓99.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓99.3%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓98.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Compiler

Compiled 145 to 85 computations (41.4% saved)

regimes9.0ms (0.1%)

Memory
-25.7MiB live, 11.5MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
Calls

2 calls:

6.0ms
x
3.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0%)

Memory
7.8MiB live, 7.8MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/45 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes2.0ms (0%)

Memory
5.0MiB live, 5.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
98.9%1x
98.9%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify41.0ms (0.3%)

Memory
4.2MiB live, 52.6MiB allocated
Algorithm
1×egg-herbie
Rules
2×1-exp-binary32-exp.f32
2×*-commutative-binary64-*.f64
2×1-exp-binary64-exp.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02461
12861
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

soundness605.0ms (4%)

Memory
4.5MiB live, 390.2MiB allocated
Rules
18 970×lower-fma.f64
18 970×lower-fma.f32
10 150×lower-fma.f64
10 150×lower-fma.f32
8 520×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0771054
11981054
24941054
311581054
424231054
553331054
08386994
019101
029101
1123101
2933101
08743101
067324
1179324
2458318
31332318
42094318
53093318
63682318
73949318
85089318
97269318
08431300
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 60 to 48 computations (20% saved)

preprocess62.0ms (0.4%)

Memory
16.4MiB live, 95.9MiB allocated
Remove

(negabs x)

Compiler

Compiled 142 to 106 computations (25.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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