invcot (example 3.9)

Time bar (total: 15.6s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze5.0ms (0%)

Memory
4.1MiB live, 4.1MiB 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)

sample9.6s (61.5%)

Memory
26.7MiB live, 8 816.7MiB allocated
Samples
7.7s3 923×2valid
1.4s4 239×1valid
8.0ms94×0valid
Precisions
Click to see histograms. Total time spent on operations: 8.7s
ival-tan: 7.5s (86.5% of total)
ival-div: 523.0ms (6% of total)
const: 234.0ms (2.7% of total)
adjust: 212.0ms (2.4% of total)
ival-sub: 101.0ms (1.2% of total)
ival-<: 87.0ms (1% 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

explain558.0ms (3.6%)

Memory
-11.8MiB live, 623.7MiB 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
354.0ms256×2valid
138.0ms254×1valid
0.0ms2×0valid
Compiler

Compiled 51 to 22 computations (56.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 469.0ms
ival-tan: 430.0ms (91.6% of total)
ival-div: 19.0ms (4% of total)
adjust: 13.0ms (2.8% of total)
ival-sub: 6.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess25.0ms (0.2%)

Memory
7.7MiB live, 44.9MiB 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) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
Symmetry

(negabs x)

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶6.4%
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify17.0ms (0.1%)

Memory
-31.9MiB live, 14.3MiB 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) 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)

localize209.0ms (1.3%)

Memory
35.2MiB live, 268.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 #s(literal 1 binary64) x)
accuracy0
(tan.f64 x)
accuracy0.00390625
(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy59.90623406715714
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Samples
172.0ms128×2valid
27.0ms127×1valid
0.0ms1×0valid
Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 185.0ms
ival-tan: 167.0ms (90.1% of total)
ival-div: 10.0ms (5.4% of total)
adjust: 5.0ms (2.7% of total)
ival-sub: 3.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory
7.1MiB live, 7.0MiB 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 (/ (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 (/ (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 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 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 (/ 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 (/ 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 (/ (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 (/ (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 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 (/ (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 (/ (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

12 calls:

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

simplify356.0ms (2.3%)

Memory
-8.1MiB live, 398.8MiB 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
31321318
42085318
53083318
63670318
73941318
85080318
97268318
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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin 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)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 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)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin 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))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.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 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (sin.f64 (neg.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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/45 binary64)) #s(literal -1/3 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) #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))
(/ (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))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/15 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 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64))) 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))
(/ (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))

rewrite186.0ms (1.2%)

Memory
-17.6MiB live, 245.9MiB 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
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))) #s(literal -1 binary64)))
(+.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 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.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 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (tan.f64 x) x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(fma.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 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(fma.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 #s(literal 1 binary64) x))
(fma.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 x (*.f64 (sin.f64 x) x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (tan.f64 x) x)) (*.f64 (tan.f64 x) x) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) #s(literal 3 binary64)))) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))))
(fma.f64 (/.f64 (tan.f64 x) (*.f64 (sin.f64 x) x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) #s(literal 1 binary64)))
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eval65.0ms (0.4%)

Memory
23.8MiB live, 71.7MiB allocated
Compiler

Compiled 6 028 to 755 computations (87.5% saved)

prune73.0ms (0.5%)

Memory
-15.2MiB live, 97.9MiB 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 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
▶99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
▶99.1%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 30 to 18 computations (40% saved)

simplify90.0ms (0.6%)

Memory
14.1MiB live, 95.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
cost-diff0
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
cost-diff0
(*.f64 x #s(literal 1/45 binary64))
cost-diff0
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
cost-diff0
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
cost-diff0
(*.f64 #s(literal 1/3 binary64) x)
cost-diff0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Rules
2 368×lower-fma.f32
2 362×lower-fma.f64
1 024×lower-*.f32
1 012×lower-*.f64
646×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021116
033116
168116
2137116
3217116
4244116
5267116
6306116
7339116
8590116
91943116
102652116
112752116
122752116
132754116
142755116
02755116
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))
(*.f64 x #s(literal 2/945 binary64))
#s(literal 2/945 binary64)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
x
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64))
(*.f64 x #s(literal 2/945 binary64))
#s(literal 2/945 binary64)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize352.0ms (2.3%)

Memory
-10.7MiB live, 422.3MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy0.0078125
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy0.33984375
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy0.4296875
(*.f64 x #s(literal 2/945 binary64))
accuracy0.006191259768442017
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy0.0078125
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy0.203125
(*.f64 x #s(literal 1/45 binary64))
accuracy0.33984375
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy0.2680052385368041
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
accuracy0.34765625
(*.f64 #s(literal 1/3 binary64) x)
Samples
242.0ms128×2valid
65.0ms127×1valid
0.0ms1×0valid
Compiler

Compiled 98 to 23 computations (76.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 249.0ms
ival-tan: 173.0ms (69.6% of total)
ival-mult: 24.0ms (9.6% of total)
adjust: 18.0ms (7.2% of total)
const: 14.0ms (5.6% of total)
ival-div: 10.0ms (4% of total)
ival-add: 6.0ms (2.4% of total)
ival-sub: 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)

series11.0ms (0.1%)

Memory
21.6MiB live, 21.6MiB allocated
Counts
11 → 132
Calls
Call 1
Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (patch (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 1/45 binary64)) (patch (*.f64 x #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (patch (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #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 (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #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 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #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 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #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 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan 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))) (*.f64 #s(literal 1/3 binary64) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) x) (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 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>) () ())) ())
#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>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor inf x) (#s(alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #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 (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/945 binary64)) (patch (*.f64 x #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
Calls

33 calls:

TimeVariablePointExpression
1.0ms
x
@0
(+ (* (* x x) (+ (* x (* x 2/945)) 1/45)) 1/3)
1.0ms
x
@0
(* 1/3 x)
0.0ms
x
@inf
(* x (+ (* (* x x) (+ (* x (* x 2/945)) 1/45)) 1/3))
0.0ms
x
@inf
(* x (+ (* x (* x 1/45)) 1/3))
0.0ms
x
@0
(* x (+ (* x (* x 1/45)) 1/3))

simplify218.0ms (1.4%)

Memory
7.6MiB live, 327.6MiB allocated
Algorithm
1×egg-herbie
Rules
13 112×lower-fma.f64
13 112×lower-fma.f32
3 672×lower-*.f64
3 672×lower-*.f32
1 610×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061906
1182906
2455906
31058906
42211906
55759906
08095840
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 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))
(* (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))
(* (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)))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (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 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 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 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))))))
(* 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 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)))
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)))))
(* 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 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))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 2/945 (pow x 5))
(*.f64 x (*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) (*.f64 x (*.f64 x x)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 2/945 (pow x 5))
(*.f64 x (*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 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 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 2/945 (pow x 4))
(*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 2/945 (pow x 4))
(*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))

rewrite400.0ms (2.6%)

Memory
11.4MiB live, 357.1MiB allocated
Rules
11 116×lower-fma.f32
11 110×lower-fma.f64
5 340×lower-*.f32
5 328×lower-*.f64
2 938×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021101
033101
1143101
21082101
08750101
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
11 → 275
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x x)
(*.f64 x #s(literal 2/945 binary64))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
(+.f64 (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(+.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x #s(literal 1/45 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/135 binary64)))) (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (*.f64 (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64))) (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) (*.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64))) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) (*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 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 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x)))) (-.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/135 binary64)))))
(/.f64 (*.f64 (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(/.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64))) (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64))))
(/.f64 (*.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)) x) (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) #s(literal -1/135 binary64))))
(/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/27 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/135 binary64))))))
(/.f64 (neg.f64 (*.f64 (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))) (neg.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
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(*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/9 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/9 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 x (neg.f64 x)) #s(literal 1/3 binary64))))
(*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(/.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2/945 binary64)))
(*.f64 x #s(literal 2/945 binary64))
(*.f64 #s(literal 2/945 binary64) x)
(*.f64 (*.f64 x #s(literal 2/945 binary64)) #s(literal 1 binary64))

eval51.0ms (0.3%)

Memory
5.1MiB live, 78.2MiB allocated
Compiler

Compiled 10 050 to 753 computations (92.5% saved)

prune75.0ms (0.5%)

Memory
-18.2MiB live, 71.7MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New4043407
Fresh000
Picked033
Done000
Total4046410
Accuracy
100.0%
Counts
410 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
▶100.0%
#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)))))
▶98.9%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.1%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 61 to 38 computations (37.7% saved)

simplify41.0ms (0.3%)

Memory
7.0MiB live, 45.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

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

Useful iterations: 1 (0.0ms)

IterNodesCost
020118
031112
151104
273104
397104
4115104
5139104
6174104
7207104
8381104
9823104
101079104
111105104
121107104
131110104
141111104
01111104
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 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)))))
(/.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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 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))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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)))
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 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 x (*.f64 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(*.f64 x (*.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)

localize305.0ms (2%)

Memory
20.3MiB live, 529.1MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.006191259768442017
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
accuracy0.0078125
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
accuracy0.07421875
(*.f64 x (*.f64 x x))
accuracy0.34765625
(*.f64 x #s(literal 1/3 binary64))
accuracy0.00390625
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
accuracy0.006191259768442017
#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)))))
accuracy0.0078125
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy0.0078125
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
accuracy0
(/.f64 #s(literal 1 binary64) x)
accuracy0.2680052385368041
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
accuracy0.43359375
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
Samples
201.0ms128×2valid
77.0ms127×1valid
0.0ms1×0valid
Compiler

Compiled 96 to 20 computations (79.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 233.0ms
ival-tan: 170.0ms (73.1% of total)
ival-div: 21.0ms (9% of total)
const: 15.0ms (6.4% of total)
adjust: 11.0ms (4.7% of total)
ival-mult: 8.0ms (3.4% of total)
ival-add: 4.0ms (1.7% of total)
ival-sub: 3.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory
-27.8MiB live, 13.4MiB allocated
Counts
12 → 144
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 x (/.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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* 1/45 (pow x 2)) (taylor inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#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 (* 1/45 (pow x 2)) (taylor -inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (* 1/3 x) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.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))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.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))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.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))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.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))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#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 inf 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 inf 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 inf 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 inf 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 -inf 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 -inf 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 -inf 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 -inf x) (#s(alt (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
Calls

36 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(+ (* (* x (* x x)) 1/45) (* x 1/3))
0.0ms
x
@-inf
(* x (* x x))
0.0ms
x
@0
(+ (* (* x (* x x)) 1/45) (* x 1/3))
0.0ms
x
@inf
(/ 1 (+ (* 1/45 (* x x)) 1/3))
0.0ms
x
@0
(/ 1 (+ (* 1/45 (* x x)) 1/3))

simplify416.0ms (2.7%)

Memory
-29.6MiB live, 293.8MiB 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
076936
1196936
2494936
31172936
42414936
55304936
08343885
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin 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)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 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))
(* (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))
(* (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)))))
(* 1/3 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
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)))
(/ 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))
(/ 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))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (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 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)))))
(* 1/3 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))
(* (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))
(* (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)))))
(* 1/3 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -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 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/75 binary64) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/1125 binary64)) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.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 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.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 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)

rewrite239.0ms (1.5%)

Memory
-4.8MiB live, 351.9MiB allocated
Rules
9 760×lower-fma.f32
9 756×lower-fma.f64
5 184×lower-*.f32
5 178×lower-*.f64
2 890×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020105
03199
113291
298191
0860491
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
12 → 441
Calls
Call 1
Inputs
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) 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 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 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(*.f64 x (*.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/3 binary64))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/3 binary64)))
(neg.f64 (*.f64 x #s(literal -1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
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(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 x (pow.f64 (fma.f64 x (*.f64 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 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/91125 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)))) (/.f64 (neg.f64 x) (+.f64 #s(literal 1/9 binary64) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 (neg.f64 x) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) x) (/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))) (/.f64 x (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/91125 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)))) (/.f64 x (+.f64 #s(literal 1/9 binary64) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/91125 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/9 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 1/91125 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/135 binary64))))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 x (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (*.f64 x x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)) (neg.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/3 binary64)))
(neg.f64 (*.f64 x #s(literal -1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.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 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/3 binary64)))
(*.f64 #s(literal -1/3 binary64) (neg.f64 x))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)) #s(literal -1/2 binary64)))

eval76.0ms (0.5%)

Memory
5.0MiB live, 118.2MiB allocated
Compiler

Compiled 12 124 to 936 computations (92.3% saved)

prune129.0ms (0.8%)

Memory
3.3MiB live, 87.5MiB allocated
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New6082610
Fresh000
Picked213
Done033
Total6106616
Accuracy
100.0%
Counts
616 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
▶100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
▶99.6%
#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 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.1%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 59 to 34 computations (42.4% saved)

simplify76.0ms (0.5%)

Memory
-4.5MiB live, 33.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
cost-diff0
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))
cost-diff0
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #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
568×lower-fma.f32
566×lower-fma.f64
440×lower-*.f32
438×lower-*.f64
176×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022121
027121
139121
251121
360121
473121
593121
6132121
7164121
8280121
9577121
10795121
11995121
121205121
131269121
141321121
151345121
161350121
171351121
01351115
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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(*.f64 x #s(literal -1/5 binary64))
#s(literal -1/5 binary64)
#s(literal 3 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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(*.f64 x #s(literal -1/5 binary64))
#s(literal -1/5 binary64)
#s(literal 3 binary64)

localize440.0ms (2.8%)

Memory
33.2MiB live, 223.8MiB allocated
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))
accuracy0.006191259768442017
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
accuracy0.0078125
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))
accuracy0.37890625
(*.f64 x #s(literal -1/5 binary64))
accuracy0.006191259768442017
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
accuracy0.0078125
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
accuracy0.2725138987143279
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
Samples
376.0ms128×2valid
44.0ms127×1valid
0.0ms1×0valid
Compiler

Compiled 73 to 20 computations (72.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 403.0ms
ival-tan: 304.0ms (75.5% of total)
ival-div: 63.0ms (15.6% of total)
const: 12.0ms (3% of total)
adjust: 11.0ms (2.7% of total)
ival-mult: 6.0ms (1.5% of total)
ival-sub: 3.0ms (0.7% of total)
ival-add: 3.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series150.0ms (1%)

Memory
-38.6MiB live, 5.3MiB allocated
Counts
8 → 96
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 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<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 (/ (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 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>) () ())) ())
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#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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) (patch (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/5 binary64)) (patch (*.f64 x #s(literal -1/5 binary64)) #<representation binary64>) () ())) ())
Calls

24 calls:

TimeVariablePointExpression
145.0ms
x
@inf
(+ (* x (* x -1/5)) 3)
0.0ms
x
@inf
(* x -1/5)
0.0ms
x
@-inf
(* x -1/5)
0.0ms
x
@0
(* x -1/5)
0.0ms
x
@0
(+ (* x (* x -1/5)) 3)

simplify314.0ms (2%)

Memory
23.8MiB live, 251.8MiB 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
079830
1199830
2495830
31160830
42270830
53887830
66469830
08104779
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 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))
(* (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))
(* (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)))))
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)))
(/ 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))
(/ 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))
(* 1/3 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 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))
(* (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))
(* (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)))))
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)))
(/ 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))
(/ 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))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (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))
(* -1/5 (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))
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/1125 binary64) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 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) (*.f64 x (*.f64 x (*.f64 x x))))) (/.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 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 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) (*.f64 x (*.f64 x (*.f64 x x))))) (/.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 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/1125 binary64) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 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) (*.f64 x (*.f64 x (*.f64 x x))))) (/.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 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 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) (*.f64 x (*.f64 x (*.f64 x x))))) (/.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 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* -1/5 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* -1/5 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))

rewrite296.0ms (1.9%)

Memory
-4.9MiB live, 191.0MiB allocated
Rules
6 144×lower-fma.f32
6 142×lower-fma.f64
4 394×lower-*.f32
4 392×lower-*.f64
3 460×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022116
027116
1121116
2862116
08645110
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
8 → 140
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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(*.f64 x #s(literal -1/5 binary64))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.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 0 binary64) (neg.f64 (/.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)))) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) 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)))
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (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 (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) (*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #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 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (neg.f64 x)) #s(literal -1 binary64))
(pow.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) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) x)
(*.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 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)) x)
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #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 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
(*.f64 #s(literal 1 binary64) #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) (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 x (*.f64 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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64)))
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))))
(/.f64 (neg.f64 x) (*.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(*.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(*.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) x)
(*.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) #s(literal 1 binary64)) x)
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eval31.0ms (0.2%)

Memory
-9.1MiB live, 39.9MiB allocated
Compiler

Compiled 3 905 to 432 computations (88.9% saved)

prune40.0ms (0.3%)

Memory
0.4MiB live, 39.2MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New2360236
Fresh000
Picked022
Done044
Total2366242
Accuracy
100.0%
Counts
242 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
✓100.0%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
✓99.6%
#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 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.5%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓99.1%
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
Compiler

Compiled 138 to 65 computations (52.9% saved)

regimes6.0ms (0%)

Memory
9.7MiB live, 9.7MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan 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)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
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)))))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0%)

Memory
7.6MiB live, 7.6MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan 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)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0%)

Memory
6.6MiB live, 6.6MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 x) (/ 1 (tan 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)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 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
99.6%1x
99.6%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes2.0ms (0%)

Memory
4.3MiB live, 4.3MiB 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 #s(literal 1/3 binary64) x))
Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
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
99.1%1x
99.1%1(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0%)

Memory
-29.7MiB live, 9.1MiB allocated
Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
2×1-exp_binary64
2×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02980
13480
Stop Event
1×saturated
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)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 #s(literal 1/3 binary64) x))
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 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #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 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

soundness640.0ms (4.1%)

Memory
39.1MiB live, 468.3MiB allocated
Rules
18 970×lower-fma.f64
18 970×lower-fma.f32
11 116×lower-fma.f32
11 110×lower-fma.f64
10 150×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021101
033101
1143101
21082101
08750101
076936
1196936
2494936
31172936
42414936
55304936
08343885
067324
1179324
2458318
31321318
42085318
53083318
63670318
73941318
85080318
97268318
08431300
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 98 to 58 computations (40.8% saved)

preprocess55.0ms (0.4%)

Memory
-20.6MiB live, 134.1MiB allocated
Remove

(negabs x)

Compiler

Compiled 178 to 108 computations (39.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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