2tan (problem 3.3.2)

Time bar (total: 7.1s)

start0.0ms (0%)

Memory
0.2MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze28.0ms (0.4%)

Memory
18.0MiB live, 18.0MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample4.7s (66.2%)

Memory
-54.0MiB live, 3 972.7MiB allocated; 1.6s collecting garbage
Samples
2.1s26 421×0invalid
685.0ms5 623×1valid
201.0ms2 633×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-tan: 675.0ms (34.3% of total)
ival-fabs: 318.0ms (16.2% of total)
ival-add!: 219.0ms (11.1% of total)
ival-mult!: 193.0ms (9.8% of total)
adjust: 188.0ms (9.6% of total)
ival-<: 186.0ms (9.5% of total)
ival-sub!: 115.0ms (5.8% of total)
ival-and: 60.0ms (3% of total)
ival-assert: 12.0ms (0.6% of total)
Bogosity

preprocess56.0ms (0.8%)

Memory
2.4MiB live, 39.8MiB allocated; 20ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02146
18442
240042
3340742
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶61.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 12 to 12 computations (0% saved)

series12.0ms (0.2%)

Memory
27.1MiB live, 27.1MiB allocated; 0ms collecting garbage
Counts
6 → 31
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
x
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))

rewrite265.0ms (3.7%)

Memory
-10.2MiB live, 180.7MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01961230
02011087
11505874
08507844
127185844
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
37 → 72
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(/.f64 (-.f64 (*.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (cos.f64 x)) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (sin.f64 (-.f64 (+.f64 eps x) x))) (neg.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(neg.f64 (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(+.f64 (tan.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(*.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))))
(/.f64 (neg.f64 (sin.f64 (neg.f64 (+.f64 eps x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 eps x)))))
(/.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (cos.f64 (+.f64 eps x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(neg.f64 (tan.f64 (-.f64 (neg.f64 eps) x)))
(neg.f64 (tan.f64 (-.f64 (neg.f64 x) eps)))
(tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 eps x) (PI.f64)))
(tan.f64 (+.f64 eps x))
(-.f64 (/.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 (+.f64 eps x))) (/.f64 (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) (cos.f64 (+.f64 eps x))))
(-.f64 (/.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) (/.f64 (*.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) (cos.f64 (+.f64 eps x))))
(+.f64 (/.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) (/.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(neg.f64 (-.f64 (neg.f64 eps) x))
(neg.f64 (-.f64 (neg.f64 x) eps))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 eps (*.f64 #s(literal 1 binary64) x))
(+.f64 eps (neg.f64 (neg.f64 x)))
(+.f64 eps x)
(+.f64 x (*.f64 #s(literal 1 binary64) eps))
(+.f64 x (neg.f64 (neg.f64 eps)))
(+.f64 x eps)
x
eps
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 x (PI.f64)))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (*.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))))) #s(literal 1/2 binary64)) x)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))))) #s(literal 1/6 binary64)) x)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (tan x) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval7.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 798 to 314 computations (60.7% saved)

prune6.0ms (0.1%)

Memory
12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New57764
Fresh000
Picked011
Done000
Total57865
Accuracy
100.0%
Counts
65 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓61.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶61.8%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶61.6%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
▶99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
Compiler

Compiled 308 to 260 computations (15.6% saved)

series81.0ms (1.1%)

Memory
-33.7MiB live, 116.5MiB allocated; 16ms collecting garbage
Counts
53 → 190
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps))
(*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)
(+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64))
(+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
eps
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* 4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* 17/9 (* eps (pow x 2))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* 248/135 (* eps (pow x 2))) (* -17/9 eps))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* -1/3 eps)))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -17/9 (* eps (pow x 2))) (* -4/3 eps))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -4/3 eps) (* (pow x 2) (+ (* -17/9 eps) (* -248/135 (* eps (pow x 2))))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 -1/2))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* x x) 1/3) 1) x) #s(hole binary64 (* 1/3 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/3) 1) x) #s(hole binary64 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (* 1/3 (pow x 2))))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 2/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 2/15 (pow x 4))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* 2/15 (pow x 2))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* (pow x 2) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
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#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
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Calls

6 calls:

TimeVariablePointExpression
17.0ms
x
@-inf
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15.0ms
eps
@inf
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12.0ms
x
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11.0ms
x
@0
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9.0ms
eps
@-inf
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rewrite278.0ms (3.9%)

Memory
0.5MiB live, 227.0MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093710974
010229226
165439226
080278926
1233768926
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
243 → 438
Calls
Call 1
Inputs
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#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* x x) 1/3) 1) x) #s(hole binary64 (* 1/3 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/3) 1) x) #s(hole binary64 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (* 1/3 (pow x 2))))
#s(approx (+ (* (* x x) 1/3) 1) #s(hole binary64 (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 2/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 2/15 (pow x 4))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* 2/15 (pow x 2))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* (pow x 2) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
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#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
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#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (neg.f64 (-.f64 (-.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))) #s(literal -1/6 binary64))) eps (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
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#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (tan (+ x eps)) (fma.f64 x (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))))) (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 x (*.f64 (sin.f64 eps) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))))) (cos.f64 eps))) #s(literal 1 binary64)) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))))) x (tan.f64 eps)))
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#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (+ (* (* x x) 1/3) 1) (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(literal 1/3 binary64))
#s(approx (+ (* 2/15 (* x x)) 1/3) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (+.f64 (fma.f64 (-.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps)) eps #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (-.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps)) eps #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (fma.f64 (-.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps)) eps #s(literal 1 binary64)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps)))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg.f64 (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps)))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) eps))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))))
#s(approx (- 1 (neg (pow (tan x) 2))) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
#s(approx (neg (pow (tan x) 2)) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (tan x) 2) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (tan x) (tan.f64 x))
#s(approx (* (pow (tan x) 2) 1/6) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (neg.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 x))) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 x)) (cos.f64 (+.f64 x x)))
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#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
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#s(approx (sin x) (sin.f64 x))
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#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
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#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 eps (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
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#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (+.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) (-.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (fma.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 eps eps) (+.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) (-.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))))) eps))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (/.f64 #s(literal 1 binary64) eps)) eps))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (neg.f64 (*.f64 (+.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/6 binary64)) (*.f64 eps eps))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) eps)) (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))))) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) (/.f64 #s(literal 1 binary64) eps)) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))))))))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval92.0ms (1.3%)

Memory
15.1MiB live, 118.7MiB allocated; 41ms collecting garbage
Compiler

Compiled 12 551 to 3 946 computations (68.6% saved)

prune14.0ms (0.2%)

Memory
-23.5MiB live, 25.0MiB allocated; 3ms collecting garbage
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4647471
Fresh202
Picked415
Done101
Total4718479
Accuracy
100.0%
Counts
479 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.9%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x)))))
✓61.8%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
▶99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
Compiler

Compiled 471 to 392 computations (16.8% saved)

series40.0ms (0.6%)

Memory
41.1MiB live, 41.1MiB allocated; 0ms collecting garbage
Counts
39 → 141
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps))
#s(literal 4/3 binary64)
x
(*.f64 #s(literal 4/3 binary64) eps)
eps
#s(literal 1 binary64)
(*.f64 #s(literal 1/3 binary64) eps)
#s(literal 1/3 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps)
#s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps))
(fma.f64 (*.f64 x x) eps eps)
(*.f64 x x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)
(fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps)
#s(literal 2/3 binary64)
(*.f64 (*.f64 x x) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ x (* 1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* 4/3 (* eps x)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 eps)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (+ (* 4/3 eps) (* 4/3 x))))
#s(approx x #s(hole binary64 x))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (+ (* 2/3 (* (* x x) eps)) eps) #s(hole binary64 (+ eps (* 2/3 (* eps (pow x 2))))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 2/3 (pow x 2)))))
#s(approx (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
#s(approx (+ (* 17/45 (* x x)) 2/3) #s(hole binary64 2/3))
#s(approx (+ (* 17/45 (* x x)) 2/3) #s(hole binary64 (+ 2/3 (* 17/45 (pow x 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 x)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* x (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
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#s(approx (+ (* 2/3 (* (* x x) eps)) eps) #s(hole binary64 (* 2/3 (* eps (pow x 2)))))
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#s(approx (+ (* 17/45 (* x x)) 2/3) #s(hole binary64 (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
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#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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Calls

6 calls:

TimeVariablePointExpression
6.0ms
eps
@-inf
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6.0ms
eps
@inf
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6.0ms
x
@inf
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6.0ms
eps
@0
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) (+ (* 4/3 x) (* 4/3 eps)) 4/3 x (* 4/3 eps) eps 1 (* 1/3 eps) 1/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2 (- (tan (+ x eps)) (tan x)) (* (- 1 (neg (pow (tan x) 2))) eps) (- 1 (neg (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (* (- 1 (neg (pow (tan x) 2))) eps) (+ (* (* x x) eps) eps) (* x x) (- (tan (+ x eps)) (tan x)) (* (- 1 (neg (pow (tan x) 2))) eps) (+ (* (+ (* 2/3 (* (* x x) eps)) eps) (* x x)) eps) (+ (* 2/3 (* (* x x) eps)) eps) 2/3 (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (* (- 1 (neg (pow (tan x) 2))) eps) (- 1 (neg (pow (tan x) 2))) (+ (* (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) (* x x)) 1) (+ (* (+ (* 17/45 (* x x)) 2/3) (* x x)) 1) (+ (* 17/45 (* x x)) 2/3) 17/45)
6.0ms
x
@-inf
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rewrite251.0ms (3.5%)

Memory
-21.5MiB live, 206.1MiB allocated; 24ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06938906
07367620
150067620
083607230
1240977230
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
180 → 300
Calls
Call 1
Inputs
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#s(literal 4/3 binary64)
x
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#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
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#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 x)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* x (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
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#s(approx (+ (* 2/3 (* (* x x) eps)) eps) #s(hole binary64 (* 2/3 (* eps (pow x 2)))))
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#s(approx (+ (* 17/45 (* x x)) 2/3) #s(hole binary64 (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
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#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* eps (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* eps (+ 1/3 (* 4/3 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* 4/3 (* eps x))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* eps (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* eps (+ 4/3 (* 4/3 (/ x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* (pow eps 2) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps)) eps))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* eps (- (* -4/3 (pow x 2)) 1/3)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps)))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* -1 (* eps (- (* -4/3 (/ x eps)) 4/3)))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* 2/3 (* (* x x) eps)) eps) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))))
#s(approx (+ (* 2/3 (* (* x x) eps)) eps) #s(hole binary64 (* -1 (* eps (- (* -2/3 (pow x 2)) 1)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(*.f64 eps (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(neg.f64 (-.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64))))
(fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(+.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
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(fma.f64 eps #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) #s(literal 1 binary64))
(-.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) #s(literal -1 binary64))
(+.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps)))
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(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (neg.f64 (*.f64 #s(literal -1/3 binary64) eps)))
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#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 (/.f64 eps x) #s(literal -4/3 binary64) #s(literal -4/3 binary64))))
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#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (fma.f64 eps (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) #s(literal 1 binary64)))
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))))) eps))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) eps)) #s(literal 1/3 binary64)) eps))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal 4/3 binary64)))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) (*.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) eps))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 4/3 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (/.f64 #s(literal 1 binary64) eps)) eps))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (neg.f64 (*.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 eps eps))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) eps)) (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))))) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) (/.f64 #s(literal 1 binary64) eps)) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg.f64 (*.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (neg.f64 eps) (-.f64 (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) (neg.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) eps))) #s(literal 1/3 binary64))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -4/3 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -4/3 binary64))))
#s(approx (+ (* (* x x) eps) eps) (*.f64 (neg.f64 eps) (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
#s(approx (+ (* (+ (* 2/3 (* (* x x) eps)) eps) (* x x)) eps) (*.f64 (neg.f64 eps) (fma.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal -1 binary64))))
#s(approx (+ (* 2/3 (* (* x x) eps)) eps) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64))))

eval42.0ms (0.6%)

Memory
33.0MiB live, 78.3MiB allocated; 5ms collecting garbage
Compiler

Compiled 7 307 to 1 776 computations (75.7% saved)

prune18.0ms (0.2%)

Memory
-30.6MiB live, 21.3MiB allocated; 10ms collecting garbage
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2855290
Fresh202
Picked325
Done011
Total2908298
Accuracy
100.0%
Counts
298 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓61.8%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
▶99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
✓99.6%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
✓99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
▶52.6%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
▶99.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
Compiler

Compiled 459 to 373 computations (18.7% saved)

series60.0ms (0.8%)

Memory
4.4MiB live, 94.6MiB allocated; 12ms collecting garbage
Counts
47 → 173
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps)
(-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x))))
(fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps))
#s(literal 4/3 binary64)
x
(*.f64 #s(literal 4/3 binary64) eps)
eps
#s(literal 1 binary64)
(*.f64 #s(literal 1/3 binary64) eps)
#s(literal 1/3 binary64)
#s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))
(*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64))
#s(literal -2/3 binary64)
(*.f64 x x)
#s(literal -1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x))))
#s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))
(*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x))
(+.f64 (/.f64 eps (*.f64 x x)) eps)
(/.f64 eps (*.f64 x x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps)
#s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64)))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
#s(literal 2/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps)
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ x (* 1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* 4/3 (* eps x)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 eps)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (+ (* 4/3 eps) (* 4/3 x))))
#s(approx x #s(hole binary64 x))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 (- (* -2/3 (pow x 2)) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
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#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (/ (+ eps (* eps (pow x 2))) (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
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#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 2/3 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 2/3))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 (+ 2/3 (* 17/45 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (* 1/3 (pow eps 2))))
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#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
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#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
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#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* 4/3 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* (pow x 3) (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* (pow x 3) (+ 4/3 (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* (pow x 3) (+ 4/3 (+ (* 1/3 (/ eps (pow x 3))) (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* 4/3 (pow x 2))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* (pow x 2) (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* (pow x 2) (+ 4/3 (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 x)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* x (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* (+ (* -2/3 (* x x)) -1) (* x x)) #s(hole binary64 (* -2/3 (pow x 4))))
#s(approx (* (+ (* -2/3 (* x x)) -1) (* x x)) #s(hole binary64 (* -1 (* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 (* -2/3 (pow x 2))))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 (* -1 (* (pow x 2) (+ 2/3 (/ 1 (pow x 2)))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (+ eps (/ eps (pow x 2)))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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#s(approx (+ (* (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) x) 1) #s(hole binary64 (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) x) 1) #s(hole binary64 (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* 17/45 (pow x 5))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (* 17/45 (pow x 4))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 (* 17/45 (pow x 2))))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x))))))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (* x (+ 1 (* 4/3 (pow eps 2))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -4/3 (/ eps x)) 4/3)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 4/3 eps) (/ 1 x)) x)) 4/3)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)) x)) 4/3)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* (pow x 2) (+ 4/3 (* -1 (/ (- (* -4/3 eps) (/ 1 x)) x))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* -1 (* x (- (* -4/3 (/ eps x)) 4/3)))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 2/3 (/ 1 (pow x 2))) (pow x 2))) 17/45)))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (+ 1 (pow x 2)))))
#s(approx (* (+ (/ eps (* x x)) eps) (* x x)) #s(hole binary64 (* eps (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (* eps (+ 1 (/ 1 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (+ 1 (+ (* eps x) (pow x 2)))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (+ (* eps x) (pow x 2))))
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#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (+ x (* eps (+ 1 (* 4/3 (* eps x)))))))
#s(approx (+ (* (* eps eps) 4/3) 1) #s(hole binary64 (+ 1 (* 4/3 (pow eps 2)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
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Calls

6 calls:

TimeVariablePointExpression
14.0ms
eps
@-inf
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13.0ms
x
@-inf
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8.0ms
eps
@inf
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7.0ms
x
@inf
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6.0ms
eps
@0
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rewrite243.0ms (3.4%)

Memory
47.6MiB live, 223.1MiB allocated; 41ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081110241
08628853
159128851
081328402
1228708402
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
220 → 370
Calls
Call 1
Inputs
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#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
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#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ x (* 1/3 eps))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* 4/3 (* eps x)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 eps)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (+ (* 4/3 eps) (* 4/3 x))))
#s(approx x #s(hole binary64 x))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 (- (* -2/3 (pow x 2)) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (/ (+ eps (* eps (pow x 2))) (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 2/3 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 2/3))
#s(approx (+ (* (* x x) 17/45) 2/3) #s(hole binary64 (+ 2/3 (* 17/45 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* eps x))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
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#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* 4/3 (pow x 3))))
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#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* (pow x 3) (+ 4/3 (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* (pow x 3) (+ 4/3 (+ (* 1/3 (/ eps (pow x 3))) (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2))))))))
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#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* (pow x 2) (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* (pow x 2) (+ 4/3 (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2)))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* 4/3 x)))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* x (+ 4/3 (* 4/3 (/ eps x))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* (+ (* -2/3 (* x x)) -1) (* x x)) #s(hole binary64 (* -2/3 (pow x 4))))
#s(approx (* (+ (* -2/3 (* x x)) -1) (* x x)) #s(hole binary64 (* -1 (* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* -2/3 (* x x)) -1) #s(hole binary64 (* -2/3 (pow x 2))))
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#s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (/ eps (* x x)) eps) #s(hole binary64 (+ eps (/ eps (pow x 2)))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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#s(approx (+ (* (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) x) 1) #s(hole binary64 (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* 17/45 (pow x 5))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (* 17/45 (pow x 4))))
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#s(approx (+ (* (+ (* (* x x) 17/45) 2/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
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#s(approx (+ (* (* eps eps) 4/3) 1) #s(hole binary64 (+ 1 (* 4/3 (pow eps 2)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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#s(approx (+ (* (* eps eps) 4/3) 1) #s(hole binary64 (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* (pow eps 2) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps)) eps))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* eps (- (* -4/3 (pow x 2)) 1/3)))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3)))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps)))))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) #s(hole binary64 (* -1 (* eps (- (* -4/3 (/ x eps)) 4/3)))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))) eps))
(*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))) eps)
(*.f64 eps (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))))
(neg.f64 (-.f64 #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)) (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64))))
(fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))))
(fma.f64 eps #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))))
(-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)))
(+.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))))
(+.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x))))
(fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64))
(fma.f64 eps #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) #s(literal 1 binary64))
(-.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) #s(literal -1 binary64))
(+.f64 (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps)))
(neg.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) eps) (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x)))
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (neg.f64 (*.f64 #s(literal -1/3 binary64) eps)))
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))
(fma.f64 #s(literal 1/3 binary64) eps (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x))
(fma.f64 eps #s(literal 1/3 binary64) (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x))
(fma.f64 x (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) (neg.f64 (*.f64 #s(literal -1/3 binary64) eps)))
(fma.f64 x (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) (*.f64 #s(literal 1/3 binary64) eps))
(-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x) (neg.f64 (*.f64 #s(literal 1/3 binary64) eps)))
(-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x) (*.f64 #s(literal -1/3 binary64) eps))
(-.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64))))
(-.f64 (*.f64 #s(literal 1/3 binary64) eps) (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x)))
(+.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x) (neg.f64 (*.f64 #s(literal -1/3 binary64) eps)))
(+.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x) (*.f64 #s(literal 1/3 binary64) eps))
(+.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) #s(literal 1 binary64))
(-.f64 (*.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (*.f64 #s(literal 4/3 binary64) (+.f64 eps x))))
(-.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x)))
(+.f64 (*.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x))
(*.f64 #s(literal 4/3 binary64) (+.f64 eps x))
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#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (/.f64 #s(literal 1 binary64) eps)) eps))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (neg.f64 (*.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 eps eps))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) eps)) (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))))) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 eps eps) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) (/.f64 #s(literal 1 binary64) eps)) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg.f64 (*.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (-.f64 (-.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64))))))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64))))
#s(approx (+ (* (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) x) (* 1/3 eps)) (*.f64 (neg.f64 eps) (-.f64 (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) (neg.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) eps))) #s(literal 1/3 binary64))))
#s(approx (+ (* (+ (* 4/3 x) (* 4/3 eps)) x) 1) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -4/3 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -4/3 binary64))))
#s(approx (+ (* (* x x) eps) eps) (*.f64 (neg.f64 eps) (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
#s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (*.f64 x x) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 4/3 binary64) x (neg.f64 (/.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)) eps)))))

eval77.0ms (1.1%)

Memory
-30.4MiB live, 92.0MiB allocated; 73ms collecting garbage
Compiler

Compiled 8 501 to 2 347 computations (72.4% saved)

prune24.0ms (0.3%)

Memory
-2.2MiB live, 45.8MiB allocated; 5ms collecting garbage
Pruning

13 alts after pruning (8 fresh and 5 done)

PrunedKeptTotal
New3368344
Fresh000
Picked325
Done033
Total33913352
Accuracy
100.0%
Counts
352 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓61.8%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)))) eps))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
47.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
✓99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
✓99.6%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
✓99.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
✓99.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
Compiler

Compiled 1 316 to 801 computations (39.1% saved)

regimes23.0ms (0.3%)

Memory
-3.2MiB live, 43.1MiB allocated; 2ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

7.0ms
eps
7.0ms
x
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes20.0ms (0.3%)

Memory
-7.1MiB live, 39.4MiB allocated; 1ms collecting garbage
Counts
24 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal -1 binary64)) x) x)))) eps))
Calls

3 calls:

7.0ms
x
6.0ms
eps
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes17.0ms (0.2%)

Memory
-22.5MiB live, 28.5MiB allocated; 4ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 x) (* 4/3 eps)) (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
Calls

3 calls:

7.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes13.0ms (0.2%)

Memory
26.0MiB live, 26.0MiB allocated; 0ms collecting garbage
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 x) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
Calls

3 calls:

4.0ms
eps
4.0ms
x
4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.2%)

Memory
-24.5MiB live, 22.5MiB allocated; 2ms collecting garbage
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps))
Calls

3 calls:

4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes9.0ms (0.1%)

Memory
25.2MiB live, 25.2MiB allocated; 0ms collecting garbage
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (*.f64 x x))) #s(literal 1 binary64))) eps))
Calls

3 calls:

3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes10.0ms (0.1%)

Memory
-25.7MiB live, 19.5MiB allocated; 3ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64))) eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.1%)

Memory
18.4MiB live, 18.4MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) eps) eps) (*.f64 x x) eps)))
Calls

3 calls:

2.0ms
x
2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.1%)

Memory
13.6MiB live, 13.6MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) #s(approx (+ (* (* x x) eps) eps) (*.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) (*.f64 x x)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 eps x (*.f64 x x))) #s(literal 1 binary64))) eps))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 x x) eps eps)))
Calls

3 calls:

1.0ms
x
1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
eps
Results
AccuracySegmentsBranch
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes9.0ms (0.1%)

Memory
-36.7MiB live, 9.6MiB allocated; 3ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- 1 (neg (pow (tan x) 2))) eps) eps))
Calls

3 calls:

6.0ms
x
1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
eps
Results
AccuracySegmentsBranch
99.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.0%1x
99.0%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

derivations421.0ms (5.9%)

Memory
57.1MiB live, 422.5MiB allocated; 54ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 369 to 143 computations (61.2% saved)

preprocess266.0ms (3.7%)

Memory
-10.5MiB live, 177.0MiB allocated; 64ms collecting garbage
Compiler

Compiled 403 to 173 computations (57.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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